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Opus in profectus | https://physics.info/about/ | # Opus in profectus
### philosophy
> *La dernière chose qu'on trouve en faisant un ouvrage est de savoir celle qu'il faut mettre la première.*
>
>
> The last thing one knows when writing a book is what to put first.
>
>
> [Blaise Pascal, 1662](https://books.google.com/books?id=tO4wAQAAMAAJ&pg=PA120 "Pensées sur la religion et sur quelques autres sujets. Blaise Pascal. Chez Guillaume Desprez (1669).")
The Physics Hypertextbook is a reaction to three problems with textbooks in the US at the turn of the 21st century - lack of writer's voice, layouts that reduce readability, and outdated economics.
Too many textbooks are written by corporations, not authors. This is especially true of the textbooks for secondary schools. They sound like they were written by no one. The Physics Hypertextbook is written by me and should have a recognizable voice to it. Whether or not it's a good voice is, of course, open to debate.
The Physics Hypertextbook is presented as a work in progress. Some parts of this book are essentially finished. Some parts are comically underdone (containing only placeholder text). I work on this project in my spare time. I never add anything to it out of obligation. I only work on it when I feel like it. I hope that results in better writing, but I expect that I will never finish this project.
Too many textbooks are layout disasters with special sections not part of any topic and images with no relation to the main text floating in little boxes off to the side. This crazy quilt style decreases readability. Every page of the Physics Hypertextbook is designed to be read from top to bottom. When an image appears, the text around it is discussing it. You read the text, read the image, and read some more text. Images are a part of the stories being told.
Although every page is meant to be read from top to bottom. The whole of this book will probably never be read from start to finish by anyone - including me. It's not a scroll. The Physics Hypertextbook is like a book in that you can flip to any page at any time. It's a random access repository of information. In this respect, a hypertextbook is no different than a conventional book.
We don't buy physical media much any more. I haven't listened to a CD, cassette tape, or phonograph record in years. I took all the music I collected and converted it to digital data in the early 2000s. If I want to listen to new music, I stream it. If I want to own new music, I download it. I stopped renting DVDs and videocassettes a little later. The only time I ever put a newspaper in my hands is when I visit my parents.
We're living in the future. Every form of media has been affected by the stupendous growth of the internet - except textbooks. They are the last holdout of the old media economy. Why are schools still buying textbooks? Why do professors still make their students buy textbooks? It's time for textbooks to die so they can be reborn. It's time for the textbook companies to die too. They need us more than we need them.
The Physics Hypertextbook exists! Read it if you want to learn more about physics. Read it if you need to learn more about physics to achieve some other end. Read it if you are curious about physics or enjoy science in general. It's an interesting diversion and you just might learn something in the process. Certainly no harm can come from any of these objectives.
### structure
> *Dimidium facti qui coepit habet; sapere aude; incipe!*
>
>
> He who has begun has half done. Dare to be wise; begin!
>
>
> [Horace, ca. 20 BCE](https://books.google.com/books?id=FJooAAAAYAAJ&pg=PA218 "Epistularum Quinti Horatii Flacci. Liber Primus. Epistula II. (ca. 20 BCE).")
The Physics Hypertextbook is organized like many printed physics textbooks. The whole of physics is divided into five major books. Each book is divided into chapters and sections.
1. Mechanics (8 chapters, 60 sections)
2. Thermal physics (4 chapters, 18 sections)
3. Waves and optics (4 chapters, 23 sections)
4. Electricity and magnetism (8 chapters, 31 sections)
5. Modern physics (5 chapters, 25 sections)
Supplementary sections on units and mathematics as well as reference material are gathered into a sixth book.
6. Foundations (5 chapters, 23 sections)
Each section is divided into five pages (except the sections that contain only reference material).
* *Discussion* of the conceptual, historical, and mathematical aspects of the topic.
* *Summary* of the key concepts embedded in in the topic presented in outline form.
* *Practice* problems showing how to apply the concepts described.
* *Problems* to exercise your mind and construct the topic for yourself.
* *Resources* for further information on the topic and its applications.
Special colors are used whenever a word or phrase is explained for the first time on a page. (I'd say "defined", but that's not quite the right word.) Primary concepts are highlighted in bright red, secondary concepts in dark red, and [important persons](https://en.wikipedia.org/wiki/Mr_Creosote "Mr. Creosote a.k.a. Monsieur Creosote (1942-1983) England") in blue. (Blue because they are links to the Wikipedia page for that person.)
### legal
> If there's one thing America needs, it's more lawyers.
>
>
> [Lionel Hutz, 1993](https://frinkiac.com/caption/S04E21/881279 "Lionel Hutz, your new agent, unauthorized biographer, and drug dealer... er keeper awayer.")
The Physics Hypertextbook was not designed to satisfy the requirements of any syllabus nor was it designed to integrate into any specific curriculum. Reading it will not build character nor will it provide moral guidance. The author makes no claims of accuracy, efficacy, or user-friendliness. It is expected that someone will read it and be offended, but it is strongly hoped that someone will read it and be educated, entertained, or enlightened. I am telling you this because I will not guarantee that you will pass your upcoming homework, quiz, test, etc. because you accessed any page on this website. I also do not guarantee that your scores in these items will increase as a result of you interacting with any parts of this website. You are responsible for learning anything you are asked to learn.
The Physics Hypertextbook is the intellectual property of [Glenn Elert](https://glennelert.us "Say my name. You know who I am.") who is solely responsible for its content. No person or organization besides the author played any part in its creation (except where explicitly cited). You can view, copy, and reproduce any part of this work for non-commercial purposes as described in the [fair use](https://www.copyright.gov/title17/92chap1.html#107 "Copyright Law of the United States: Title 17, Chapter 1, Section 107. Limitations on exclusive rights: Fair use.") clause of United States Copyright Law. Reproduction of any part of this work in any form for commercial purposes is strictly forbidden. I am telling you this because I want you to respect my intellectual property. Just because you found something on the internet does not mean you have any rights to use that material for any purposes you think are valid - now or ever.
As an
[Amazon Associate](https://amzn.to/3lWRiR1 "Amazon.com: Online Shopping for Electronics, Apparel, Computers, Books, DVDs & more")
I earn from qualifying purchases.
I also sell designs on
[Spreadshirt](https://hypertextbook.spreadshirt.com "Shop The Physics Hypertextbook")
and
[Red Bubble](https://elert.redbubble.com "elert Shop | Redbubble").
This website does not receive revenue from any other sources. I am telling you this so as to be compliant with certain regulations. Your actions will sometimes (rarely) result in me making money.
This website uses cookies. If that bothers you, gather every internet connected device you own or have interacted with into a capsule and project it into the Sun. This website uses analytics provided by
[google.com](https://policies.google.com/technologies/cookies "How Google uses cookies - Privacy & Terms - Google"),
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[amazon.com](https://affiliate-program.amazon.com/help/operating/policies "Amazon.com Associates Central - Associates Program Policies"),
and
[addthis.com](https://www.addthis.com/academy/what-are-http-cookies/ "What Are HTTP Cookies? - AddThis Academy").
Using these services I can determine things like the approximate location of a user, the approximate time they spent using this website, features of their device like screen dimensions and color depth, the kind of device they use, the browser they use, the network they are on, etc. All of this information is aggregated, which means I do not have the ability to track individual users. Why would I want to be able to do that? What purpose would it serve? All I see are summaries of where users have gone and how they have used this website. As a public person on the internet, you know more about me that I know about you. This site has cookie statements so as to be compliant with certain regulations. Cookie opt-in/opt-out regulations are idiotic, but this is not a reason for Britain to leave the EU. |
people | https://physics.info/people/ | # people
Reference
---------
### nobel laureates in physics
Since 1901, the [Nobel Prize](https://www.nobelprize.org) has been honoring men and women from all corners of the globe for outstanding achievements in [physics](https://www.nobelprize.org/prizes/physics/), [chemistry](https://www.nobelprize.org/prizes/chemistry/), [medicine](https://www.nobelprize.org/prizes/medicine/), [literature](https://www.nobelprize.org/prizes/literature/), and for work in [peace](https://www.nobelprize.org/prizes/peace/). The foundations for the prize were laid in 1895 when Alfred Nobel wrote his last will and testament, leaving much of his wealth to the establishment of the Nobel Prize.
Nobel laureates in physics
| year | laureate(s) | achievement |
| --- | --- | --- |
| [2023](https://www.nobelprize.org/prizes/physics/2023/summary/summary/) | Pierre AgostiniFerenc KrauszAnne L'Huillier | for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter. |
| [2022](https://www.nobelprize.org/prizes/physics/2022/summary/summary/) | Alain AspectJohn F. Clauser Anton Zeilinger | for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science |
| [2021](https://www.nobelprize.org/prizes/physics/2021/summary/summary/) | Syukuro ManabeKlaus HasselmannGiorgio Parisi | for groundbreaking contributions to our understanding of complex systems; [Manabe and Hasselmann] for the physical modelling of Earth's climate, quantifying variability and reliably predicting global warming; [Parisi] for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales. |
| [2020](https://www.nobelprize.org/prizes/physics/2020/summary/summary/) | [Roger Penrose](https://en.wikipedia.org/wiki/Roger_Penrose "Roger Penrose (1931-0000) England")[Reinhard Genzel](https://en.wikipedia.org/wiki/Reinhard_Genzel "Reinhard Genzel (1952-0000) Germany")[Andrea Ghez](https://en.wikipedia.org/wiki/Andrea_M._Ghez "Andrea Mia Ghez (1965-0000) USA") | [Penrose] for the discovery that black hole formation is a robust prediction of the general theory of relativity, [Genzel and Ghez] for the discovery of a supermassive compact object at the centre of our galaxy. |
| [2019](https://www.nobelprize.org/prizes/physics/2019/summary/summary/) | James PeeblesMichel MayorDidier Queloz | for contributions to our understanding of the evolution of the universe and Earth's place in the cosmos, [Peebles] for theoretical discoveries in physical cosmology, [Mayor and Queloz] for the discovery of an exoplanet orbiting a solar-type star. |
| [2018](https://www.nobelprize.org/prizes/physics/2018/summary/) | Arthur AshkinGérard MourouDonna Strickland | for groundbreaking inventions in the field of laser physics, [Ashkin] for the optical tweezers and their application to biological systems, [Mourou and Strickland] for their method of generating high-intensity, ultra-short optical pulses |
| [2017](https://www.nobelprize.org/prizes/physics/2017/summary/) | Rainer WeissBarry C. Barish[Kip Thorne](https://en.wikipedia.org/wiki/Kip_Thorne "Kip Stephen Thorne (1940-0000) USA") | for decisive contributions to the LIGO detector and the observation of gravitational waves |
| [2016](https://www.nobelprize.org/prizes/physics/2016/summary/) | David J. ThoulessF. Duncan M. HaldaneJ. Michael Kosterlitz | for theoretical discoveries of topological phase transitions and topological phases of matter |
| [2015](https://www.nobelprize.org/prizes/physics/2015/summary/) | Takaaki KajitaArthur B. McDonald | for the discovery of neutrino oscillations, which shows that neutrinos have mass |
| [2014](https://www.nobelprize.org/prizes/physics/2014/summary/) | Isamu AkasakiHiroshi AmanoShuji Nakamura | for the invention of efficient blue light emitting diodes which has enabled bright and energy-saving white light sources |
| [2013](https://www.nobelprize.org/prizes/physics/2013/summary/) | [François Englert](https://en.wikipedia.org/wiki/François_Englert "François Baron Englert (1932-0000) Belgium")[Peter Higgs](https://en.wikipedia.org/wiki/Peter_Higgs "Peter Ware Higgs (1929-2024) England") | for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider |
| [2012](https://www.nobelprize.org/prizes/physics/2012/summary/) | Serge HarocheDavid J. Wineland | for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems |
| [2011](https://www.nobelprize.org/prizes/physics/2011/summary/) | Saul PerlmutterBrian P. SchmidtAdam G. Riess | for the discovery of the accelerating expansion of the universe through observations of distant supernovae |
| [2010](https://www.nobelprize.org/prizes/physics/2010/summary/) | [Andre Geim](https://en.wikipedia.org/wiki/Andre_Geim "Andre Konstantinovich Geim a.k.a. Андрей Константинович Гейм (1958-0000) Russia")Konstantin Novoselov | for groundbreaking experiments regarding the two-dimensional material graphene |
| [2009](https://www.nobelprize.org/prizes/physics/2009/summary/) | Charles K. KaoWillard S. BoyleGeorge E. Smith | [Kao] for groundbreaking achievements concerning the transmission of light in fibers for optical communication, [Boyle and Smith] for the invention of an imaging semiconductor circuit - the CCD sensor |
| [2008](https://www.nobelprize.org/prizes/physics/2008/summary/) | [Yoichiro Nambu](https://en.wikipedia.org/wiki/Yoichiro_Nambu "Yoichiro Nambu a.k.a. 南部 陽一郎 (1921-2015) Japan-USA")Makoto KobayashiToshihide Maskawa | [Nambu] for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics, [Kobayashi and Maskawa] for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature |
| [2007](https://www.nobelprize.org/prizes/physics/2007/summary/) | Albert FertPeter Grünberg | for the discovery of giant magnetoresistance |
| [2006](https://www.nobelprize.org/prizes/physics/2006/summary/) | John C. MatherGeorge F. Smoot | for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation |
| [2005](https://www.nobelprize.org/prizes/physics/2005/summary/) | Roy J. GlauberJohn L. HallTheodor W. Hänsch | [Glauber] for his contribution to the quantum theory of optical coherence, [Hall and Hänsch] for their contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique |
| [2004](https://www.nobelprize.org/prizes/physics/2004/summary/) | David J. GrossH. David Politzer[Frank Wilczek](https://en.wikipedia.org/wiki/Frank_Wilczek "Frank Anthony Wilczek (1951-0000) USA") | for the discovery of asymptotic freedom in the theory of the strong interaction |
| [2003](https://www.nobelprize.org/prizes/physics/2003/summary/) | Alexei A. AbrikosovVitaly L. GinzburgAnthony J. Leggett | for pioneering contributions to the theory of superconductors and superfluids |
| [2002](https://www.nobelprize.org/prizes/physics/2002/summary/) | Raymond Davis Jr.Masatoshi KoshibaRiccardo Giacconi | for pioneering contributions to astrophysics, [Davis and Koshiba] for the detection of cosmic neutrinos, [Giacconi] for pioneering contributions to astrophysics, which have led to the discovery of cosmic x-ray sources |
| [2001](https://www.nobelprize.org/prizes/physics/2001/summary/) | Eric A. CornellWolfgang KetterleCarl E. Wieman | for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates |
| [2000](https://www.nobelprize.org/prizes/physics/2000/summary/) | Zhores AlferovHerbert KroemerJack Kilby | for basic work on information and communication technology, [Alferov and Kroemer] for developing semiconductor heterostructures used in high-speed- and opto-electronics, [Kilby] for his part in the invention of the integrated circuit |
| [1999](https://www.nobelprize.org/prizes/physics/1999/summary/) | [Gerard't Hooft](https://en.wikipedia.org/wiki/Gerard_'t_Hooft "Gerardus't Hooft a.k.a. Gerard't Hooft (1946-0000) Netherlands")Martinus Veltman | for elucidating the quantum structure of electroweak interactions in physics |
| [1998](https://www.nobelprize.org/prizes/physics/1998/summary/) | Robert LaughlinHorst StörmerDaniel Tsui | for their discovery of a new form of quantum fluid with fractionally charged excitations |
| [1997](https://www.nobelprize.org/prizes/physics/1997/summary/) | Steven ChuClaude Cohen-TannoudjiWilliam Phillips | for development of methods to cool and trap atoms with laser light |
| [1996](https://www.nobelprize.org/prizes/physics/1996/summary/) | David LeeDouglas OsheroffRobert Richardson | for their discovery of superfluidity in helium-3 |
| [1995](https://www.nobelprize.org/prizes/physics/1995/summary/) | Martin PerlFrederick Reines | for pioneering experimental contributions to lepton physics, [Perl] for the discovery of the tau lepton, [Reines] for the detection of the [tau] neutrino |
| [1994](https://www.nobelprize.org/prizes/physics/1994/summary/) | Bertram BrockhouseClifford Shull | for pioneering contributions to the development of neutron scattering techniques for studies of condensed matte, [Brockhouse] for the development of neutron spectroscopy, [Shull] for the development of the neutron diffraction technique |
| [1993](https://www.nobelprize.org/prizes/physics/1993/summary/) | [Russell Hulse](https://en.wikipedia.org/wiki/Russell_Alan_Hulse "Russell Alan Hulse (1950-0000) USA")[Joseph Taylor](https://en.wikipedia.org/wiki/Joseph_Hooton_Taylor,_Jr. "Joseph Hooton Taylor Jr. (1941-0000) USA") | for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation |
| [1992](https://www.nobelprize.org/prizes/physics/1992/summary/) | Georges Charpak | for his invention and development of particle detectors, in particular the multiwire proportional chamber |
| [1991](https://www.nobelprize.org/prizes/physics/1991/summary/) | Pierre-Gilles de Gennes | for discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers |
| [1990](https://www.nobelprize.org/prizes/physics/1990/summary/) | Jerome FriedmanHenry KendallRichard Taylor | for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics |
| [1989](https://www.nobelprize.org/prizes/physics/1989/summary/) | Norman RamseyHans DehmeltWolfgang Paul | [Ramsey] for the invention of the separated oscillatory fields method and its use in the hydrogen maser and other atomic clocks, [Dehmelt and Paul] for the development of the ion trap technique |
| [1988](https://www.nobelprize.org/prizes/physics/1988/summary/) | [Leon Lederman](https://en.wikipedia.org/wiki/Leon_M._Lederman "Leon Max Lederman (1922-2018) USA")Melvin SchwartzJack Steinberger | for the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muon neutrino |
| [1987](https://www.nobelprize.org/prizes/physics/1987/summary/) | [Georg Bednorz](https://en.wikipedia.org/wiki/Georg_Bednorz "Johannes Georg Bednorz (1950-0000) Germany")[Alex Müller](https://en.wikipedia.org/wiki/K._Alex_Müller "Karl Alexander Müller (1927-0000) Switzerland") | for their important break-through in the discovery of superconductivity in ceramic materials |
| [1986](https://www.nobelprize.org/prizes/physics/1986/summary/) | Ernst RuskaGerd BinnigHeinrich Rohrer | [Ruska] for his fundamental work in electron optics, and for the design of the first electron microscope, [Rohrer] for their design of the scanning tunneling microscope |
| [1985](https://www.nobelprize.org/prizes/physics/1985/summary/) | Klaus von Klitzing | for the discovery of the quantized Hall effect |
| [1984](https://www.nobelprize.org/prizes/physics/1984/summary/) | Carlo RubbiaSimon van der Meer | for their decisive contributions to the large project, which led to the discovery of the field particles W and Z, communicators of weak interaction |
| [1983](https://www.nobelprize.org/prizes/physics/1983/summary/) | [Subrahmanyan Chandrasekhar](https://en.wikipedia.org/wiki/Subrahmanyan_Chandrasekhar "Subrahmanyan Chandrasekhar (1910-1995) Pakistan-USA")William Fowler | [Chandrasekhar] for his theoretical studies of the physical processes of importance to the structure and evolution of the stars, [Fowler] for his theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe |
| [1982](https://www.nobelprize.org/prizes/physics/1982/summary/) | Kenneth Wilson | for his theory for critical phenomena in connection with phase transitions |
| [1981](https://www.nobelprize.org/prizes/physics/1981/summary/) | Nicolaas BloembergenArthur SchawlowKai Siegbahn | [Bloembergen and Schawlow] for their contribution to the development of laser spectroscopy, [Siegbahn] for his contribution to the development of high-resolution electron spectroscopy |
| [1980](https://www.nobelprize.org/prizes/physics/1980/summary/) | James CroninVal Fitch | for the discovery of violations of fundamental symmetry principles in the decay of neutral K-mesons |
| [1979](https://www.nobelprize.org/prizes/physics/1979/summary/) | [Sheldon Glashow](https://en.wikipedia.org/wiki/Sheldon_Lee_Glashow "Sheldon Lee Glashow (1932-0000) USA")[Abdus Salam](https://en.wikipedia.org/wiki/Abdus_Salam "Mohammad Abdus Salam (1926-1996) Pakistan-England")[Steven Weinberg](https://en.wikipedia.org/wiki/Steven_Weinberg "Steven Weinberg (1933-2021) USA") | for their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including, inter alia, the prediction of the weak neutral current |
| [1978](https://www.nobelprize.org/prizes/physics/1978/summary/) | [Pyotr Kapitsa](https://en.wikipedia.org/wiki/Pyotr_Kapitsa "Pyotr Leonidovich Kapitsa a.k.a. Пётр Леони́дович Капи́ца a.k.a. Peter Kapitza (1894-1984) Russia")Arno PenziasRobert Wilson | [Kapitsa] for his basic inventions and discoveries in the area of low-temperature physics, [Penzias and Wilson] for their discovery of cosmic microwave background radiation |
| [1977](https://www.nobelprize.org/prizes/physics/1977/summary/) | Philip AndersonNevill MottJohn van Vleck | for their fundamental theoretical investigations of the electronic structure of magnetic and disordered systems |
| [1976](https://www.nobelprize.org/prizes/physics/1976/summary/) | Burton RichterSamuel Ting | for their pioneering work in the discovery of a heavy elementary particle of a new kind |
| [1975](https://www.nobelprize.org/prizes/physics/1975/summary/) | Aage BohrBen MottelsonLeo Rainwater | for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection |
| [1974](https://www.nobelprize.org/prizes/physics/1974/summary/) | Martin RyleAntony Hewish | for their pioneering research in radio astrophysics: Ryle for his observations and inventions, in particular of the aperture synthesis technique, and Hewish for his decisive role in the discovery of pulsars |
| [1973](https://www.nobelprize.org/prizes/physics/1973/summary/) | Leo EsakiIvar GiaeverBrian Josephson | [Esaki and Giaever] for their experimental discoveries regarding tunneling phenomena in semiconductors and superconductors, respectively, [Josephson] for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects |
| [1972](https://www.nobelprize.org/prizes/physics/1972/summary/) | John BardeenLeon CooperJohn Schrieffer | for their jointly developed theory of superconductivity, usually called the BCS-theory |
| [1971](https://www.nobelprize.org/prizes/physics/1971/summary/) | Dennis Gabor | for his invention and development of the holographic method |
| [1970](https://www.nobelprize.org/prizes/physics/1970/summary/) | Hannes Alfvén[Louis Néel](https://en.wikipedia.org/wiki/Louis_Néel "Louis Eugène Félix Néel (1904-2000) France") | [Alfvén] for fundamental work and discoveries in magneto-hydrodynamics with fruitful applications in different parts of plasma physics, [Néel] for fundamental work and discoveries concerning antiferromagnetism and ferrimagnetism which have led to important applications in solid state physics |
| [1969](https://www.nobelprize.org/prizes/physics/1969/summary/) | [Murray Gell-Mann](https://en.wikipedia.org/wiki/Murray_Gell-Mann "Murray Gell-Mann (1929-2019) USA") | for his contributions and discoveries concerning the classification of elementary particles and their interactions |
| [1968](https://www.nobelprize.org/prizes/physics/1968/summary/) | Luis Alvarez | for his decisive contributions to elementary particle physics, in particular the discovery of a large number of resonance states, made possible through his development of the technique of using hydrogen bubble chamber and data analysis |
| [1967](https://www.nobelprize.org/prizes/physics/1967/summary/) | [Hans Bethe](https://en.wikipedia.org/wiki/Hans_Bethe "Hans Albrecht Bethe (1906-2005) Germany-USA") | for his contributions to the theory of nuclear reactions, especially his discoveries concerning the energy production in stars |
| [1966](https://www.nobelprize.org/prizes/physics/1966/summary/) | Alfred Kastler | for the discovery and development of optical methods for studying Hertzian resonances in atoms |
| [1965](https://www.nobelprize.org/prizes/physics/1965/summary/) | [Sin-Itiro Tomonaga](https://en.wikipedia.org/wiki/Sin-Itiro_Tomonaga "Sin-Itiro Tomonaga a.k.a. Shinichirō Tomonaga a.k.a. 朝永 振一郎 (1906-1979) Japan")[Julian Schwinger](https://en.wikipedia.org/wiki/Julian_Schwinger "Julian Seymour Schwinger (1918-1994) USA")[Richard Feynman](https://en.wikipedia.org/wiki/Richard_Feynman "Richard Phillips Feynman (1918-1988) USA") | for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles |
| [1964](https://www.nobelprize.org/prizes/physics/1964/summary/) | Charles TownesNicolay BasovAleksandr Prokhorov | for fundamental work in the field of quantum electronics, which has led to the construction of oscillators and amplifiers based on the maser-laser principle |
| [1963](https://www.nobelprize.org/prizes/physics/1963/summary/) | Eugene Wigner[Maria Goeppert-Mayer](https://en.wikipedia.org/wiki/Maria_Goeppert-Mayer "Maria Goeppert-Mayer (1906-1972) Poland-USA")[Hans Jensen](https://en.wikipedia.org/wiki/J._Hans_D._Jensen "Johannes Hans Daniel Jensen a.k.a. J. Hans D. Jensen (1907-1973) Germany") | [Wigner] for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles, [Mayer and Jensen] for their discoveries concerning nuclear shell structure |
| [1962](https://www.nobelprize.org/prizes/physics/1962/summary/) | Lev Landau | for his pioneering theories for condensed matter, especially liquid helium |
| [1961](https://www.nobelprize.org/prizes/physics/1961/summary/) | Robert HofstadterRudolf Mössbauer | [Hofstadter] for his pioneering studies of electron scattering in atomic nuclei and for his thereby achieved discoveries concerning the stucture of the nucleons, [Mössbauer] for his researches concerning the resonance absorption of gamma radiation and his discovery in this connection of the effect which bears his name |
| [1960](https://www.nobelprize.org/prizes/physics/1960/summary/) | Donald Glaser | for the invention of the bubble chamber |
| [1959](https://www.nobelprize.org/prizes/physics/1959/summary/) | Emilio SegrèOwen Chamberlain | for their discovery of the antiproton |
| [1958](https://www.nobelprize.org/prizes/physics/1958/summary/) | Pavel CherenkovIlya FrankIgor Tamm | for the discovery and the interpretation of the Cherenkov effect |
| [1957](https://www.nobelprize.org/prizes/physics/1957/summary/) | Chen Ning YangTsung-Dao Lee | for their penetrating investigation of the so-called parity laws which has led to important discoveries regarding the elementary particles |
| [1956](https://www.nobelprize.org/prizes/physics/1956/summary/) | William ShockleyJohn BardeenWalter Brattain | for their researches on semiconductors and their discovery of the transistor effect |
| [1955](https://www.nobelprize.org/prizes/physics/1955/summary/) | Willis LambPolykarp Kusch | [Lamb] for his discoveries concerning the fine structure of the hydrogen spectrum, [Kusch] for his precision determination of the magnetic moment of the electron |
| [1954](https://www.nobelprize.org/prizes/physics/1954/summary/) | Max BornWalther Bothe | [Born] for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction, [Bothe] for the coincidence method and his discoveries made therewith |
| [1953](https://www.nobelprize.org/prizes/physics/1953/summary/) | Frits Zernike | for his demonstration of the phase contrast method, especially for his invention of the phase contrast microscope |
| [1952](https://www.nobelprize.org/prizes/physics/1952/summary/) | Felix BlochEdward Purcell | for their development of new methods for nuclear magnetic precision measurements and discoveries in connection therewith |
| [1951](https://www.nobelprize.org/prizes/physics/1951/summary/) | John CockcroftErnest Walton | for their pioneer work on the transmutation of atomic nuclei by artificially accelerated atomic particles |
| [1950](https://www.nobelprize.org/prizes/physics/1950/summary/) | Cecil Powell | for his development of the photographic method of studying nuclear processes and his discoveries regarding mesons made with this method |
| [1949](https://www.nobelprize.org/prizes/physics/1949/summary/) | Hideki Yukawa | for his prediction of the existence of mesons on the basis of theoretical work on nuclear forces |
| [1948](https://www.nobelprize.org/prizes/physics/1948/summary/) | Patrick Blackett | for his development of the Wilson cloud chamber method, and his discoveries therewith in the fields of nuclear physics and cosmic radiation |
| [1947](https://www.nobelprize.org/prizes/physics/1947/summary/) | Edward Appleton | for his investigations of the physics of the upper atmosphere especially for the discovery of the so-called Appleton layer |
| [1946](https://www.nobelprize.org/prizes/physics/1946/summary/) | Percy Bridgman | for the invention of an apparatus to produce extremely high pressures, and for the discoveries he made therewith in the field of high pressure physics |
| [1945](https://www.nobelprize.org/prizes/physics/1945/summary/) | [Wolfgang Pauli](https://en.wikipedia.org/wiki/Wolfgang_Pauli "Wolfgang Ernst Pauli (1900-1958) Austria-Switzerland") | for the discovery of the Exclusion Principle, also called the Pauli Principle |
| [1944](https://www.nobelprize.org/prizes/physics/1944/summary/) | I.I. Rabi | for his resonance method for recording the magnetic properties of atomic nuclei |
| [1943](https://www.nobelprize.org/prizes/physics/1943/summary/) | [Otto Stern](https://en.wikipedia.org/wiki/Otto_Stern "Otto Stern (1888-1969) Germany-USA") | for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton |
| [1942](https://www.nobelprize.org/prizes/physics/1942/summary/) | | |
| [1941](https://www.nobelprize.org/prizes/physics/1941/summary/) | | |
| [1940](https://www.nobelprize.org/prizes/physics/1940/summary/) | | |
| [1939](https://www.nobelprize.org/prizes/physics/1939/summary/) | Ernest Lawrence | for the invention and development of the cyclotron and for results obtained with it, especially with regard to artificial radioactive elements |
| [1938](https://www.nobelprize.org/prizes/physics/1938/summary/) | [Enrico Fermi](https://en.wikipedia.org/wiki/Enrico_Fermi "Enrico Fermi (1901-1954) Italy-USA") | for his demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons |
| [1937](https://www.nobelprize.org/prizes/physics/1937/summary/) | [Clinton Davisson](https://en.wikipedia.org/wiki/Clinton_Davisson "Clinton Joseph Davisson (1881-1958) USA")George Thomson | for their experimental discovery of the diffraction of electrons by crystals |
| [1936](https://www.nobelprize.org/prizes/physics/1936/summary/) | Victor HessCarl Anderson | [Hess] for his discovery of cosmic radiation, [Anderson] for his discovery of the positron |
| [1935](https://www.nobelprize.org/prizes/physics/1935/summary/) | [James Chadwick](https://en.wikipedia.org/wiki/James_Chadwick "James Chadwick (1891-1974) England") | for the discovery of the neutron |
| [1934](https://www.nobelprize.org/prizes/physics/1934/summary/) | | |
| [1933](https://www.nobelprize.org/prizes/physics/1933/summary/) | [Erwin Schrödinger](https://en.wikipedia.org/wiki/Erwin_Schrödinger "Erwin Rudolf Josef Alexander Schrödinger a.k.a. Schroedinger (1887-1961) Austria")[Paul Dirac](https://en.wikipedia.org/wiki/Paul_Dirac "Paul Adrien Maurice Dirac a.k.a. P.A.M. Dirac (1902-1984) England-USA") | for the discovery of new productive forms of atomic theory |
| [1932](https://www.nobelprize.org/prizes/physics/1932/summary/) | [Werner Heisenberg](https://en.wikipedia.org/wiki/Werner_Heisenberg "Werner Karl Heisenberg (1901-1976) Germany") | for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen |
| [1931](https://www.nobelprize.org/prizes/physics/1931/summary/) | | |
| [1930](https://www.nobelprize.org/prizes/physics/1930/summary/) | [C.V. Raman](https://en.wikipedia.org/wiki/C._V._Raman "Sir Chandrasekhara Venkata Raman a.k.a. चंद्रशेखर वेंकट रामन (1888-1970) India") | for his work on the scattering of light and for the discovery of the effect named after him |
| [1929](https://www.nobelprize.org/prizes/physics/1929/summary/) | [Louis de Broglie](https://en.wikipedia.org/wiki/Louis_de_Broglie "Louis Victor Pierre Raymond de Broglie (1892-1987) France") | for his discovery of the wave nature of electrons |
| [1928](https://www.nobelprize.org/prizes/physics/1928/summary/) | Owen Richardson | for his work on the thermionic phenomenon and especially for the discovery of the law named after him |
| [1927](https://www.nobelprize.org/prizes/physics/1927/summary/) | [Arthur Compton](https://en.wikipedia.org/wiki/Arthur_Compton "Arthur Holly Compton (1892-1962) USA")Charles Wilson | [Compton] for his discovery of the effect named after him, [Wilson] for his method of making the paths of electrically charged particles visible by condensation of vapour |
| [1926](https://www.nobelprize.org/prizes/physics/1926/summary/) | Jean Perrin | for his work on the discontinuous structure of matter, and especially for his discovery of sedimentation equilibrium |
| [1925](https://www.nobelprize.org/prizes/physics/1925/summary/) | James FranckGustav Hertz | for their discovery of the laws governing the impact of an electron upon an atom |
| [1924](https://www.nobelprize.org/prizes/physics/1924/summary/) | Karl Siegbahn | for his discoveries and research in the field of x-ray spectroscopy |
| [1923](https://www.nobelprize.org/prizes/physics/1923/summary/) | [Robert Millikan](https://en.wikipedia.org/wiki/Robert_Andrews_Millikan "Robert Andrews Millikan (1865-1953) USA") | for his work on the elementary charge of electricity and on the photoelectric effect |
| [1922](https://www.nobelprize.org/prizes/physics/1922/summary/) | [Niels Bohr](https://en.wikipedia.org/wiki/Niels_Bohr "Niels Henrik David Bohr (1885-1962) Denmark") | for his services in the investigation of the structure of atoms and of the radiation emanating from them |
| [1921](https://www.nobelprize.org/prizes/physics/1921/summary/) | [Albert Einstein](https://en.wikipedia.org/wiki/Albert_Einstein "Albert Einstein (1879-1955) Germany-Italy-Switzerland-Austria-Belgium-USA") | for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect |
| [1920](https://www.nobelprize.org/prizes/physics/1920/summary/) | Charles Guillaume | in recognition of the service he has rendered to precision measurements in Physics by his discovery of anomalies in nickel steel alloys |
| [1919](https://www.nobelprize.org/prizes/physics/1919/summary/) | Johannes Stark | for his discovery of the Doppler effect in canal rays and the splitting of spectral lines in electric fields |
| [1918](https://www.nobelprize.org/prizes/physics/1918/summary/) | [Max Planck](https://en.wikipedia.org/wiki/Max_Planck "Max Karl Ernst Ludwig Planck (1858-1947) Germany") | in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta |
| [1917](https://www.nobelprize.org/prizes/physics/1917/summary/) | Charles Barkla | for his discovery of the characteristic Röntgen radiation of the elements |
| [1916](https://www.nobelprize.org/prizes/physics/1916/summary/) | | |
| [1915](https://www.nobelprize.org/prizes/physics/1915/summary/) | William Henry BraggWilliam Lawrence Bragg | for their services in the analysis of crystal structure by means of x-rays |
| [1914](https://www.nobelprize.org/prizes/physics/1914/summary/) | Max von Laue | for his discovery of the diffraction of x-rays by crystals |
| [1913](https://www.nobelprize.org/prizes/physics/1913/summary/) | [Heike Kamerlingh Onnes](https://en.wikipedia.org/wiki/Heike_Kamerlingh_Onnes "Heike Kamerlingh Onnes (1853-1926) Netherlands") | for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium |
| [1912](https://www.nobelprize.org/prizes/physics/1912/summary/) | Nils Dalén | for his invention of automatic regulators for use in conjunction with gas accumulators for illuminating lighthouses and buoys |
| [1911](https://www.nobelprize.org/prizes/physics/1911/summary/) | [Wilhelm Wien](https://en.wikipedia.org/wiki/Wilhelm_Wien "Wilhelm Carl Werner Otto Fritz Franz Wien a.k.a. Willy Wien (1864-1928) Russia-Germany") | for his discoveries regarding the laws governing the radiation of heat |
| [1910](https://www.nobelprize.org/prizes/physics/1910/summary/) | Johannes van der Waals | for his work on the equation of state for gases and liquids |
| [1909](https://www.nobelprize.org/prizes/physics/1909/summary/) | Guglielmo MarconiCarl Braun | in recognition of their contributions to the development of wireless telegraphy |
| [1908](https://www.nobelprize.org/prizes/physics/1908/summary/) | Gabriel Lippmann | for his method of reproducing colours photographically based on the phenomenon of interference |
| [1907](https://www.nobelprize.org/prizes/physics/1907/summary/) | [Albert Michelson](https://en.wikipedia.org/wiki/Albert_Abraham_Michelson "Albert Abraham Michelson (1852-1931) Prussia-USA") | for his optical precision instruments and the spectroscopic and metrological investigations carried out with their aid |
| [1906](https://www.nobelprize.org/prizes/physics/1906/summary/) | [J.J. Thomson](https://en.wikipedia.org/wiki/J._J._Thomson "Sir Joseph John Thomson (1856-1940) England") | in recognition of the great merits of his theoretical and experimental investigations on the conduction of electricity by gases |
| [1905](https://www.nobelprize.org/prizes/physics/1905/summary/) | [Philipp Lenard](https://en.wikipedia.org/wiki/Philipp_Lenard "Philipp Eduard Anton von Lenard (1862-1947) Slovakia-Germany") | for his work on cathode rays |
| [1904](https://www.nobelprize.org/prizes/physics/1904/summary/) | [John Strutt, Lord Rayleigh](https://en.wikipedia.org/wiki/John_William_Strutt,_3rd_Baron_Rayleigh "John William Strutt, 3rd Baron Rayleigh a.k.a. Lord Rayleigh (1842-1919) England") | for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies |
| [1903](https://www.nobelprize.org/prizes/physics/1903/summary/) | [Henri Becquerel](https://en.wikipedia.org/wiki/Henri_Becquerel "Antoine Henri Becquerel (1852-1908) France")[Pierre Curie](https://en.wikipedia.org/wiki/Pierre_Curie "Pierre Curie (1859-1906) France")[Marie Curie](https://en.wikipedia.org/wiki/Marie_Curie "Maria Salomea Skłodowska-Curie a.k.a. Marie Curie (1867-1934) Poland-France") | [Becquerel] in recognition of the extraordinary services he has rendered by his discovery of spontaneous radioactivity, [the Curies] in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel |
| [1902](https://www.nobelprize.org/prizes/physics/1902/summary/) | Hendrik LorentzPieter Zeeman | in recognition of the extraordinary service they rendered by their researches into the influence of magnetism upon radiation phenomena |
| [1901](https://www.nobelprize.org/prizes/physics/1901/summary/) | [Wilhelm Röntgen](https://en.wikipedia.org/wiki/Wilhelm_Röntgen "Wilhelm Conrad Röntgen a.k.a. Roentgen (1845-1923) Germany") | in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him |
### ig nobel laureates in physics
The [Ig Nobel Prizes](https://www.improbable.com) honor achievements that first make people laugh, and then make them think. The prizes are intended to celebrate the unusual, honor the imaginative - and spur people's interest in science, medicine, and technology.
Ig Nobel laureates in physics
| year | laureate(s) | achievement |
| --- | --- | --- |
| [2023](https://improbable.com/ig/winners/#ig2023) | Bieito Fernández CastroMarian PeñaEnrique NogueiraMiguel GilcotoEsperanza BroullónAntonio ComesañaDamien BouffardAlberto C. Naveira GarabatoBeatriz Mouriño-Carballido | [for measuring the extent to which ocean-water mixing is affected by the sexual activity of anchovies](https://doi.org/10.1038/s41561-022-00916-3 "Intense Upper Ocean Mixing Due to Large Aggregations of Spawning Fish. Bieito Fernández Castro, Marian Peña, Enrique Nogueira, Miguel Gilcoto, Esperanza Broullón, Antonio Comesaña, Damien Bouffard, Alberto C. Naveira Garabato, and Beatriz Mouriño-Carballido. Nature Geoscience. Vol. 15 No. 4 (2022): 287-292.") |
| [2022](https://improbable.com/ig/winners/#ig2022) | Frank FishZhi-Ming YuanMinglu ChenLaibing JiaChunyan JiAtilla Incecik | [for trying to understand how ducklings manage to swim in formation](https://doi.org/10.1017/jfm.2021.820 "Wave-riding and wave-passing by ducklings in formation swimming. Zhi-Ming Yuan, Minglu Chen, Laibing Jia, Chunyan Ji, Atilla Incecik. Journal of Fluid Mechanics. Vol. 928 No. R2 (2021).") |
| [2021](https://improbable.com/ig/winners/#ig2021) | Alessandro CorbettaJasper MeeusenChung-Min LeeRoberto BenziFederico Toschi | [for conducting experiments to learn why pedestrians do not constantly collide with other pedestrians](https://doi.org/10.1103/PhysRevE.98.062310 "Physics-based modeling and data representation of pairwise interactions among pedestrians. Alessandro Corbetta, Jasper A. Meeusen, Chung-min Lee, Roberto Benzi, and Federico Toschi. Physical Review E. Vol. 98 No. 6 (2018): 062310") |
| [2020](https://improbable.com/ig/winners/#ig2020) | Ivan MaksymovAndriy Pototsky | [for determining, experimentally, what happens to the shape of a living earthworm when one vibrates the earthworm at high frequency](https://doi.org/10.1101/868521 "Excitation of Faraday-like body waves in vibrated living earthworms") |
| [2019](https://improbable.com/ig/winners/#ig2019) | Patricia YangAlexander LeeMiles ChanAlynn MartinAshley EdwardsScott CarverDavid Hu | [for studying how, and why, wombats make cube-shaped poo](http://ecite.utas.edu.au/134954 "How do wombats make cubed poo?") |
| [2018](https://improbable.com/ig/winners/#ig2018) | | |
| [2017](https://improbable.com/ig/winners/#ig2017) | Marc-Antoine Fardin | [for using fluid dynamics to probe the question "Can a Cat Be Both a Solid and a Liquid?"](https://www.drgoulu.com/wp-content/uploads/2017/09/Rheology-of-cats.pdf "On the rheology of cats") |
| [2016](https://improbable.com/ig/winners/#ig2016) | Gábor HorváthMiklós BlahóGyörgy KriskaRamón HegedüsBalázs GericsRóbert FarkasSusanne ÅkessonPéter MalikHansruedi Wildermuth | [for discovering why white-haired horses are the most horsefly-proof horses, and for discovering why dragonflies are fatally attracted to black tombstones](https://doi.org/10.1098/rspb.2009.2202 "An unexpected advantage of whiteness in horses: the most horsefly-proof horse has a depolarizing white coat") |
| [2015](https://improbable.com/ig/winners/#ig2015) | Patricia J. YangJonathan C. PhamJerome ChooDavid L. Hu | [for testing the biological principle that nearly all mammals empty their bladders in about 21 seconds ± 13 seconds](https://doi.org/10.1073/pnas.1402289111 "Duration of urination does not change with body size") |
| [2014](https://improbable.com/ig/winners/#ig2014) | Kiyoshi MabuchiKensei TanakaDaichi UchijimaRina Sakai | [for measuring the amount of friction between a shoe and a banana skin, and between a banana skin and the floor, when a person steps on a banana skin that's on the floor](https://doi.org/10.2474/trol.7.147 "Frictional Coefficient under Banana Skin") |
| [2013](https://improbable.com/ig/winners/#ig2013) | Alberto E. MinettiYuri P. IvanenkoGermana CappelliniNadia DominiciFrancesco Lacquaniti | [for discovering that some people would be physically capable of running across the surface of a pond - if those people, and that pond, were on the Moon](https://doi.org/10.1371/journal.pone.0037300 "Humans Running in Place on Water at Simulated Reduced Gravity") |
| [2012](https://improbable.com/ig/winners/#ig2012) | Joseph KellerRaymond GoldsteinPatrick WarrenRobin Ball | [for calculating the balance of forces that shape and move the hair in a human ponytail](https://doi.org/10.1103/PhysRevLett.108.078101 "Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles") |
| [2011](https://improbable.com/ig/winners/#ig2011) | Philippe PerrinCyril PerrotDominique DeviterneBruno RagaruHerman Kingma | [for determining why discus throwers become dizzy, and why hammer throwers don't](https://doi.org/10.1080/000164800750000621 "Dizziness in Discus Throwers is Related to Motion Sickness Generated While Spinning") |
| [2010](https://improbable.com/ig/winners/#ig2010) | Lianne ParkinSheila WilliamsPatricia Priest | [for demonstrating that, on icy footpaths in wintertime, people slip and fall less often if they wear socks on the outside of their shoes](https://pubmed.ncbi.nlm.nih.gov/19680302/ "Preventing winter falls: a randomised controlled trial of a novel intervention") |
| [2009](https://improbable.com/ig/winners/#ig2009) | Katherine K. WhitcomeDaniel E. LiebermanLiza J. Shapiro | [for analytically determining why pregnant women don't tip over](https://doi.org/10.1038/nature06342 "Fetal load and the evolution of lumbar lordosis in bipedal hominins") |
| [2008](https://improbable.com/ig/winners/#ig2008) | Dorian RaymerDouglas Smith | [for proving mathematically that heaps of string or hair or almost anything else will inevitably tangle themselves up in knots](https://doi.org/10.1073/pnas.0611320104 "Spontaneous knotting of an agitated string") |
| [2007](https://improbable.com/ig/winners/#ig2007) | L. MahadevanEnrique Cerda | [for studying how sheets become wrinkled](https://doi.org/10.1103/PhysRevLett.90.074302 "Geometry and Physics of Wrinkling") |
| [2006](https://improbable.com/ig/winners/#ig2006) | Basile AudolySebastien Neukirch | [for their insights into why, when you bend dry spaghetti, it often breaks into more than two pieces](https://doi.org/10.1103/PhysRevLett.95.095505 "Fragmentation of Rods by Cascading Cracks: Why Spaghetti Does Not Break in Half") |
| [2005](https://improbable.com/ig/winners/#ig2005) | John MainstoneThomas Parnell | [for patiently conducting an experiment that began in the year 1927 in which a glob of congealed black tar has been slowly, slowly dripping through a funnel, at a rate of approximately one drop every nine years](https://doi.org/10.1088/0143-0807/5/4/003 "The pitch drop experiment") |
| [2004](https://improbable.com/ig/winners/#ig2004) | Ramesh BalasubramaniamMichael Turvey | [for exploring and explaining the dynamics of hula-hooping](https://doi.org/10.1007/s00422-003-0460-4 "Coordination modes in the multisegmental dynamics of hula hooping") |
| [2003](https://improbable.com/ig/winners/#ig2003) | Jack HarveyJohn CulvenorWarren PayneSteve CowleyMichael LawranceDavid StuartRobyn Williams | [for their irresistible report "An analysis of the forces required to drag sheep over various surfaces"](https://doi.org/10.1016/S0003-6870(02) 00071-6 "An analysis of the forces required to drag sheep over various surfaces") |
| [2002](https://improbable.com/ig/winners/#ig2002) | Arnd Leike | [for demonstrating that beer froth obeys the mathematical Law of Exponential Decay](https://doi.org/10.1088/0143-0807/23/1/304 "Demonstration of the exponential decay law using beer froth") |
| [2001](https://improbable.com/ig/winners/#ig2001) | David Schmidt | [for his partial solution to the question of why shower curtains billow inwards](https://www.umass.edu/newsoffice/article/umass-amherst-researcher-solves-mystery-billowing-shower-curtain "UMass Amherst Researcher Solves the Mystery of the Billowing Shower Curtain") |
| [2000](https://improbable.com/ig/winners/#ig2000) | [Andre Geim](https://en.wikipedia.org/wiki/Andre_Geim "Andre Konstantinovich Geim a.k.a. Андрей Константинович Гейм (1958-0000) Russia")Michael Berry | [for using magnets to levitate a frog](https://doi.org/10.1088/0143-0807/18/4/012 "Of flying frogs and levitrons") |
| [1999](https://improbable.com/ig/winners/#ig1999) | Len FisherJean-Marc Vanden-BroeckJoseph Keller | [Fisher] [for calculating the optimal way to dunk a biscuit](https://www.nature.com/articles/17203 "Physics takes the biscuit"), [Vanden-Broeck and Keller] [for calculating how to make a teapot spout that does not drip](https://doi.org/10.1063/1.865735 "Pouring flows") |
| [1998](https://improbable.com/ig/winners/#ig1998) | Deepak Chopra | for his unique interpretation of quantum physics as it applies to life, liberty, and the pursuit of economic happiness |
| [1997](https://improbable.com/ig/winners/#ig1997) | John Bockris | for his wide-ranging achievements in cold fusion, in the transmutation of base elements into gold, and in the electrochemical incineration of domestic rubbish |
| [1996](https://improbable.com/ig/winners/#ig1996) | Robert Matthews | [for his studies of Murphy's Law, and especially for demonstrating that toast often falls on the buttered side](https://doi.org/10.1088/0143-0807/16/4/005 "Tumbling toast, Murphy's Law and the fundamental constants") |
| [1995](https://improbable.com/ig/winners/#ig1995) | D.M.R. GeorgetR. ParkerA.C. Smith | [for their rigorous analysis of soggy breakfast cereal, published in the report entitled "A Study of the Effects of Water Content on the Compaction Behaviour of Breakfast Cereal Flakes"](https://doi.org/10.1016/0032-5910(94) 02882-6 "A study of the effects of water content on the compaction behaviour of breakfast cereal flakes") |
| [1994](https://improbable.com/ig/winners/#ig1994) | | |
| [1993](https://improbable.com/ig/winners/#ig1993) | Louis Kervran | for his conclusion that the calcium in chickens' eggshells is created by a process of cold fusion |
| [1992](https://improbable.com/ig/winners/#ig1992) | David ChorleyDoug Bower | for their circular contributions to field theory based on the geometrical destruction of English crops |
| [1991](https://improbable.com/ig/winners/#ig1991) | | |
### names that appear in this book
* [Edoardo Amaldi](https://en.wikipedia.org/wiki/Edoardo_Amaldi "Edoardo Amaldi (1908-1989) Italy") (1908-1989) Italy
* [Guillaume Amontons](https://en.wikipedia.org/wiki/Guillaume_Amontons "Guillaume Amontons (1663-1705) France") (1663-1705) France
* [André-Marie Ampère](https://en.wikipedia.org/wiki/André-Marie_Ampère "André-Marie Ampère (1775-1836) France") (1775-1836) France
* [Anders Ångström](https://en.wikipedia.org/wiki/Anders_Jonas_Ångström "Anders Jonas Ångström (1814-1874) Sweden") (1814-1874) Sweden
* [Archimedes of Syracuse](https://en.wikipedia.org/wiki/Archimedes "Archimedes of Syracuse a.k.a. Αρχιμήδης ο Συρακούσιος (287 BCE-212 BCE) Italy") (287 BCE-212 BCE) Italy
* [Aristarchus of Samos](https://en.wikipedia.org/wiki/Aristarchus_of_Samos "Aristarchus of Samos a.k.a. Αρίσταρχος ο Σάμιος (310 BCE-230 BCE) Greece") (310 BCE-230 BCE) Greece
* [Aristotle of Stagira](https://en.wikipedia.org/wiki/Aristotle "Aristotle of Stagira a.k.a. Αριστοτέλης ο Στάγειρα (384 BCE-322 BCE) Greece") (384 BCE-322 BCE) Greece
* [Edwin Howard Armstrong](https://en.wikipedia.org/wiki/Edwin_Howard_Armstrong "Edwin Howard Armstrong (1890-1954) USA") (1890-1954) USA
* [Svante Arrhenius](https://en.wikipedia.org/wiki/Svante_Arrhenius "Svante August Arrhenius (1859-1927) Sweden") (1859-1927) Sweden
* [Amedeo Avogadro](https://en.wikipedia.org/wiki/Amedeo_Avogadro "Lorenzo Romano Amedeo Carlo Avogadro, conte di Quaregna e Cerreto (1776-1856) Italy") (1776-1856) Italy
* [Felix Baumgartner](https://en.wikipedia.org/wiki/Felix_Baumgartner "Felix Baumgartner (1969-0000) Austria") (1969-0000) Austria
* [Bob Beamon](https://en.wikipedia.org/wiki/Bob_Beamon "Robert Beamon (1946-0000) USA") (1946-0000) USA
* [Henri Becquerel](https://en.wikipedia.org/wiki/Henri_Becquerel "Antoine Henri Becquerel (1852-1908) France") (1852-1908) France
* [Georg Bednorz](https://en.wikipedia.org/wiki/Georg_Bednorz "Johannes Georg Bednorz (1950-0000) Germany") (1950-0000) Germany
* [Alexander Graham Bell](https://en.wikipedia.org/wiki/Alexander_Graham_Bell "Alexander Graham Bell (1847-1922) Scotland-USA-Canada") (1847-1922) Scotland-USA-Canada
* [Daniel Bernoulli](https://en.wikipedia.org/wiki/Daniel_Bernoulli "Daniel Bernoulli (1700-1782) Netherlands-Switzerland") (1700-1782) Netherlands-Switzerland
* [Hans Bethe](https://en.wikipedia.org/wiki/Hans_Bethe "Hans Albrecht Bethe (1906-2005) Germany-USA") (1906-2005) Germany-USA
* [Jean-Baptiste Biot](https://en.wikipedia.org/wiki/Jean-Baptiste_Biot "Jean-Baptiste Biot (1774-1862) France") (1774-1862) France
* [Sidney Bludman](https://physics.info/physics/link.txt "Sidney Arnold Bludman (1927-0000) USA") (1927-0000) USA
* [Niels Bohr](https://en.wikipedia.org/wiki/Niels_Bohr "Niels Henrik David Bohr (1885-1962) Denmark") (1885-1962) Denmark
* [Ludwig Boltzmann](https://en.wikipedia.org/wiki/Ludwig_Boltzmann "Ludwig Eduard Boltzmann (1844-1906) Austria") (1844-1906) Austria
* [Satyendra Bose](https://en.wikipedia.org/wiki/Satyendra_Nath_Bose "Satyendra Nath Bose a.k.a. সত্যেন্দ্র নাথ বসু (1894-1974) India") (1894-1974) India
* [Robert Boyle](https://en.wikipedia.org/wiki/Robert_Boyle "Robert Boyle (1627-1691) Ireland-England") (1627-1691) Ireland-England
* [Lawrence Bragg](https://en.wikipedia.org/wiki/Lawrence_Bragg "Sir William Lawrence Bragg (1890-1971) Australia-England") (1890-1971) Australia-England
* [William Bragg](https://en.wikipedia.org/wiki/William_Henry_Bragg "Sir William Henry Bragg (1862-1942) England") (1862-1942) England
* [George Brayton](https://en.wikipedia.org/wiki/George_Brayton "George Brayton (1830-1892) US") (1830-1892) USA
* [Robert Brout](https://en.wikipedia.org/wiki/Robert_Brout "Robert Brout (1928-2011) USA-Belgium") (1928-2011) USA-Belgium
* [Giordano Bruno](https://en.wikipedia.org/wiki/Giordano_Bruno "Giordano Bruno a.k.a. Filippo Bruno a.k.a. Iordanus Brunus Nolanus (1548-1600) Italy") (1548-1600) Italy
* [Robert Bunsen](https://en.wikipedia.org/wiki/Robert_Bunsen "Robert Wilhelm Eberhard Bunsen (1811-1899) Germany") (1811-1899) Germany
* [Sadi Carnot](https://en.wikipedia.org/wiki/Nicolas_Léonard_Sadi_Carnot "Nicolas Léonard Sadi Carnot (1796-1832) France") (1796-1832) France
* [Henry Cavendish](https://en.wikipedia.org/wiki/Henry_Cavendish "Henry Cavendish (1731-1810) England") (1731-1810) England
* [Anders Celsius](https://en.wikipedia.org/wiki/Anders_Celsius "Anders Celsius (1701-1744) Sweden") (1701-1744) Sweden
* [James Chadwick](https://en.wikipedia.org/wiki/James_Chadwick "James Chadwick (1891-1974) England") (1891-1974) England
* [Subrahmanyan Chandrasekhar](https://en.wikipedia.org/wiki/Subrahmanyan_Chandrasekhar "Subrahmanyan Chandrasekhar (1910-1995) Pakistan-USA") (1910-1995) Pakistan-USA
* [Jacques Charles](https://en.wikipedia.org/wiki/Jacques_Charles "Jacques Alexander Cèsare Charles (1746-1823) France") (1746-1823) France
* [Ernst Chladni](https://en.wikipedia.org/wiki/Ernst_Chladni "Ernst Florens Friedrich Chladni (1756-1827) Germany-Poland") (1756-1827) Germany-Poland
* [James Christy](https://en.wikipedia.org/wiki/James_W._Christy "James Walter Christy a.k.a. Jim Christy (1938-0000) USA") (1938-0000) USA
* [Rudolf Clausius](https://en.wikipedia.org/wiki/Rudolf_Clausius "Rudolf Julius Emanuel Gottlieb a.k.a. Clausius (1822-1888) Poland-Germany") (1822-1888) Poland-Germany
* [Arthur Compton](https://en.wikipedia.org/wiki/Arthur_Compton "Arthur Holly Compton (1892-1962) USA") (1892-1962) USA
* [William Coolidge](https://en.wikipedia.org/wiki/William_D._Coolidge "William David Coolidge (1873-1975) USA") (1873-1975) USA
* [Nicolaus Copernicus](https://en.wikipedia.org/wiki/Nicolaus_Copernicus "Mikołaj Kopernik a.k.a. Nicolaus Copernicus a.k.a. Niklas Koppernigk (1473-1543) Poland") (1473-1543) Poland
* [Gustave Coriolis](https://en.wikipedia.org/wiki/Gaspard-Gustave_Coriolis "Gaspard-Gustave de Coriolis (1792-1843) France") (1792-1843) France
* [Charles-Augustin Coulomb](https://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb "Charles-Augustin Coulomb (1736-1806) France") (1736-1806) France
* [Clyde Cowan](https://en.wikipedia.org/wiki/Clyde_Cowan "Clyde Lorrain Cowan Jr. (1919-1974) USA") (1919-1974) USA
* [Monsieur Creosote](https://en.wikipedia.org/wiki/Mr_Creosote "Mr. Creosote a.k.a. Monsieur Creosote (1942-1983) England") (1942-1983) England
* [Andreas Cunæus](https://physics.info/physics/link.txt "Andreas Cunæus (1712-1788) Netherlands") (1712-1788) Netherlands
* [Marie Curie](https://en.wikipedia.org/wiki/Marie_Curie "Maria Salomea Skłodowska-Curie a.k.a. Marie Curie (1867-1934) Poland-France") (1867-1934) Poland-France
* [Pierre Curie](https://en.wikipedia.org/wiki/Pierre_Curie "Pierre Curie (1859-1906) France") (1859-1906) France
* [John Dalton](https://en.wikipedia.org/wiki/John_Dalton "John Dalton (1766-1844) England") (1766-1844) England
* [John Daniell](https://en.wikipedia.org/wiki/John_Frederic_Daniell "John Frederic Daniell (1790-1845) England") (1790-1845) England
* [Clinton Davisson](https://en.wikipedia.org/wiki/Clinton_Davisson "Clinton Joseph Davisson (1881-1958) USA") (1881-1958) USA
* [Louis de Broglie](https://en.wikipedia.org/wiki/Louis_de_Broglie "Louis Victor Pierre Raymond de Broglie (1892-1987) France") (1892-1987) France
* [René Descartes](https://en.wikipedia.org/wiki/René_Descartes "René Descartes a.k.a. Renatus Cartesius (1596-1650) France") (1596-1650) France
* [Rudolf Diesel](https://en.wikipedia.org/wiki/Rudolf_Diesel "Rudolf Christian Karl Diesel (1858-1916) France-England") (1858-1916) France-England
* [Paul Dirac](https://en.wikipedia.org/wiki/Paul_Dirac "Paul Adrien Maurice Dirac a.k.a. P.A.M. Dirac (1902-1984) England-USA") (1902-1984) England-USA
* [Émilie du Châtelet](https://en.wikipedia.org/wiki/Émilie_du_Châtelet "Gabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet a.k.a. du Chastellet (1706-1749) France") (1706-1749) France
* [Tom Duff](https://en.wikipedia.org/wiki/Tom_Duff "Thomas Douglas Selkirk Duff (1952-0000) Canada") (1952-0000) Canada
* [Pierre Louis Dulong](https://en.wikipedia.org/wiki/Pierre_Louis_Dulong "Pierre Louis Dulong (1785-1838) France") (1785-1838) France
* [Freeman Dyson](https://en.wikipedia.org/wiki/Freeman_Dyson "Freeman John Dyson (1923-2020) England-USA") (1923-2020) England
* [Arthur Eddington](https://en.wikipedia.org/wiki/Arthur_Eddington "Sir Arthur Stanley Eddington (1882-1944) England") (1882-1944) England
* [Albert Einstein](https://en.wikipedia.org/wiki/Albert_Einstein "Albert Einstein (1879-1955) Germany-Italy-Switzerland-Austria-Belgium-USA") (1879-1955) Germany-Italy-Switzerland-Austria-Belgium-USA
* [François Englert](https://en.wikipedia.org/wiki/François_Englert "François Baron Englert (1932-0000) Belgium") (1932-0000) Belgium
* [Loránd Eötvös](https://en.wikipedia.org/wiki/Loránd_Eötvös "Baron Loránd Eötvös de Vásárosnamény a.k.a. Vásárosnaményi báró Eötvös Loránd Ágoston a.k.a. Roland Eötvös (1848-1919) Hungary") (1848-1919) Hungary
* [Immanuel Estermann](https://de.wikipedia.org/wiki/Immanuel_Estermann "Immanuel Estermann (1900-1973) Germany-Israel") (1900-1973) Germany-Israel
* [Euclid of Alexandria](https://en.wikipedia.org/wiki/Euclid "Euclid of Alexandria a.k.a. Ευκλείδης ο Αλεξάνδρεια (323 BCE-283 BCE) Egypt") (323 BCE-283 BCE) Egypt
* [Alan Eustace](https://en.wikipedia.org/wiki/Alan_Eustace "Robert Alan Eustace (1956-0000) USA") (1956-0000) USA
* [Daniel Gabriel Fahrenheit](https://en.wikipedia.org/wiki/Daniel_Gabriel_Fahrenheit "Daniel Gabriel Fahrenheit (1686-1736) Poland-Netherlands") (1686-1736) Poland-Netherlands
* [Michael Faraday](https://en.wikipedia.org/wiki/Michael_Faraday "Michael Faraday (1791-1867) England") (1791-1867) England
* [Philo T. Farnsworth](https://en.wikipedia.org/wiki/Philo_Farnsworth "Philo Taylor Farnsworth (1906-1971) USA") (1906-1971) USA
* [Pierre de Fermat](https://en.wikipedia.org/wiki/Pierre_de_Fermat "Pierre de Fermat (1601-1665) France") (1601-1665) France
* [Enrico Fermi](https://en.wikipedia.org/wiki/Enrico_Fermi "Enrico Fermi (1901-1954) Italy-USA") (1901-1954) Italy-USA
* [Reginald Fessenden](https://en.wikipedia.org/wiki/Reginald_Fessenden "Reginald Aubrey Fessenden (1866-1932) Canada-Bermuda") (1866-1932) Canada-Bermuda
* [Richard Feynman](https://en.wikipedia.org/wiki/Richard_Feynman "Richard Phillips Feynman (1918-1988) USA") (1918-1988) USA
* [Thomas Fincke](https://en.wikipedia.org/wiki/Thomas_Fincke "Thomas Fincke a.k.a. Thomas Finkius a.k.a. Thomas Finchius (1561-1656) Denmark") (1561-1656) Denmark
* [Léon Foucault](https://en.wikipedia.org/wiki/Léon_Foucault "Jean Bernard Léon Foucault (1819-1868) France") (1819-1868) France
* [Joseph Fourier](https://en.wikipedia.org/wiki/Joseph_Fourier "Jean Baptiste Joseph Fourier (1768-1830) France") (1768-1830) France
* [Benjamin Franklin](https://en.wikipedia.org/wiki/Benjamin_Franklin "Benjamin Franklin (1706-1790) USA") (1706-1790) USA
* [Rosalind Franklin](https://en.wikipedia.org/wiki/Rosalind_Franklin "Rosalind Elsie Franklin (1920-1958) England") (1920-1958) England
* [Augustin-Jean Fresnel](https://en.wikipedia.org/wiki/Augustin-Jean_Fresnel "Augustin-Jean Fresnel (1788-1827) France") (1788-1827) France
* [Alexander Friedmann](https://en.wikipedia.org/wiki/Alexander_Friedmann "Alexander Alexandrovich Friedmann a.k.a. Александр Александрович Фридман (1888-1925) Russia") (1888-1925) Russia
* [Galileo Galilei](https://en.wikipedia.org/wiki/Galileo_Galilei "Galileo Galilei (1564-1642) Italy") (1564-1642) Italy
* [Johann Galle](https://en.wikipedia.org/wiki/Johann_Gottfried_Galle "Johann Gottfried Galle (1812-1910) Germany") (1812-1910) Germany
* [Luigi Galvani](https://en.wikipedia.org/wiki/Luigi_Galvani "Luigi Aloisio Galvani a.k.a. Aloysius Galvani (1737-1798) Italy") (1737-1798) Italy
* [Carl Friedrich Gauss](https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss "Johann Carl Friedrich Gauss a.k.a. Gauß a.k.a. Carolus Fridericus Gauss (1777-1855) Germany") (1777-1855) Germany
* [Joseph Gay-Lussac](https://en.wikipedia.org/wiki/Joseph_Louis_Gay-Lussac "Joseph Louis Gay-Lussac (1778-1850) France") (1778-1850) France
* [Andre Geim](https://en.wikipedia.org/wiki/Andre_Geim "Andre Konstantinovich Geim a.k.a. Андрей Константинович Гейм (1958-0000) Russia") (1958-0000) Russia
* [Murray Gell-Mann](https://en.wikipedia.org/wiki/Murray_Gell-Mann "Murray Gell-Mann (1929-2019) USA") (1929-2019) USA
* [Reinhard Genzel](https://en.wikipedia.org/wiki/Reinhard_Genzel "Reinhard Genzel (1952-0000) Germany") (1952-0000) Germany
* [Lester Germer](https://en.wikipedia.org/wiki/Lester_Germer "Lester Halbert Germer (1896-1971) USA") (1896-1971) USA
* [Andrea Ghez](https://en.wikipedia.org/wiki/Andrea_M._Ghez "Andrea Mia Ghez (1965-0000) USA") (1965-0000) USA
* [William Gilbert](https://en.wikipedia.org/wiki/William_Gilbert_(astronomer) "William Gilbert (1544-1603) England") (1544-1603) England
* [James Glaisher](https://en.wikipedia.org/wiki/James_Glaisher "James Glaisher (1809-1903) England") (1809-1903) England
* [Sheldon Glashow](https://en.wikipedia.org/wiki/Sheldon_Lee_Glashow "Sheldon Lee Glashow (1932-0000) USA") (1932-0000) USA
* [Maria Goeppert-Mayer](https://en.wikipedia.org/wiki/Maria_Goeppert-Mayer "Maria Goeppert-Mayer (1906-1972) Poland-USA") (1906-1972) Poland-USA
* [Johann Wolfgang von Goethe](https://en.wikipedia.org/wiki/Johann_Wolfgang_von_Goethe "Johann Wolfgang von Goethe (1749-1832) Germany") (1749-1832) Germany
* [Louis Gray](https://en.wikipedia.org/wiki/Louis_Harold_Gray "Louis Harold Gray (1905-1965) England") (1905-1965) England
* [Oscar Greenberg](https://en.wikipedia.org/wiki/Oscar_W._Greenberg "Oscar Wallace Greenberg (1932-0000) USA") (1932-0000) USA
* [Edmund Gunter](https://en.wikipedia.org/wiki/Edmund_Gunter "Edmund Gunter (1581-1626) Wales-England") (1581-1626) Wales-England
* [Gerald Guralnik](https://en.wikipedia.org/wiki/Gerald_Guralnik "Gerald Stanford Guralnik a.k.a. Gerry Guralnik (1936-2014) USA") (1936-2014) USA
* [Alan Guth](https://en.wikipedia.org/wiki/Alan_Guth "Alan Harvey Guth (1947-0000) USA") (1947-0000) USA
* [Carl Hagen](https://en.wikipedia.org/wiki/C._R._Hagen "Carl Richard Hagen (1937-0000) USA") (1937-0000) USA
* [Gotthilf Hagen](https://en.wikipedia.org/wiki/Gotthilf_Hagen "Gotthilf Heinrich Ludwig Hagen (1797-1884) Germany") (1797-1884) Germany
* [Edmond Halley](https://en.wikipedia.org/wiki/Edmond_Halley "Edmond Halley (1656-1742) England") (1656-1742) England
* [Moo-Young Han](https://en.wikipedia.org/wiki/Moo-Young_Han "Moo-Young Han a.k.a. 한무영 (1934-2016) Korea-USA") (1934-2016) Korea-USA
* [Stephen Hawking](https://en.wikipedia.org/wiki/Stephen_Hawking "Stephen William Hawking (1942-2018) England") (1942-2018) England
* [Werner Heisenberg](https://en.wikipedia.org/wiki/Werner_Heisenberg "Werner Karl Heisenberg (1901-1976) Germany") (1901-1976) Germany
* [Hermann Helmholtz](https://en.wikipedia.org/wiki/Hermann_von_Helmholtz "Hermann Ludwig Ferdinand von Helmholtz (1821-1894) Germany") (1821-1894) Germany
* [Joseph Henry](https://en.wikipedia.org/wiki/Joseph_Henry "Joseph Henry (1797-1878) USA") (1797-1878) USA
* [Heraclitis of Ephesus](https://en.wikipedia.org/wiki/Heraclitus "Heraclitus of Ephesus a.k.a. Ηράκλειτος ο Εφέσιος (544 BCE-484 BCE) Turkey") (544 BCE-484 BCE) Turkey
* [William Herschel](https://en.wikipedia.org/wiki/William_Herschel "Sir Frederick William Herschel (1738-1822) Germany-England") Germany-England
* [Heinrich Hertz](https://en.wikipedia.org/wiki/Heinrich_Hertz "Heinrich Rudolf Hertz (1857-1894) Germany") (1857-1894) Germany
* [Friedrich Heusler](https://en.wikipedia.org/wiki/Friedrich_Heusler "Friedrich Heusler a.k.a. Fritz Heusler (1866-1947) Germany") (1866-1947) Germany
* [William Heytesbury](https://en.wikipedia.org/wiki/William_of_Heytesbury "William of Heytesbury a.k.a. Gugliemus Hentisberus (1313-1372) England") (1313-1372) England
* [Peter Higgs](https://en.wikipedia.org/wiki/Peter_Higgs "Peter Ware Higgs (1929-2024) England")(1929-2024) England
* [Hipparchus of Nicaea](https://en.wikipedia.org/wiki/Hipparchus "Hipparchus of Nicaea a.k.a. Ιππαρχος ο Νικαευς (c. 190 BCE-c. 120 BCE) Turkey-Greece") (c. 190 BCE-c. 120 BCE) Turkey-Greece
* [Robert Hooke](https://en.wikipedia.org/wiki/Robert_Hooke "Robert Hooke (1635-1703) England") (1635-1703) England
* [Russell Hulse](https://en.wikipedia.org/wiki/Russell_Alan_Hulse "Russell Alan Hulse (1950-0000) USA") (1950-0000) USA
* [Edwin Hubble](https://en.wikipedia.org/wiki/Edwin_Hubble "Edwin Powell Hubble (1889-1953) USA") (1889-1953) USA
* [Christiaan Huygens](https://en.wikipedia.org/wiki/Christiaan_Huygens "Christiaan Huygens (1629-1695) Netherlands") (1629-1695) Netherlands
* [James Jeans](https://en.wikipedia.org/wiki/James_Jeans "Sir James Hopwood Jeans (1877-1946) England") (1877-1946) England
* [Hans Jensen](https://en.wikipedia.org/wiki/J._Hans_D._Jensen "Johannes Hans Daniel Jensen a.k.a. J. Hans D. Jensen (1907-1973) Germany") (1907-1973) Germany
* [Frédéric Joliot-Curie](https://en.wikipedia.org/wiki/Frédéric_Joliot-Curie "Jean Frédéric Joliot-Curie (1900-1958) France") (1900-1958) France
* [Irène Joliot-Curie](https://en.wikipedia.org/wiki/Irène_Joliot-Curie "Irène Joliot-Curie (1897-1956) France") (1897-1956) France
* [James Joule](https://en.wikipedia.org/wiki/James_Prescott_Joule "James Prescott Joule (1818-1889) England") (1818-1889) England
* [Heike Kamerlingh Onnes](https://en.wikipedia.org/wiki/Heike_Kamerlingh_Onnes "Heike Kamerlingh Onnes (1853-1926) Netherlands") (1853-1926) Netherlands
* [Pyotr Kapitsa](https://en.wikipedia.org/wiki/Pyotr_Kapitsa "Pyotr Leonidovich Kapitsa a.k.a. Пётр Леони́дович Капи́ца a.k.a. Peter Kapitza (1894-1984) Russia") (1894-1984) Russia
* [Heinrich Kayser](https://en.wikipedia.org/wiki/Heinrich_Kayser "Heinrich Gustav Johannes Kayser (1853-1940) Germany") (1853-1940) Germany
* [William Thomson, Lord Kelvin](https://en.wikipedia.org/wiki/William_Thomson,_1st_Baron_Kelvin "William Thomson, 1st Baron Kelvin a.k.a. Lord Kelvin (1824-1907) Ireland-Scotland") (1824-1907) Ireland-Scotland
* [Johannes Kepler](https://en.wikipedia.org/wiki/Johannes_Kepler "Johannes Kepler a.k.a. Ioannes Keplerus (1571-1630) Germany") (1571-1630) Germany
* [Tom Kibble](https://en.wikipedia.org/wiki/Tom_W._B._Kibble "Thomas Walter Bannerman Kibble (1932-2016) England") (1932-2016) England
* [Gustav Kirchhoff](https://en.wikipedia.org/wiki/Gustav_Kirchhoff "Gustav Robert Kirchhoff (1824-1887) Germany") (1824-1887) Germany
* [Daniel Kirkwood](https://en.wikipedia.org/wiki/Daniel_Kirkwood "Daniel Kirkwood (1814-1895) USA") (1814-1895) USA
* [Joseph Kittinger](https://en.wikipedia.org/wiki/Joseph_Kittinger "Joseph William Kittinger II (1928-0000) USA") (1928-0000) USA
* [Oskar Klein](https://en.wikipedia.org/wiki/Oskar_Klein "Oskar Benjamin Klein (1894-1977) Sweden") (1894-1977) Sweden
* [Nicholas Kurti](https://en.wikipedia.org/wiki/Nicholas_Kurti "Nicholas Kurti a.k.a. Kürti Miklós (1908-1998) Hungary-Germany-England") (1908-1998) Hungary-Germany-England
* [Guillaume de l'Hôpital](https://en.wikipedia.org/wiki/Guillaume_de_l'Hôpital "Guillaume François Antoine, Marquis de l'Hôpital (1661-1704) France") (1661-1704) France
* [Frederick Lanchester](https://en.wikipedia.org/wiki/Frederick_W._Lanchester "Frederick William Lanchester (1868-1946) England") (1868-1946) England
* [Edwin Land](https://en.wikipedia.org/wiki/Edwin_H._Land "Edwin Herbert Land (1909-1991) USA") (1909-1991) USA
* [William Lassell](https://en.wikipedia.org/wiki/William_Lassell "William Lassell (1799-1880) England") (1799-1880) England
* [Urbain Le Verrier](https://en.wikipedia.org/wiki/Urbain_Le_Verrier "Urbain Jean Joseph Le Verrier (1811-1877) France") (1811-1877) France
* [Georges Leclanché](https://en.wikipedia.org/wiki/Georges_Leclanché "Georges Leclanché (1839-1882) France") (1839-1882) France
* [Paul-Émile Lecoq de Boisbaudran](https://en.wikipedia.org/wiki/Paul-Émile_Lecoq_de_Boisbaudran "Paul-Émile Lecoq de Boisbaudran a.k.a. François Lecoq de Boisbaudran (1838-1912) France") (1838-1912) France
* [Leon Lederman](https://en.wikipedia.org/wiki/Leon_M._Lederman "Leon Max Lederman (1922-2018) USA") (1922-2018) USA
* [Gottfried Leibniz](https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz "Gottfried Wilhelm von Leibniz (1646-1716) Germany") (1646-1716) Germany
* [Georges Lemaître](https://en.wikipedia.org/wiki/Georges_Lemaître "Monseigneur Georges Henri Joseph Édouard Lemaître a.k.a. Abbé Lemaître (1894-1966) Belgium") (1894-1966) Belgium
* [Philipp Lenard](https://en.wikipedia.org/wiki/Philipp_Lenard "Philipp Eduard Anton von Lenard (1862-1947) Slovakia-Germany") (1862-1947) Slovakia-Germany
* [Max von Laue](https://en.wikipedia.org/wiki/Max_von_Laue "Max Theodor Felix von Laue (1879-1960) Germany") (1879-1960) Germany
* [Heinrich Lenz](https://en.wikipedia.org/wiki/Heinrich_Lenz "Heinrich Friedrich Emil Lenz a.k.a. Генрих Фридрих Эмиль Ленц a.k.a. Ильюха Христианович Ленц (1804-1865) Estonia-Russia") (1804-1865) Estonia-Russia
* [Carolus Linnæus](https://en.wikipedia.org/wiki/Carl_Linnaeus "Carl Nilsson Linnaeus a.k.a. Carolus Linnæus a.k.a. Carl von Linné (1707-1778) Sweden") (1707-1778) Sweden
* [Kathleen Lonsdale](https://en.wikipedia.org/wiki/Kathleen_Lonsdale "Dame Kathleen Lonsdale (1903-1971) Ireland-England") (1903-1971) Ireland-England
* [Josef Loschmidt](https://en.wikipedia.org/wiki/Johann_Josef_Loschmidt "Johann Josef Loschmidt (1821-1895) Czech Republic-Austria") (1821-1895) Czech Republic-Austria
* [Ernst Mach](https://en.wikipedia.org/wiki/Ernst_Mach "Ernst Waldfried Josef Wenzel Mach (1838-1916) Czech Republic-Germany") (1838-1916) Czech Republic-Germany
* [Guglielmo Marconi](https://en.wikipedia.org/wiki/Guglielmo_Marconi "Marchese Guglielmo Giovanni Maria Marconi (1874-1937) Italy") (1874-1937) Italy
* [Edme Mariotte](https://en.wikipedia.org/wiki/Edme_Mariotte "Abbé Edme Mariotte (1620-1684) France") (1620-1684) France
* [Moisey Markov](https://en.wikipedia.org/wiki/Moisey_Markov "Moisey Alexandrovich Markov a.k.a. Моисей Александрович Марков (1908-1994) Russia") (1908-1994) Russia
* [Pierre Louis Maupertuis](https://en.wikipedia.org/wiki/Pierre_Louis_Maupertuis "Pierre Louis Moreau de Maupertuis (1698-1759) France-Switzerland") (1698-1759) France-Switzerland
* [James Clerk Maxwell](https://en.wikipedia.org/wiki/James_Clerk_Maxwell "James Clerk Maxwell (1831-1879) Scotland-England") (1831-1879) Scotland-England
* [Julius von Mayer](https://en.wikipedia.org/wiki/Julius_von_Mayer "Julius Robert von Mayer (1814-1878) German") (1814-1878) German
* [Walther Meissner](https://en.wikipedia.org/wiki/Walther_Meissner "Fritz Walther Meißner a.k.a. Meissner (1882-1974) Germany") (1882-1974) Germany
* [Dmitri Mendeleev](https://en.wikipedia.org/wiki/Dmitri_Mendeleev "Dmitri Ivanovich Mendeleev (Mendeleyev, Mendeleef) a.k.a. Дмитрий Иванович Менделеев a.k.a. Дмитрій Ивановичъ Менделѣевъ (1834-1907) Russia") (1834-1907) Russia
* [Johann Rudolf Merian](https://de.wikipedia.org/wiki/Johann_Rudolf_Merian " Johann Rudolf Merian (1797-1871) Switzerland") (1797-1871) Switzerland
* [Albert Michelson](https://en.wikipedia.org/wiki/Albert_Abraham_Michelson "Albert Abraham Michelson (1852-1931) Prussia-USA") (1852-1931) Prussia-USA
* [Ralph Miller](https://physics.info/physics/link.txt "Ralph Miller (1890-????) Denmark-USA") (1890-????) Denmark-USA
* [Robert Millikan](https://en.wikipedia.org/wiki/Robert_Andrews_Millikan "Robert Andrews Millikan (1865-1953) USA") (1865-1953) USA
* [Gordon Moore](https://en.wikipedia.org/wiki/Gordon_Moore "Gordon Earle Moore (1929-0000) USA") (1929-0000) USA
* [Henry Moseley](https://en.wikipedia.org/wiki/Henry_Moseley "Henry Gwyn Jeffreys Moseley (1887-1915) England-Turkey") (1887-1915) England-Turkey
* [Alex Müller](https://en.wikipedia.org/wiki/K._Alex_Müller "Karl Alexander Müller (1927-0000) Switzerland") (1927-0000) Switzerland
* [Yoichiro Nambu](https://en.wikipedia.org/wiki/Yoichiro_Nambu "Yoichiro Nambu a.k.a. 南部 陽一郎 (1921-2015) Japan-USA") (1921-2015) Japan-USA
* [John Napier](https://en.wikipedia.org/wiki/John_Napier "John Napier of Merchiston a.k.a. Jhone Neper (1550-1617) Scotland") (1550-1617) Scotland
* [Louis Néel](https://en.wikipedia.org/wiki/Louis_Néel "Louis Eugène Félix Néel (1904-2000) France") (1904-2000) France
* [Yuval Ne'eman](https://en.wikipedia.org/wiki/Yuval_Ne'eman "Yuval Ne'eman (1925-2006) Israel") (1925-2006) Israel
* [Walther Nernst](https://en.wikipedia.org/wiki/Walther_Nernst "Walther Hermann Nernst (1864-1941) Poland") (1864-1941) Poland
* [Thomas Newcomen](https://en.wikipedia.org/wiki/Thomas_Newcomen "Thomas Newcomen (1664-1729) England") (1664-1729) England
* [Isaac Newton](https://en.wikipedia.org/wiki/Isaac_Newton "Sir Isaac Newton (1642-1727) England") (1642-1727) England
* [Lars Fredrik Nilson](https://en.wikipedia.org/wiki/Lars_Fredrik_Nilson "Lars Fredrik Nilson (1840-1899) Sweden") (1840-1899) Sweden
* [Jean Antoine Nollet](https://en.wikipedia.org/wiki/Jean-Antoine_Nollet "Jean Antoine Nollet a.k.a. Abbé Nollet (1700-1770) France") (1700-1770) France
* [Yuri Oganessian](https://en.wikipedia.org/wiki/Yuri_Oganessian "Yuri Tsolakovich Oganessian a.k.a. Юрий Цолакович Оганесян (1933-0000) Russia") (1933-0000) Russia
* [Georg Ohm](https://en.wikipedia.org/wiki/Georg_Ohm "Georg Simon Ohm (1787-1854) Germany") (1787-1854) Germany
* [Gerard K. O'Neill](https://en.wikipedia.org/wiki/Gerard_K._O'Neill "Gerard Kitchen O'Neill (1927-1992) USA") (1927-1992) USA
* [Hans Christian Ørsted](https://en.wikipedia.org/wiki/Hans_Christian_Ørsted "Hans Christian Ørsted a.k.a. Oersted (1777-1851) Denmark") (1777-1851) Denmark
* [Nicolaus Otto](https://en.wikipedia.org/wiki/Nikolaus_Otto "Nicolaus August Otto (1831-1891) Germany") (1831-1891) Germany
* [Blaise Pascal](https://en.wikipedia.org/wiki/Blaise_Pascal "Blaise Pascal (1623-1662) France") (1623-1662) France
* [Claire Patterson](https://en.wikipedia.org/wiki/Claire_Patterson "Clair Cameron Patterson (1922-1995) USA") (1922-1995) USA
* [Wolfgang Pauli](https://en.wikipedia.org/wiki/Wolfgang_Pauli "Wolfgang Ernst Pauli (1900-1958) Austria-Switzerland") (1900-1958) Austria-Switzerland
* [Roger Penrose](https://en.wikipedia.org/wiki/Roger_Penrose "Roger Penrose (1931-0000) England") (1931-0000) England
* [Peter Peregrinus](https://en.wikipedia.org/wiki/Petrus_Peregrinus_de_Maricourt "Peter Peregrinus of Maricourt a.k.a. Petrus Peregrinus a.k.a. Pierre le Pèlerin (13th century) France") (13th century) France
* [Aléxis Thérèse Petit](https://en.wikipedia.org/wiki/Alexis_Thérèse_Petit "Aléxis Thérèse Petit (1791-1820) France") (1791-1820) France
* [Giuseppe Piazzi](https://en.wikipedia.org/wiki/Giuseppe_Piazzi "Giuseppe Piazzi (1746-1826) Italy") (1746-1826) Italy
* [Max Planck](https://en.wikipedia.org/wiki/Max_Planck "Max Karl Ernst Ludwig Planck (1858-1947) Germany") (1858-1947) Germany
* [Henri Poincaré](https://en.wikipedia.org/wiki/Henri_Poincaré "Jules Henri Poincaré (1854-1912) France") (1854-1912) France
* [Jean Poiseuille](https://en.wikipedia.org/wiki/Jean_Léonard_Marie_Poiseuille "Jean-Léonard-Marie Poiseuille (1799-1869) France") (1799-1869) France
* [Siméon Poisson](https://en.wikipedia.org/wiki/Siméon_Denis_Poisson "Siméon Denis Poisson (1781-1840) France") (1781-1840) France
* [Robert Pound](https://en.wikipedia.org/wiki/Robert_Pound "Robert Vivian Pound (1919-2010) Canada-USA") (1919-2010) Canada-USA
* [John Poynting](https://en.wikipedia.org/wiki/John_Henry_Poynting "John Henry Poynting (1852-1914) England") (1852-1914) England
* [Claudius Ptolemy](https://en.wikipedia.org/wiki/Ptolemy "Claudius Ptolemy a.k.a. Κλαύδιος Πτολεμαῖος (85-165) Egypt") (85-165) Egypt
* [Pythagoras of Samos](https://en.wikipedia.org/wiki/Pythagoras "Pythagoras of Samos a.k.a. Πυθαγόρας ο Σάμιος (570 BCE-496 BCE) Greece-Italy") (570 BCE-496 BCE) Greece-Italy
* [C.V. Raman](https://en.wikipedia.org/wiki/C._V._Raman "Sir Chandrasekhara Venkata Raman a.k.a. चंद्रशेखर वेंकट रामन (1888-1970) India") (1888-1970) India
* [William Rankine](https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine "William John Macquorn Rankine (1820-1872) Scotland") (1820-1872) Scotland
* [John Strutt, Lord Rayleigh](https://en.wikipedia.org/wiki/John_William_Strutt,_3rd_Baron_Rayleigh "John William Strutt, 3rd Baron Rayleigh a.k.a. Lord Rayleigh (1842-1919) England") (1842-1919) England
* [René Réaumur](https://en.wikipedia.org/wiki/René_Antoine_Ferchault_de_Réaumur "René-Antoine Ferchault de Réaumur (1683-1757) France") (1683-1757) France
* [Glen Rebka](https://en.wikipedia.org/wiki/Glen_Rebka "Glen Anderson Rebka Jr. (1931-2015) USA") (1931-2015) USA
* [Andrew Reid](https://physics.info/parts/link.txt "Andrew Reid (????-1928) England") (????-1928) England
* [Frederick Reines](https://en.wikipedia.org/wiki/Frederick_Reines "Frederick Reines (1918-1998) USA") (1918-1998) USA
* [Osborne Reynolds](https://en.wikipedia.org/wiki/Osborne_Reynolds "Osborne Reynolds (1842-1912) Ireland-England") (1842-1912) Ireland-England
* [Jean Richer](https://en.wikipedia.org/wiki/Jean_Richer "Jean Richer (1630-1696) France") (1630-1696) France
* [William Chandler Roberts-Austen](https://en.wikipedia.org/wiki/William_Chandler_Roberts-Austen "Sir William Chandler Roberts-Austen (1843-1902) England") (1843-1902) England
* [Édouard Roche](https://en.wikipedia.org/wiki/Édouard_Roche "Édouard Albert Roche (1820-1883) France") (1820-1883) France
* [Ole Rømer](https://en.wikipedia.org/wiki/Ole_Rømer "Ole Christensen Rømer a.k.a. Roemer (1644-1710) Denmark") (1644-1710) Denmark
* [Wilhelm Röntgen](https://en.wikipedia.org/wiki/Wilhelm_Röntgen "Wilhelm Conrad Röntgen a.k.a. Roentgen (1845-1923) Germany") (1845-1923) Germany
* [Benjamin Thompson, Count Rumford](https://en.wikipedia.org/wiki/Benjamin_Thompson "Sir Benjamin Thompson, Reichsgraf von Rumford a.k.a. Count Rumford (1753-1814) USA-England-Germany-France") (1753-1814) USA-England-Germany-France
* [Bertrand Russell](https://en.wikipedia.org/wiki/Bertrand_Russell "Bertrand Arthur William Russell, 3rd Earl Russell (1872-1970) England") (1872-1970) England
* [Ernest Rutherford](https://en.wikipedia.org/wiki/Ernest_Rutherford "Ernest Rutherford a.k.a. 1st Baron Rutherford of Nelson (1871-1937) New Zealand-Canada-England") (1871-1937) New Zealand-Canada-England
* [Carl Sagan](https://en.wikipedia.org/wiki/Carl_Sagan "Carl Edward Sagan (1934-1996) USA") (1934-1996) USA
* [Giovanni Francesco Sagredo](https://en.wikipedia.org/wiki/Giovanni_Francesco_Sagredo "Giovanni Francesco Sagredo (1571-1620) Italy") (1571-1620) Italy
* [Andrei Sakharov](https://en.wikipedia.org/wiki/Andrei_Sakharov "Andrei Dmitrievich Sakharov a.k.a. Андрей Дмитриевич Сахаров (1921-1989) Russia") (1921-1989) Russia
* [Abdus Salam](https://en.wikipedia.org/wiki/Abdus_Salam "Mohammad Abdus Salam (1926-1996) Pakistan-England") (1926-1996) Pakistan-England
* [Filippo Salviati](https://en.wikipedia.org/wiki/Filippo_Salviati "Filippo Vincenzo Romolo Salviati (1583-1614) Italy") (1582-1614) Italy
* [Sanctorius Sanctorius](https://en.wikipedia.org/wiki/Sanctorius "Sanctorius Sanctorius a.k.a. Santorio Santorio a.k.a. Santorio Santorii (1561-1636) Slovenia-Italy") (1561-1636) Slovenia-Italy
* [Félix Savart](https://en.wikipedia.org/wiki/Félix_Savart "Félix Savart (1791-1841) France") (1791-1841) France
* [Erwin Schrödinger](https://en.wikipedia.org/wiki/Erwin_Schrödinger "Erwin Rudolf Josef Alexander Schrödinger a.k.a. Schroedinger (1887-1961) Austria") (1887-1961) Austria
* [Winfried Schumann](https://en.wikipedia.org/wiki/Winfried_Otto_Schumann "Winfried Otto Schumann (1888-1974) Germany") (1888-1974) Germany
* [Heinrich Schwabe](https://en.wikipedia.org/wiki/Heinrich_Schwabe "Samuel Heinrich Schwabe a.k.a. Herrn Hofrath Schwabe (1789-1875) Germany") (1789-1875) Germany
* [Julian Schwinger](https://en.wikipedia.org/wiki/Julian_Schwinger "Julian Seymour Schwinger (1918-1994) USA") (1918-1994) USA
* [Claude Shannon](https://en.wikipedia.org/wiki/Claude_Shannon "Claude Elwood Shannon (1916-2001) USA") (1916-2001) USA
* [Werner von Siemens](https://en.wikipedia.org/wiki/Werner_von_Siemens "Ernst Werner von Siemens (1816-1892) Germany") (1816-1892) Germany
* [Rolf Sievert](https://en.wikipedia.org/wiki/Rolf_Maximilian_Sievert "Rolf Maximilian Sievert (1896-1966) Sweden") (1896-1966) Sweden
* [Francis Simon](https://en.wikipedia.org/wiki/Francis_Simon "Sir Francis Simon a.k.a. Franz Eugen Simon (1893-1956) Germany-England") (1893-1956) Germany-England
* [Willebrord Snel](https://en.wikipedia.org/wiki/Willebrord_Snellius "Willebrord Snel van Royen a.k.a. Willebrord Snellius (1580-1626) Netherlands") (1580-1626) Netherlands
* [Socrates of Athens](https://en.wikipedia.org/wiki/Socrates "Socrates of Athens a.k.a. Σωκράτης ο Αθήνα (469 BCE-399 BCE) Greece") (469 BCE-399 BCE) Greece
* [Arnold Sommerfeld](https://en.wikipedia.org/wiki/Arnold_Sommerfeld "Arnold Johannes Wilhelm Sommerfeld (1868-1951) Germany") (1868-1951) Germany
* [Joseph Stefan](https://en.wikipedia.org/wiki/Joseph_Stefan "Joseph Stefan a.k.a. Jožef Stefan (1835-1893) Austria") (1835-1893) Austria
* [Otto Stern](https://en.wikipedia.org/wiki/Otto_Stern "Otto Stern (1888-1969) Germany-USA") (1888-1969) Germany-USA
* [Simon Stevin](https://en.wikipedia.org/wiki/Simon_Stevin "Simon Stevin a.k.a. Stevinus (1548-1620) Belgium-Netherlands") (1548-1620) Belgium-Netherlands
* [Robert Stirling](https://en.wikipedia.org/wiki/Robert_Stirling "Robert Stirling (1790-1878) Scotland") (1790-1878) Scotland
* [George Stokes](https://en.wikipedia.org/wiki/George_Gabriel_Stokes "Sir George Gabriel Stokes, 1st Baronet (1819-1903) Ireland-England") (1819-1903) Ireland-England
* [Antonio Stradivari](https://en.wikipedia.org/wiki/Antonio_Stradivari "Antonio Stradivari a.k.a. Antonius Stradivarius (1644-1737) Italy") (1644-1737) Italy
* [Hans Suess](https://en.wikipedia.org/wiki/Hans_Suess "Hans Eduard Suess (1909-1993) Austria-USA") (1909-1993) Austria-USA
* [Harald Sverdrup](https://en.wikipedia.org/wiki/Harald_Sverdrup_(oceanographer) "Harald Ulrik Sverdrup (1888-1957) Norway") (1888-1957) Norway
* [Leo Szilard](https://en.wikipedia.org/wiki/Leo_Szilard "Leo Szilard a.k.a. Szilárd Leó (1898-1964) Hungary-USA") (1898-1964) Hungary-US
* [Gerard't Hooft](https://en.wikipedia.org/wiki/Gerard_'t_Hooft "Gerardus't Hooft a.k.a. Gerard't Hooft (1946-0000) Netherlands") (1946-0000) Netherlands
* [Peter Tait](https://en.wikipedia.org/wiki/Peter_Tait_(physicist) "Peter Guthrie Tait a.k.a. P.G. Tait (1831-1901) Scotland") (1831-1901) Scotland
* [Joseph Taylor](https://en.wikipedia.org/wiki/Joseph_Hooton_Taylor,_Jr. "Joseph Hooton Taylor Jr. (1941-0000) USA") (1941-0000) USA
* [Edward Teller](https://en.wikipedia.org/wiki/Edward_Teller "Edward Teller a.k.a. Teller Ede (1908-2003) Hungary-USA") (1908-2003) Hungary-USA
* [Nikola Tesla](https://en.wikipedia.org/wiki/Nikola_Tesla "Nikola Tesla (1856-1943) Croatia-USA") (1856-1943) Croatia-USA
* [Thales of Miletus](https://en.wikipedia.org/wiki/Thales "Thales of Miletus a.k.a. Θαλής ο μιλήσιος (635 BCE-543 BCE) Turkey") (635 BCE-543 BCE) Turkey
* [George Thomson](https://en.wikipedia.org/wiki/George_Paget_Thomson "George Paget Thomson (1892-1975) England") (1892-1975) England
* [J.J. Thomson](https://en.wikipedia.org/wiki/J._J._Thomson "Sir Joseph John Thomson (1856-1940) England") (1856-1940) England
* [Kip Thorne](https://en.wikipedia.org/wiki/Kip_Thorne "Kip Stephen Thorne (1940-0000) USA") (1940-0000) USA
* [Clyde Tombaugh](https://en.wikipedia.org/wiki/Clyde_Tombaugh "Clyde William Tombaugh (1906-1997) USA") (1906-1997) USA
* [Sin-Itiro Tomonaga](https://en.wikipedia.org/wiki/Sin-Itiro_Tomonaga "Sin-Itiro Tomonaga a.k.a. Shinichirō Tomonaga a.k.a. 朝永 振一郎 (1906-1979) Japan") (1906-1979) Japan
* [Konstantin Tsiolkovsky](https://en.wikipedia.org/wiki/Konstantin_Tsiolkovsky "Konstantin Eduardovich Tsiolkovsky a.k.a. Константи́н Эдуа́рдович Циолко́вский a.k.a. Konstanty Edwardowicz Ciołkowski (1857-1935) Russia") (1857-1935) Russia
* [Tycho Brahe](https://en.wikipedia.org/wiki/Tycho_Brahe "Thyge Ottesen Brahe a.k.a. Tycho (1546-1601) Denmark-Czech Republic") (1546-1601) Denmark-Czech Republic
* [Ulugh Beg](https://en.wikipedia.org/wiki/Ulugh_Beg "Mīrzā Muḥammad Ṭaraghāy ibn Shāhrukh ibn Tīmūr a.k.a. Ulugh Beg (1394-1449) Iran-Uzbekistan") (1394-1449) Iran-Uzbekistan
* [Robert Van de Graaff](https://en.wikipedia.org/wiki/Robert_J._Van_de_Graaff "Robert Jemison Van de Graaff (1901-1967) USA") (1901-1967) USA
* [Jan van Helmont](https://en.wikipedia.org/wiki/Jan_Baptist_van_Helmont "Jan Baptist van Helmont (1577-1644) Netherlands") (1577-1644) Netherlands
* [Pieter van Musschenbroek](https://en.wikipedia.org/wiki/Pieter_van_Musschenbroek "Pieter van Musschenbroeck (1692-1761) Netherlands") (1692-1761) Netherlands
* [Alessandro Volta](https://en.wikipedia.org/wiki/Alessandro_Volta "Conte Alessandro Giuseppe Antonio Anastasio Volta (1745-1827) Italy") (1745-1827) Italy
* [Voltaire](https://en.wikipedia.org/wiki/Voltaire "François-Marie Arouet a.k.a. Voltaire (1694-1778) France") (1694-1778) France
* [Ewald von Kleist](https://en.wikipedia.org/wiki/Ewald_Georg_von_Kleist "Ewald Jürgen Georg von Kleist (1715-1759) Poland") (1715-1759) Poland
* [John von Neumann](https://en.wikipedia.org/wiki/John_von_Neumann "John von Neumann a.k.a. Neumann János Lajosa (1903-1957) Hungary-USA") (1903-1957) Hungary-USA
* [Felix Wankel](https://en.wikipedia.org/wiki/Felix_Wankel "Felix Heinrich Wankel (1902-1988) Germany") (1902-1988) Germany
* [James Watt](https://en.wikipedia.org/wiki/James_Watt "James Watt (1736-1819) Scotland-England") (1736-1819) Scotland-England
* [Wilhelm Weber](https://en.wikipedia.org/wiki/Wilhelm_Eduard_Weber "Wilhelm Eduard Weber (1804-1891) Germany") (1804-1891) Germany
* [Steven Weinberg](https://en.wikipedia.org/wiki/Steven_Weinberg "Steven Weinberg (1933-2021) USA") (1933-2021) USA
* [John Wheeler](https://en.wikipedia.org/wiki/John_Archibald_Wheeler "John Archibald Wheeler (1911-2008) USA") (1911-2008) USA
* [Wilhelm Wien](https://en.wikipedia.org/wiki/Wilhelm_Wien "Wilhelm Carl Werner Otto Fritz Franz Wien a.k.a. Willy Wien (1864-1928) Russia-Germany") (1864-1928) Russia-Germany
* [Frank Wilczek](https://en.wikipedia.org/wiki/Frank_Wilczek "Frank Anthony Wilczek (1951-0000) USA") (1951-0000) USA
* [Clemens Winkler](https://en.wikipedia.org/wiki/Clemens_Winkler "Clemens Alexander Winkler (1838-1904) Germany") (1838-1904) Germany
* [William Hyde Wollaston](https://en.wikipedia.org/wiki/William_Hyde_Wollaston "William Hyde Wollaston (1766-1828) England") (1766-1828) England
* [Thomas Young](https://en.wikipedia.org/wiki/Thomas_Young_(scientist) "Thomas Young (1773-1829) England") (1773-1829) England
* [George Zweig](https://en.wikipedia.org/wiki/George_Zweig "George Zweig a.k.a. Джордж Цвейг (1937-0000) Russia-USA") (1937-0000) Russia-USA |
about | https://physics.info/about/ | # about
### philosophy
> *La dernière chose qu'on trouve en faisant un ouvrage est de savoir celle qu'il faut mettre la première.*
>
>
> The last thing one knows when writing a book is what to put first.
>
>
> [Blaise Pascal, 1662](https://books.google.com/books?id=tO4wAQAAMAAJ&pg=PA120 "Pensées sur la religion et sur quelques autres sujets. Blaise Pascal. Chez Guillaume Desprez (1669).")
The Physics Hypertextbook is a reaction to three problems with textbooks in the US at the turn of the 21st century - lack of writer's voice, layouts that reduce readability, and outdated economics.
Too many textbooks are written by corporations, not authors. This is especially true of the textbooks for secondary schools. They sound like they were written by no one. The Physics Hypertextbook is written by me and should have a recognizable voice to it. Whether or not it's a good voice is, of course, open to debate.
The Physics Hypertextbook is presented as a work in progress. Some parts of this book are essentially finished. Some parts are comically underdone (containing only placeholder text). I work on this project in my spare time. I never add anything to it out of obligation. I only work on it when I feel like it. I hope that results in better writing, but I expect that I will never finish this project.
Too many textbooks are layout disasters with special sections not part of any topic and images with no relation to the main text floating in little boxes off to the side. This crazy quilt style decreases readability. Every page of the Physics Hypertextbook is designed to be read from top to bottom. When an image appears, the text around it is discussing it. You read the text, read the image, and read some more text. Images are a part of the stories being told.
Although every page is meant to be read from top to bottom. The whole of this book will probably never be read from start to finish by anyone - including me. It's not a scroll. The Physics Hypertextbook is like a book in that you can flip to any page at any time. It's a random access repository of information. In this respect, a hypertextbook is no different than a conventional book.
We don't buy physical media much any more. I haven't listened to a CD, cassette tape, or phonograph record in years. I took all the music I collected and converted it to digital data in the early 2000s. If I want to listen to new music, I stream it. If I want to own new music, I download it. I stopped renting DVDs and videocassettes a little later. The only time I ever put a newspaper in my hands is when I visit my parents.
We're living in the future. Every form of media has been affected by the stupendous growth of the internet - except textbooks. They are the last holdout of the old media economy. Why are schools still buying textbooks? Why do professors still make their students buy textbooks? It's time for textbooks to die so they can be reborn. It's time for the textbook companies to die too. They need us more than we need them.
The Physics Hypertextbook exists! Read it if you want to learn more about physics. Read it if you need to learn more about physics to achieve some other end. Read it if you are curious about physics or enjoy science in general. It's an interesting diversion and you just might learn something in the process. Certainly no harm can come from any of these objectives.
### structure
> *Dimidium facti qui coepit habet; sapere aude; incipe!*
>
>
> He who has begun has half done. Dare to be wise; begin!
>
>
> [Horace, ca. 20 BCE](https://books.google.com/books?id=FJooAAAAYAAJ&pg=PA218 "Epistularum Quinti Horatii Flacci. Liber Primus. Epistula II. (ca. 20 BCE).")
The Physics Hypertextbook is organized like many printed physics textbooks. The whole of physics is divided into five major books. Each book is divided into chapters and sections.
1. Mechanics (8 chapters, 60 sections)
2. Thermal physics (4 chapters, 18 sections)
3. Waves and optics (4 chapters, 23 sections)
4. Electricity and magnetism (8 chapters, 31 sections)
5. Modern physics (5 chapters, 25 sections)
Supplementary sections on units and mathematics as well as reference material are gathered into a sixth book.
6. Foundations (5 chapters, 23 sections)
Each section is divided into five pages (except the sections that contain only reference material).
* *Discussion* of the conceptual, historical, and mathematical aspects of the topic.
* *Summary* of the key concepts embedded in in the topic presented in outline form.
* *Practice* problems showing how to apply the concepts described.
* *Problems* to exercise your mind and construct the topic for yourself.
* *Resources* for further information on the topic and its applications.
Special colors are used whenever a word or phrase is explained for the first time on a page. (I'd say "defined", but that's not quite the right word.) Primary concepts are highlighted in bright red, secondary concepts in dark red, and [important persons](https://en.wikipedia.org/wiki/Mr_Creosote "Mr. Creosote a.k.a. Monsieur Creosote (1942-1983) England") in blue. (Blue because they are links to the Wikipedia page for that person.)
### legal
> If there's one thing America needs, it's more lawyers.
>
>
> [Lionel Hutz, 1993](https://frinkiac.com/caption/S04E21/881279 "Lionel Hutz, your new agent, unauthorized biographer, and drug dealer... er keeper awayer.")
The Physics Hypertextbook was not designed to satisfy the requirements of any syllabus nor was it designed to integrate into any specific curriculum. Reading it will not build character nor will it provide moral guidance. The author makes no claims of accuracy, efficacy, or user-friendliness. It is expected that someone will read it and be offended, but it is strongly hoped that someone will read it and be educated, entertained, or enlightened. I am telling you this because I will not guarantee that you will pass your upcoming homework, quiz, test, etc. because you accessed any page on this website. I also do not guarantee that your scores in these items will increase as a result of you interacting with any parts of this website. You are responsible for learning anything you are asked to learn.
The Physics Hypertextbook is the intellectual property of [Glenn Elert](https://glennelert.us "Say my name. You know who I am.") who is solely responsible for its content. No person or organization besides the author played any part in its creation (except where explicitly cited). You can view, copy, and reproduce any part of this work for non-commercial purposes as described in the [fair use](https://www.copyright.gov/title17/92chap1.html#107 "Copyright Law of the United States: Title 17, Chapter 1, Section 107. Limitations on exclusive rights: Fair use.") clause of United States Copyright Law. Reproduction of any part of this work in any form for commercial purposes is strictly forbidden. I am telling you this because I want you to respect my intellectual property. Just because you found something on the internet does not mean you have any rights to use that material for any purposes you think are valid - now or ever.
As an
[Amazon Associate](https://amzn.to/3lWRiR1 "Amazon.com: Online Shopping for Electronics, Apparel, Computers, Books, DVDs & more")
I earn from qualifying purchases.
I also sell designs on
[Spreadshirt](https://hypertextbook.spreadshirt.com "Shop The Physics Hypertextbook")
and
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Motion | https://physics.info/motion/ | # Motion
### the spectrum of mechanics
The general study of the relationships between motion, forces, and energy is called mechanics. It is a large field and its study is essential to the understanding of physics, which is why these chapters appear first. Mechanics can be divided into sub-disciplines by combining and recombining its different aspects. Some of these are given special names.
Motion is the action of changing location or position. The study of motion without regard to the forces or energies that may be involved is called kinematics. It is the simplest branch of mechanics. The branch of mechanics that deals with both motion and forces together is called dynamics and the study of forces in the absence of changes in motion or energy is called statics.
The term energy refers an abstract physical quantity that is not easily perceived by humans. It can exist in many forms simultaneously and only acquires meaning through calculation. Informally, a system possesses energy if it has the ability to do work. The energy of motion is called kinetic energy.
Whenever a system is affected by an outside agent, its total energy changes. In general, a force is anything that causes a change (like a change in energy or motion or shape). When a force causes a change in the energy of a system, physicists say that work has been done. The mathematical statement that relates forces to changes in energy is called the work-energy theorem.
When the total of all the different forms of energy is determined, we find that it remains constant in systems that are isolated from their surroundings. This statement is known as the law of conservation of energy and is one of the really big concepts in all of physics, not just mechanics. The study of how energy changes forms and location during physical processes is called energetics, but the word is used more by scientists in fields outside of physics than inside.
[Magnify](../motion/mechanics-spectrum.svg)
The first few chapters of this book are basically about these topics in this order...
1. motion (kinematics)
2. forces (dynamics and statics)
3. energy
### types of motion
Motion may be divided into three basic types - translational, rotational, and oscillatory. The sections on mechanics in this book are basically arranged in that order. The fourth type of motion - random - is dealt with in [another book](https://hypertextbook.com/chaos/ "The Chaos Hypertextbook") I wrote.
Translational motion
Motion that results in a change of location is said to be translational. This category may seem ridiculous at first as motion implies a change in location, but an object can be moving and yet not go anywhere. I get up in the morning and go to work (an obvious change in location), but by evening I'm back at home - back in the very same bed where I started the day. Is this translational motion? Well, it depends. If the problem at hand is to determine how far I travel in a day, then there are two possible answers: either I've gone to work and back (22 km each way for a total of 44 km) or I've gone nowhere (22 km each way for a total of 0 km). The first answer invokes translational motion while the second invokes oscillatory motion.
Oscillatory motion
Motion that is repetitive and fluctuates between two locations is said to be oscillatory. In the previous example of going from home to work to home to work I am moving, but in the end I haven't gone anywhere. This second type of motion is seen in pendulums (like those found in grandfather clocks or [The Great Clock of Westminster](https://www.parliament.uk/bigben/ "Big Ben, UK Parliament")), vibrating strings (a guitar string moves but goes nowhere), and drawers (open, close, open, close - all that motion and nothing to show for it). Oscillatory motion is interesting in that it often takes a fixed amount of time for an oscillation to occur. This kind of motion is said to be periodic and the time for one complete oscillation (or one cycle) is called a period. Periodic motion is important in the study of sound, light, and other waves. Large chunks of physics are devoted to this kind repetitive motion. Doing the same thing over and over and going nowhere is pretty important. Which brings us to our next type of motion.
Rotational motion
Motion that occurs when an object spins is said to be rotational. The Earth is in a constant state of motion, but where does that motion take it? Every twenty-four hours it makes one complete rotation about its axis. (Actually, it's a bit less than that, but let's not get bogged down in details.) The sun does the same thing, but in about twenty-four days. So do all the planets, asteroids, and comets; each with its own period. (Note that rotational motion too is often periodic.) On a more mundane level, boccie balls, phonograph records, and wheels also rotate. That should be enough examples to keep us busy for a while.
Random motion
Random motion occurs for one of two reasons.
Chaos theory
Some motion is predictable in theory but unpredictable in practice, which makes it appear random. For example, a single molecule in a gas will move freely until it strikes another molecule or one of the walls containing it. The direction the molecule travels after a collision like this is completely predictable according to current theories of classical mechanics.
Every measurement has uncertainty associated with it. Every calculation made using the results of a measurement will carry that uncertainty along. Now imagine that you are trying to predict the motion of a billion gas atoms in a container. (That's a small amount, by the way.) After measuring the position and velocity of each one as accurately as possible, you enter the data into a monstrous computer and let it do the calculations for you. Since the measurements associated with each molecule are a little off, the first round of computation will be a little wrong. Those wrong numbers will then be used in the next round of calculation and the results will be a little more wrong. After a billion calculations, the compounded error would render the results useless. The molecule could be anywhere within the container. This type of randomness is called chaos.
Quantum theory
Some motion is unpredictable in theory and is truly random. For example, the motion of the electron in an atom is fundamentally unpredictable because of a weird conspiracy of nature described by quantum mechanics. The harder you try to locate the electron, the less you know about its velocity. The harder you try to measure its velocity, the less you know about its location. This is a fundamental quality of small objects like electrons and there is no way around it. Although the electron is often said to "orbit" the nucleus of an atom, strictly speaking, this isn't true. The probability of finding the electron at any particular point in space is predictable, but how it got from the first place you observed it to the second is actually a meaningless question. There is no name for this kind of motion because the concept of motion doesn't even apply.
### the physics
Physics
Physics is the study of the fundamental nature of all things.
Prior to the Renaissance, the most significant works in mechanics were those written in the 4th century BCE by the Greek philosopher [Aristotle of Stagira](https://en.wikipedia.org/wiki/Aristotle "Aristotle of Stagira a.k.a. Αριστοτέλης ο Στάγειρα (384 BCE-322 BCE) Greece") (384-322 BCE) - these were *Mechanics*, *On the Heavens*, and *The Nature* or in Greek Μηχανικά (*Mekhanika*), Περί ουρανού (*peri uranu*), and Φυσικῆς ἀκροάσεως (*Fysikes akroasis*). Although the first section of every general physics textbook is about mechanics, Aristotle's *Mechanics* probably wasn't written by him and won't be discussed here. *On the heavens* will be discussed [later](../geocentrism/ "Geocentrism") in this book.
*The Nature* is Aristotle's work that's most relevant to this book. That's because it's the origin of the word physics. The full name Φυσικής ακρόασις (*Fysikes akroasis*) translates literally to "Lesson on Nature" but "The Lesson on the Nature of Things" is probably more faithful. *The Nature* acquired great stature in the Western world and was identified almost reverently by academics as Τὰ Φυσικά (*Ta Fysika*) - *The Physics*. In this book Aristotle introduced the concepts of space, time, and motion as elements in a larger philosophy of the natural world. Consequently, a person who studied the nature of things was called a "natural philosopher" or "physicist" and the subject they studied was called "natural philosophy" or "physics". Incidentally, this is also the origin of the words "physician" (one who studies the nature of the human body) and "physique" (the nature or state of the human body).
[Magnify](../motion/the-physics.svg)
### moving words
#### mechanics, dynamics, statics, kinematics
The words mechanics, dynamics, statics, and kinematics are used throughout this book and heavily in the first third. Each refers to a discipline or branch of physics, thus the common suffix -ics. Each word can also be changed from a noun to an adjective. This gives us words like dynamic, static, kinematic, mechanical, dynamical, and physical. We can also make adverbs like dynamically and physically. Here are the relevant nouns, each followed by brief definition and a semi-long-winded story about its origin. For many readers, the brief definitions will be good enough.
Mechanics
The branch of physics dealing with motion and forces.
The word's origin can be traced back to the ancient Greek words for machine, μηχανή (*mekhane*), a clever device for doing work; and mechanic, μηχανικός (*mekhanikos*), a person skilled with machines. The word mechanics did not acquire its current meaning until sometime in the 17th century - probably by the Irish chemist [Robert Boyle](https://en.wikipedia.org/wiki/Robert_Boyle "Robert Boyle (1627-1691) Ireland-England") (1627-1691).
Mechanics can be divided into the subdisciplines of kinematics, statics, and dynamics. Historically statics came first (antiquity), then kinematics (1638 for the subject, 1834 for the word), then mechanics (1663 as a word), and finally dynamics (1690s as a word). Conceptually mechanics contains dynamics, which overlaps with statics and kinematics.
Dynamics
The study of motion and forces together. (That sounds a little too informal.) The study of the effect that forces have on the motion of objects. (That's better.)
The word dynamics was invented in the late 17th century just to be a word that meant the opposite of the word statics. Credit goes to the German mathematician and philosopher [Gottfried Leibniz](https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz "Gottfried Wilhelm von Leibniz (1646-1716) Germany") (1646-1716). Leibniz is mostly known as the co-creator of calculus with the English scientist and mathematician [Isaac Newton](https://en.wikipedia.org/wiki/Isaac_Newton "Sir Isaac Newton (1642-1727) England") (1642-1727). Leibniz and Newton may have argued about priority, but more of Leibniz lives on in calculus than does Newton. The lowercase d (*d*) for derivative and the crazy long s (∫) for integral were Leibniz's ideas. He also coined the term coordinate axes and named the axes abscissa and ordinate. Leibniz adapted the word dynamics from the Greek word for force, strength, or power - δύναμης (*dynamis*) - which in turn comes from the Greek word meaning "I can" or "I am able" - δύναμαι (*dynamai*). The word did not immediately jump into the English language because Leibniz thought in German, wrote in French and Latin, and wrote for a Continental European audience.
Statics
The study of forces without regard to motion. Technically, statics is the study of forces in the absence of acceleration. One way to not be accelerating is to not move. In that special case, both velocity and acceleration are zero. Since there is no way to distinguish between motion at a constant velocity (v ≠ 0, a = 0) and being in a state of rest (v = 0, a = 0), statics covers both situations.
The origin of the word goes back to ancient Greek phrase τέχνη στατική (*tekhne statike*), which now literally means "static art" but at the time meant something more like "the art of weighing". Basically, the phrase describes the skills that a structural engineer would need. A knowledge of the way the weight of a building or bridge or tower is distributed so that it stays standing in place. Although originally all about weight, statics as a branch of mechanics now covers all forces and statics as a part of structural engineering includes subjects like wind loads on tall buildings and buoyant forces from groundwater on basements. Statics and structural engineering are about more than just weight.
Kinematics
The study of motion without regard to the forces affecting it.
The concepts of distance, displacement, and time are ancient if not primitive. The concepts of speed, velocity, and acceleration seem like they should be as well, but any formal definitions prior to the 16th century do not seem to exist. Pretty much all credit for this goes to the Italian scientist [Galileo Galilei](https://en.wikipedia.org/wiki/Galileo_Galilei "Galileo Galilei (1564-1642) Italy") (1564-1642) and his groundbreaking work on the subject, known in English by the short name of [Two New Sciences](https://ebooks.adelaide.edu.au/g/galileo/dialogues/complete.html "Dialogues Concerning Two New Sciences. Galileo Galilei. Translated from the Italian and Latin into English by Henry Crew and Alfonso de Salvio. New York: Macmillan (1914)."). Galileo wrote in dialog form (and brilliantly so) with no equations. This was partly because mathematical notation didn't exist like we know it now, but mostly because he wanted to make his book approachable. Just three learned gents passing the time talking about the latest advances in science.
Galileo would not have used the word kinematics, however (or even physics). Credit for inventing that word goes to the French scientist and mathematician [André-Marie Ampère](https://en.wikipedia.org/wiki/André-Marie_Ampère "André-Marie Ampère (1775-1836) France") (1775-1836). Ampère is best known for his fundamental work in electrodynamics (a word he also invented) and for having the unit of electric current named in his honor. Ampère is almost not at all famous for what I am doing right now - organizing and assigning names to disciplines and subdisciplines in physics. Ampère took this to extremes, however, and attempted the [classification of all human knowledge](https://books.google.com/books?id=1Lx33IzzakAC&pg=PA48 "Essai sur la philosophie des sciences, ou Exposition analytique d'une classification naturelle de toutes les connaissances humaines, partie 1er. [Essay on the philosophy of science, or a natural exposure analytical classification of all human knowledge, Part 1.] André-Marie Ampère. Paris: Chez Bachelier (1834).") (subdisciplines of subdisciplines of subdisciplines of...). Prior to Ampère's work, there was no name for this branch of mechanics. It might not have even been thought of as a branch in need of a name. Nonetheless, he adapted the Greek word for movement, κίνημα (*kinema*), into the French word *cinématique*, which became the English word kinematics. He did not invent the word cinema, since motion picture technology did not evolve into a business until some 60 years after his death - although his work may have inspired the word.
#### energetics
This organizational scheme is incomplete as far as I'm concerned. It's missing one key concept, possibly the most important concept in all of mechanics, possibly in all of physics, possibly in all of science - energy. Because energy arose as a concept after this scheme was created, a name was never assigned to the branch of *mechanics* dealing with energy. There is a word energetics, but it doesn't seem to be popular in general physics textbooks. The equivalent concept in general physics is called thermodynamics, which started out as the study of work done by thermal processes but expanded into the more general law of conservation of energy.
Energetics
The study of the transformation and distribution of energy during processes within systems.
The word energy in English has been used to represent concepts such as strength, efficacy, persuasiveness, action, resourcefulness, and skill. It didn't acquire its current physical meaning until the 19th century. Its ancient Greek origins are from the prefix εν+ (*en*+, to endow with a certain quality) and the noun εργον (*ergon*, work). Think of words like enable (to make possible), enamor (to inspire love), encode (to translate into code), and endanger (to put in danger). Those four examples were all verbs begining with the suffix en+, but energy is a noun. This makes energy then literally something like "the ability to become work". The English scientist [Thomas Young](https://en.wikipedia.org/wiki/Thomas_Young_(scientist) "Thomas Young (1773-1829) England") (1773-1829) was the first to use the word energy in the modern sense. His definition is almost the same as our current definition of kinetic energy. He was also the first to formally define work as a physical quantity. He also determined that light is a wave.
The ancient Greek philosopher and scientist [Aristotle of Stagira](https://en.wikipedia.org/wiki/Aristotle "Aristotle of Stagira a.k.a. Αριστοτέλης ο Στάγειρα (384 BCE-322 BCE) Greece") (384-322 BCE) might have invented the word that eventually became energy, but his ἐνέργειά (*energeia*) was a term of philosophy, not science. Aristotle's sense of the word is often translated as "activity" or "being at work on". This was contrasted with ἕξις (*exis*), which meant "possession" or "being in the state of". *Energeia* meant doing. *Exis* meant having. To ensure happiness, Aristotle argues, positive virtues should be realized through actions and not just held as beliefs. This has nothing to do with its current scientific meaning, however.
The term energetics is more popular outside of physics than inside. Here are some examples of energetics from other branches of science.
Chemical energetics
The study of energy as it relates to chemical reactions. Terms from this field that some of you may be familiar with include endothermic, exothermic, enthalpy, activation energy, and reaction coordinates.
Biological energetics (bioenergetics)
The study of energy exchanges within the cell. Processes from this field that some of you may be familiar with include photosynthesis, cellular respiration, membrane transport, protein folding, and signal transduction.
Physiological energetics (animal bioenergetics)
The study of the rates of energy expenditure and efficiencies of energy transformations in whole organisms. Some examples of processes dealt with in this field include weight gain, weight loss, growth, healing, and thermoregulation.
Ecological energetics
The study of the transfer of energy from one trophic level to another. The study of how energy moves through the food chain, food web, or food cycle from producers to consumers (first herbivores, then carnivores) then on to decomposers and back again.
#### kinetics
Here's an oddball word that I don't know how to handle.
Kinetics
In mechanics, it's an obsolete and redundant word that means the same thing as dynamics. Kinetics is the branch of mechanics that deals with the effect that forces have on motion. The adjectival form kinetic persists in mechanics in the terms kinetic friction and kinetic energy; and in thermodynamics in the terms kinetic theory of heat, kinetic theory of gases, and kinetic molecular theory.
In chemistry, it's a word that could have been obsoleted, but it wasn't. Kinetics is the branch of chemistry that deals with rates of chemical reactions. For no apparent reason, the word chemical kinetics is favored over chemical dynamics (which is what I think it should be called).
The noun kinetics and the adjective kinetic are neologisms coined sometime in the 19th century, derived from the Greek word κινητικός (*kinetikos*), which is a form of the noun for motion, κίνησις (*kinesis*), with the double suffix -ικ-ός (*-ik-os*) to make it into a subject of study. |
Distance and Displacement | https://physics.info/displacement/ | # Distance and Displacement
### definitions
I've got to assume that everybody reading this has an idea of what distance is. It's one of those innate concepts that doesn't seem to require explanation. Nevertheless I've come up with a preliminary definition that I think is rather good. Distance is a measure of the interval between two locations. (This is not the final definition.) The "distance" is the answer to the question, "How far is it from this to that or between this and that?"
How far is it?
| how far is it | possible answer | standard answer |
| --- | --- | --- |
| [Earth to sun](https://www.google.com/search?q=1+astronomical+unit+in+meters "Google Calculator") | 1 astronomical unit | 1.5 × 1011 m |
| [66th to 86th Street in NYC](https://maps.google.com/maps?f=d&source=s_d&saddr=W+66th+Street+and+Amsterdam+Avenue,+New+York+NY&daddr=40.78119,-73.97975+to: W+86th+Street+and+Amsterdam+Avenue,+New+York+NY&geocode=FaMsbgIdWhaX-ymhQL3gX1jCiTHRmqon345oRA%3BFYZFbgIdmiiX-ymdQxcKiVjCiTHLAMvZNiDWxA%3BFedebgIdGDuX-ylTThVvhFjCiTGwXuqqFveSYA&mra=dvme&mrcr=0&mrsp=1&sz=15&via=1&sll=40.779827,-73.977642&sspn=0.027882,0.037251&t=h&t=k&z=15 "Google Maps") | 1 mile | 1.6 × 103 m |
| [heel to toe on a man's foot](https://www.google.com/search?q=1+foot+in+meters "Google Calculator") | 1 foot | 3.0 × 10−1 m |
You get the idea. The odd thing is that sometimes we state distances as times.
How far is it?
| how far is it | possible answer | standard answer |
| --- | --- | --- |
| [International Space Station](http://spaceflight.nasa.gov/realdata/tracking/index.html "NASA - Human Space Flight - Orbital Tracking") | 90 minutes per orbit | 40,000,000 m |
| [Chicago to Milwaukee](https://www.google.com/maps/dir/Chicago,+Illinois/Milwaukee,+Wisconsin/@42.4552512,-88.3570471,9z/am=t/data=!3m1!4b1!4m15!4m14!1m5!1m1!1s0x880e2c3cd0f4cbed: 0xafe0a6ad09c0c000!2m2!1d-87.6297982!2d41.8781136!1m5!1m1!1s0x880502d7578b47e7: 0x445f1922b5417b84!2m2!1d-87.9064736!2d43.0389025!3e3!5i3 "Google Maps") | 90 minutes by train | 00,150,000 m |
| [Central Park to Battery Park](https://www.google.com/maps/dir/Central+Park,+New+York,+NY/Battery+Park,+New+York,+NY+10004/@40.7431308,-74.0262967,13z/data=!3m1!4b1!4m14!4m13!1m5!1m1!1s0x89c2589a018531e3: 0xb9df1f7387a94119!2m2!1d-73.9653551!2d40.7828647!1m5!1m1!1s0x89c25a12f88ba2ad: 0xbe70465e98439c12!2m2!1d-74.0170279!2d40.7032775!3e2 "Google Maps") | 90 minutes on foot | 00,010,000 m |
They're all ninety minutes, but nobody would say they were all the same distance. What's being described in these examples is not distance, but time. In casual conversation, it's often all right to state distances this way, but in most of physics this is unacceptable.
That being said, let me deconstruct the definition of distance I just gave you. Every year in class, I do the same moronic demonstration where I start at one side of the lecture table and walk to the other side and then ask "How far have I gone?" Look at the diagram below and then answer the question.
[](../displacement/desk.svg)
There are two ways to answer this question. On the one hand, there's the sum of the smaller motions that I made: two meters east, two meters south, two meters west; resulting in a total walk of six meters. On the other hand, the end point of my walk is two meters to the south of my starting point. So which answer is correct? Well, both. The question is ambiguous and depends on whether the questioner meant to ask for the distance or displacement.
Let's clarify by defining each of these words more precisely. Distance is a *scalar* measure of the interval between two locations measured along the *actual path* connecting them. Displacement is a *vector* measure of the interval between two locations measured along the *shortest path* connecting them.
How far does the Earth travel in one year? In terms of distance, quite far (the circumference of the Earth's orbit is nearly one trillion meters), but in terms of displacement, not far at all (in some respects, zero). At the end of a year's time the Earth is right back where it started from. It hasn't gone anywhere.
[](../displacement/map.svg)
A trip to New Jersey
Your humble author occasionally rides his bicycle from Manhattan to New Jersey in search of discount そば (*soba*) and さけ (*sake*) at a large Japanese grocery store on the other side of the Hudson River. Getting there is a three step process.
1. Follow the Hudson River 8.2 km upriver.
2. Cross using the George Washington Bridge (1.8 km between anchorages).
3. Reverse direction and head downriver for 4.5 km.
The distance traveled is a reasonable 14 km, but the resultant displacement is a mere 2.7 km north. The end of this journey is actually visible from the start. Maybe I should buy a canoe.
Distance and displacement are different quantities, but they are related. If you take the first example of the walk around the desk, it should be apparent that sometimes the distance is the same as the magnitude of the displacement. This is the case for any of the one meter segments but is not always the case for groups of segments. As I trace my steps completely around the desk the distance and displacement of my journey soon begin to diverge. The distance traveled increases uniformly, but the displacement fluctuates before it eventually returns to zero.
This artificial example shows that distance and displacement have the same size only when we consider small intervals. Since the displacement is measured along the shortest path between two points, its magnitude is always less than or equal to the distance.
How small is small? The answer to this question is, "It depends". There is no hard and fast rule that can be used to distinguish large from small. DNA is a large molecule, but you still can't see it without the aid of a microscope. Compact cars are small, but you couldn't fit one in your pocket. What is small in one context may be large in another. Mathematics has developed a more formal way of dealing with the notion of smallness and that is through the use of limits. In the language of limits, distance approaches the magnitude of displacement as distance approaches zero. In symbols, that statement looks like this.
| ∆*s* → 0 | ⇒ | ∆*s* → |∆**s**| |
| --- | --- | --- |
### symbols
What would be a good symbol for distance? Hmm, I don't know. How about *d*? Well, that's a fine symbol for us Anglophones, but what about the rest of the planet? (Actually, distance in French is spelled the same as it is in English, but pronounced differently, so there may be a reason to choose *d* after all.) In the current era, English is the dominant language of science, which means that many of our symbols are based on English words used to describe the associated concept. Distance *does not* fall into this category. Still, if you want to use *d* to represent distance, how could I stop you?
All right then, how about *x*? Distance is a simple concept and *x* is a simple variable. Why not pair them up? Many textbooks do this, but this one *will not*. The variable *x* should be reserved for one-dimensional motion along a defined *x*-axis or the *x*-component of a more complex motion. Still, if you want to use *x* to represent distance, how could I stop you?
As I said a moment ago, English is currently the dominant language of science, but this has not always been the case nor is there any reason to believe that it will stay this way forever. Latin was preeminent for a long time, but it is little used today. Still, there are thousands of technical and not so technical words in the English language that have Latin roots. The Latin word for distance is *spatium*. It's also the source of the English word space. In this book, and many others, the letter s will be used for distance and displacement.
Scalar quantities are italicized. Vector quantities bolded. For these reasons, we will use the italicized symbols *s*0 (ess nought) for the initial position on a path, *s* for the position on the path any time after that, and ∆*s* (delta ess) for the space traversed going from the one position to another - the distance. Similarly, we will use the bolded symbols **s**0 (ess nought) for the initial position vector, **s** for the position vector any time after that, and ∆**s** (delta ess) for the change in position - the displacement.
[](../displacement/generic.svg)
Imagine some object traveling along an arbitrary path on top of an infinite two-dimensional grid. Place an observer anywhere in space - on or off the path, it doesn't matter. Make the observer's position the origin of the grid. Draw an arrow from the origin to the moving object at any moment. This is our position vector. It's a vector because it has a magnitude (a size) and a direction. It starts when the object is at **s**0. It ends when its at **s**. Its change, ∆**s**, is the displacement.
Keep imagining our imaginary object traveling along an arbitrary path, but this time ignore the coordinate system. Think about the path the same way you think about traveling on a highway. There is no *x* or *y* coordinate on a highway (and certainly no *z*). No up, down, left, or right. No north, south, east, or west. There is only forward. Coordinates are for sailors or pilots. Distances are for drivers. Locations on highways are indicated with mileposts or milestones. How far down the road have you gone. How much distance have you covered? It starts when the object is at *s*0. It ends when its at *s*. Its change, ∆*s*, is the distance.
If you think Latin deserves its reputation as a "dead tongue" then I can't force you to use these symbols, but I should warn you that their use is quite common. Old habits die hard. The use of *spatium* goes back to the first book on kinematics as we know it - *Dialogues Concerning Two New Sciences* (1638) by [Galileo Galilei](https://en.wikipedia.org/wiki/Galileo_Galilei "Galileo Galilei (1564-1642) Italy").
> | In uno stesso moto equabile, lo *spazio* percorso in un tempo più lungo è maggiore dello *spazio* percorso in un tempo più breve. | | In the case of one and the same uniform motion, the *distance* traversed during a longer interval of time is greater than the *distance* traversed during a shorter interval of time. |
> | --- | --- | --- |
> | | | |
> | [Galileo Galilei, 1638](http://portalegalileo.museogalileo.it/igjr.asp?c=36308 "Discorsi e dimostrazioni matematiche intorno a due nuove scienze. Galileo Galilei (1638)") | | [Galileo Galilei, 1638](https://ebooks.adelaide.edu.au/g/galileo/dialogues/complete.html "Dialogues Concerning Two New Sciences. Galileo Galilei. Translated from the Italian and Latin into English by Henry Crew and Alfonso de Salvio. New York: Macmillan (1914).") |
OK, that was actually Italian. Galileo wrote to the people of the Mediterranean boot in his regional dialect, but the rest of Europe would most likely have read a Latin translation.
> | *Spatium* transactum tempore longiori in eodem motu aequabili maius esse *spatio* transacto tempore breviori. | | In the case of one and the same uniform motion, the *distance* traversed during a longer interval of time is greater than the *distance* traversed during a shorter interval of time. |
> | --- | --- | --- |
> | | | |
> | [Galilaeus Galilaei, 1638](https://books.google.com/books?id=PzRYAAAAYAAJ&pg=PA149 "Le Opere di Galileo Galilei: Prima edizione completa condotta sugli autentici manoscritti Palatini. Firenze: Societa Editrice Fiorentina (1855).") | | [Galileo Galilei, 1638](https://ebooks.adelaide.edu.au/g/galileo/dialogues/complete.html "Dialogues Concerning Two New Sciences. Galileo Galilei. Translated from the Italian and Latin into English by Henry Crew and Alfonso de Salvio. New York: Macmillan (1914).") |
### units
The SI unit of distance and displacement is the meter [m]. A meter is a bit longer than the distance between the tip of the nose to the end of the farthest finger on the outstretched hand of a typical adult male. Originally defined as one ten millionth of the distance from the equator to the north pole as measured through Paris (so that the Earth's circumference would be 40 million meters); then the length of a precisely cut metal bar kept in a vault outside of Paris; then a certain number of wavelengths of a particular type of light. The meter is now defined in terms of the speed of light. One meter is the distance light (or any other electromagnetic radiation of any wavelength) travels through a vacuum after 1299,792,458 of a second.
Multiples (like km for road distances) and divisions (like cm for paper sizes) are also commonly used in science.
There are also several natural units that are used in astronomy and space science.
* A nautical mile is now 1,852 m (6080 feet), but was originally defined as one minute of arc of a great circle, or 160 of 1360 of the Earth's circumference. Every sixty nautical miles is then about one degree of latitude anywhere on Earth or one degree of longitude on the equator. This was considered a reasonable unit for use in navigation, which is why this mile is called the nautical mile. The ordinary mile is more precisely known as the statute mile; that is, the mile as defined by statute or law. Use of the nautical mile persists today in shipping, aviation, and at NASA (for some unknown reason).
* Distances in near outer space are sometimes compared to the radius of the Earth: 6.4 × 106 m. Some examples: the planet Mars has about ½ the radius of the Earth, the size of a geosynchronous orbit is about 6½ Earth radii, and the Earth-moon separation is about 60 Earth radii.
* The mean distance from the Earth to the Sun is called an astronomical unit: approximately 1.5 × 1011 m. The distance from the Sun to Mars is 1.5 au; from the Sun to Jupiter, 5.2 au; and from the Sun to Pluto, 40 au. The star nearest the Sun, Proxima Centauri, is about 270,000 au away.
* For really large distances, the light year is the unit of choice. A light year is the distance light would travel in a vacuum after one year. It is equal to 9.5 × 1015 m (about ten trillion kilometers or six trillion miles). This unit is described in more detail in the [next section](https://physics.info/velocity/).
### symmetry
Let's change how we observe the world and see how it affects distance and displacement. A symmetric operation is a change that results in no change. Quantities that are not affected by a change are said to show a symmetry. The opposite of symmetry is asymmetry and the opposite of symmetric is asymmetric.
First, the location of the observer does not matter. Place the origin wherever it's convenient (or wherever it's inconvenient). It won't matter. Distance and displacement are not affected by a translation of the origin. There is no special place when it comes to measuring distance and displacement. All locations in the universe are equivalent for centering your coordinate system. Space is homogeneous.
Second, the orientation of the axes is irrelevant. Point them in any direction you want (or don't want). Just keep the *x*-axis perpendicular to the *y*-axis. (This you must not change.) Distance and displacement are not affected by a rotation of the axes. There is no special direction when it comes to orienting your coordinate system. All directions are equivalent. Space is isotropic.
Third, and most difficult to state in words, the chirality or handedness of the coordinate system is also irrelevant. Frequently, the *x*-axis points to the right and the *y*-axis points up (that is, toward the top of a page, blackboard, whiteboard, computer display, etc.). If we add a third *z*-axis, in what direction should it point: in or out (that is, into or out of the page, blackboard, etc.)? If you chose out, then you've made a right-handed coordinate system. If you chose in, then it's a left-handed coordinate system.
The two possible coordinate systems are like hands because they are mirror images of one another. No amount of rotation will ever allow you to line up all the parts of your left hand onto all the parts of your right hand. Align the fingers and thumbs of both hands and your palms will face in opposite directions. Align your palms and fingers and your thumbs will point in opposite directions. The Greek word for hand is χερι (*kheri*), so this property of hands and coordinate systems (and [organic molecules](https://physics.info/polarization/) and [magnetic interactions](https://physics.info/electromagnetism/)) is called chirality. It is equivalent to a reflection in a mirror. A right-handed coordinate system is right-handed when viewed directly but left-handed when viewed in a mirror - when viewed through the looking glass, to use a literary reference.
Distance and displacement are not affected by a reflection of the coordinate system. This is not true for all physical quantities, however. The ones that don't work the same when viewed in a mirror are called pseudovectors. Some examples of pseudovectors are [torque](https://physics.info/rotational-dynamics/), [angular momentum](https://physics.info/rotational-momentum/) or spin, and [magnetic field](https://physics.info/electromagnetism/). The direction of a pseudovector is always related to a hand rule of some sort (like the one used in [vector multiplication](https://physics.info/vector-multiplication/)). But as we have just discussed and as everyone knows, right hands become left hands and left hands become right hands when viewed in a mirror. Wrong hand means wrong direction. Space appears to know the difference between left and right for some quantities. |
Speed and Velocity | https://physics.info/velocity/ | # Speed and Velocity
### speed
What's the difference between two identical objects traveling at different speeds? Nearly everyone knows that the one moving faster (the one with the greater speed) will go farther than the one moving slower in the same amount of time. Either that or they'll tell you that the one moving faster will get where it's going sooner than the slower one. Whatever speed is, it involves both distance and time. "Faster" means either "farther" (greater distance) or "sooner" (less time).
Doubling one's speed would mean doubling one's distance traveled in a given amount of time. Doubling one's speed would also mean halving the time required to travel a given distance. If you know a little about mathematics, these statements are meaningful and useful. (The symbol *v* is used for speed because of the association between speed and velocity, which will be discussed shortly.)
* Speed is directly proportional to distance when time is constant: *v* ∝ *s* (*t* constant)
* Speed is inversely proportional to time when distance is constant: *v* ∝ 1*t* (*s* constant)
Combining these two rules together gives the definition of speed in symbolic form.
| *v* = | *s* |
| --- | --- |
| *t* |
| ☞ This is not the final definition. |
| --- |
Don't like symbols? Well then, here's another way to define speed. Speed is the rate of change of *distance* with time.
In order to calculate the speed of an object we must know how far it's gone and how long it took to get there. "Farther" and "sooner" correspond to "faster". Let's say you drove a car from New York to Boston. The distance by road is roughly 300 km (200 miles). If the trip takes four hours, what was your speed? Applying the formula above gives...
| *v* = | *s* | ≈ | 300 km | = 75 km/h |
| --- | --- | --- | --- | --- |
| *t* | 4 hour |
This is the answer the equation gives us, but how right is it? Was 75 kph *the* speed of the car? Yes, of course it was... Well, maybe, I guess... No, it couldn't have been *the* speed. Unless you live in a world where cars have some kind of exceptional cruise control and traffic flows in some ideal manner, your speed during this hypothetical journey must certainly have varied. Thus, the number calculated above is not *the* speed of the car, it's the average speed for the entire journey. In order to emphasize this point, the equation is sometimes modified as follows...
| *v* = | ∆*s* |
| --- | --- |
| ∆*t* |
The bar over the *v* indicates an average or a mean and the ∆ (delta) symbol indicates a change. Read it as "vee bar is delta ess over delta tee". This is the quantity we calculated for our hypothetical trip.
In contrast, a car's speedometer shows its instantaneous speed, that is, the speed determined over a very small interval of time - an instant. Ideally this interval should be as close to zero as possible, but in reality we are limited by the sensitivity of our measuring devices. Mentally, however, it is possible to imagine calculating average speed over ever smaller time intervals until we have effectively calculated instantaneous speed. This idea is written symbolically as...
| *v* = | | lim | | --- | | ∆*t*→0 | | ∆*s* | = | *ds* |
| --- | --- | --- | --- | --- | --- | --- |
| ∆*t* | *dt* |
or, in the language of calculus speed is the first derivative of *distance* with respect to time.
If you haven't dealt with calculus, don't sweat this definition too much. There are other, simpler ways to find the instantaneous speed of a moving object. On a distance-time graph, speed corresponds to slope and thus the instantaneous speed of an object with non-constant speed can be found from the slope of a line tangent to its curve. We'll deal with that [later](https://physics.info/motion-graphs/ "Graphs of Motion") in this book.
### velocity
In order to calculate the speed of an object we need to know how far it's gone and how long it took to get there. A wise person would then ask...
> What do you mean by *how far*? Do you want the *distance* or the *displacement*?
>
>
> A wise person, once upon a time
Your choice of answer to this question determines what you calculate - speed or velocity.
* Average speed is the rate of change of *distance* with time.
* Average velocity is the rate of change of *displacement* with time.
And for the calculus people out there...
* Instantaneous speed is the first derivative of *distance* with respect to time.
* Instantaneous velocity is the first derivative of *displacement* with respect to time.
Speed and velocity are related in much the same way that distance and displacement are related. Speed is a scalar and velocity is a vector. Speed gets the symbol *v* (italic) and velocity gets the symbol **v** (boldface). Average values get a bar over the symbol.
| averagespeed | | | *v* = | ∆*s* | | --- | --- | | ∆*t* | |
| --- | --- | --- | --- | --- | --- |
| instantaneousspeed | | | *v* = | | lim | | --- | | ∆*t*→0 | | ∆*s* | = | *ds* | | --- | --- | --- | --- | --- | --- | --- | | ∆*t* | *dt* | |
| averagevelocity | | | **v** = | ∆**s** | | --- | --- | | ∆*t* | |
| --- | --- | --- | --- | --- | --- |
| instantaneousvelocity | | | **v** = | | lim | | --- | | ∆*t*→0 | | ∆**s** | = | *d***s** | | --- | --- | --- | --- | --- | --- | --- | | ∆*t* | *dt* | |
Displacement is measured along the shortest path between two points and its magnitude is always less than or equal to the distance. The magnitude of displacement approaches distance as distance approaches zero. That is, distance and displacement are effectively the same (have the same magnitude) when the interval examined is "small". Since speed is based on distance and velocity is based on displacement, these two quantities are effectively the same (have the same magnitude) when the time interval is "small" or, in the language of calculus, the magnitude of an object's average velocity approaches its average speed as the time interval approaches zero.
| ∆*t* → 0 | ⇒ | *v* → |**v**| |
| --- | --- | --- |
The instantaneous speed of an object is then the magnitude of its instantaneous velocity.
*v* = |**v**|
Speed tells you how fast. Velocity tells you how fast and in what direction.
### units
Speed and velocity are both measured using the same units. The SI unit of distance and displacement is the meter. The SI unit of time is the second. The SI unit of speed and velocity is the ratio of two - the meter per second.
| ⎡⎢⎣ | m | = | m | ⎤⎥⎦ |
| --- | --- | --- | --- | --- |
| s | s |
This unit is only rarely used outside scientific and academic circles. Most people on this planet measure speeds in kilometer per hour (km/h or kph). The United States is an exception in that we use the older mile per hour (mi/h or mph). Let's determine the conversion factors so that we can relate speeds measured in m/s with the more familiar units.
| 1 kph = | 1 km | | 1,000 m | | 1 hour | |
| --- | --- | --- | --- | --- | --- | --- |
| 1 hour | 1 km | 3,600 s | |
| 1 kph = | 0.2777... m/s ≈ ¼ m/s | | | | | |
| |
| | | | | | | |
| 1 mph = | 1 mile | | 1,609 m | | 1 hour | |
| 1 hour | 1 mile | 3,600 s | |
| 1 mph = | 0.4469... m/s ≈ ½ m/s | | | | | |
| |
The decimal values shown above are accurate to four significant digits, but the fractional values should only be considered rules of thumb (1 kph is really more like 27 m/s than 14 m/s and 1 mph is more like 49 m/s than 12 m/s).
The ratio of any unit of distance to any unit of time is a unit of speed.
* The speeds of ships, planes, and rockets are often stated in knots. One knot is one nautical mile per hour - a nautical mile being 1,852 m or 6,076 feet and an hour being 3,600 s. NASA still reports the speed of its rockets in knots and their downrange distance in nautical miles. One knot is approximately 0.5144 m/s.
* The slowest speeds are measured over the longest time periods. The continental plates creep across the surface of the Earth at the geologically slow rate of 1-10 cm/year or 1-10 m/century - about the same speed that fingernails and hair grow.
* Audio cassette tape travels at 1⅞ inches per second (ips). When magnetic tape was first invented, it was spooled on to open reels like movie film. These early reel-to-reel tape recorders ran the tape through at 15 ips. Later models could also record at half this speed (7½ ips) and then half of that (3¾ ips) and then some at half of that (1⅞ ips). When the audio cassette standard was being formulated, it was decided that the last of these values would be sufficient for the new medium. One inch per second is exactly 0.0254 m/s by definition.
Sometimes, the speed of an object is described relative to the speed of something else; preferably some physical phenomenon.
* Aerodynamics is the study of moving air and how objects interact with it. In this field, the speed of an object is often measured relative to the speed of sound. This ratio is known as the Mach number. The speed of sound is roughly 295 m/s (660 mph) at the altitude at which commercial jet aircraft normally fly. The now decommissioned British Airways and Air France supersonic Concorde cruised at 600 m/s (1,340 mph). Simple division shows that this speed is roughly twice the speed of sound or Mach 2.0, which is exceptionally fast. A Boeing 777, in comparison, cruises at 248 m/s (555 mph) or Mach 0.8, which only seems slow in comparison to the Concorde.
* The speed of light in a vacuum is defined in the SI system to be 299,792,458 m/s (about a billion km/h). This is usually stated with a more reasonable precision as 3.00 × 108 m/s. The speed of light in a vacuum is assigned the symbol *c* (italic) when used in an equation and c (roman) when used as a unit. The speed of light in a vacuum is a universal limit, so real objects always move slower than *c*. It is used frequently in particle physics and the astronomy of distant objects. The most distant observed objects are quasars; short for "quasi-stellar radio objects". They are visually similar to stars (the prefix quasi means resembling) but emit far more energy than any star possibly could. They lie at the edges of the observable universe and are rushing away from us at incredible speeds. The most distant quasars are moving away from us at nearly 0.9 c. By the way, the symbol *c* was chosen not because the speed of light is a universal constant (which it is) but because it is the first letter of the Latin word for swiftness - *celeritas*.
Selected speeds (slowest to fastest)
| m/s | km/h | device, event, phenomenon, process |
| --- | --- | --- |
| 10−9~10−8 | | continental plates, hair growth, fingernail growth |
| 10−4 | | human sperm cells |
| 10−3 | | snails |
| 0.013 | 0.045 | [ketchup pouring from a bottle](https://www.heinz.com.hk/en/trivia/tomato-ketchup "Heinz Hong Kong " Heinz Trivia " Tomato Ketchup") |
| 10−1 | | sloths, tortoises, turtles |
| 0.65-1.29 | 2.34-4.64 | [cockroaches](https://doi.org/10.1126/science.327.5967.776-a "Racing Crash-Happy Cockroaches. Elizabeth Pennisi. Science. Vol. 327 No. 5967 (2010): 776.") |
| 1 | 3.6 | nerve impulses, unmyelinated cells |
| 1 | 3.6 | ocean currents |
| 0.06-1.14 | 0.22-4.10 | [manatees](https://doi.org/10.1242/jeb.02790 "Swimming kinematics of the Florida manatee (Trichechus manatus latirostris): hydrodynamic analysis of an undulatory mammalian swimmer. Tricia Kojeszewski and Frank E. Fish. Journal of Experimental Biology. Vol. 210 (2007): 2411-2418.") |
| 1.3 | 4.8 | human, typical walking pace |
| 2.391 | 8.608 | fastest human: swimming ([César Cielo](https://www.fina.org/swimming/records?recordCode=WR&eventTypeId=®ion=&countryId=&gender=M&pool=LCM "Fédération Internationale de Natation (FINA)")) |
| 8 | 30 | [maximum comfortable elevator speed](https://www.pbs.org/wgbh/nova/tech/trapped-elevator.html "Trapped in an Elevator. NOVA. PBS. (Tuesday, November 2, 2010).") |
| 10 | 40 | dolphins, porpoises, whales |
| 10 | 40 | falling raindrops |
| 10.422 | 37.520 | fastest human: running ([Usain Bolt](https://www.worldathletics.org/records/by-category/world-records "World Athletics")) |
| 12 | 43 | [stadium wave](https://doi.org/doi: 10.1038/419131a "Social behaviour: Mexican waves in an excitable medium. I. Farkas, D. Helbing, T. Vicsek. Nature. Vol. 419 (2002): 131-132.") |
| 12 | 44 | [champagne cork](https://www.wired.com/2015/12/the-physics-behind-popping-champagne-bottles/ "The Physics Behind Popping Champagne Bottles. Rhett Allain. Wired (30 December 2015).") |
| 15.223 | 54.803 | fastest human: ice skating ([Pavel Kulizhnikov](https://www.isu.org/speed-skating/entries-results/biographies-statistics "International Skating Union (ISU)")) |
| 20 | 70 | rabbits, hares, horses, greyhounds, tuna, sharks |
| 30 | 100 | typical freeway speed limit |
| 33 | 118 | cheetahs |
| 34.42 | 123.9 | fastest human: softball pitch ([Monica Abbott](https://www.guinnessworldrecords.com/world-records/fastest-womens-softball-pitch "Guinness World Records")) |
| 40 | 140 | falling hailstones |
| 42.47 | 152.9 | fastest human: flying disc throw ([Simon Lizotte](https://wfdf.sport/world-records/other/ "World Flying Disc Federation (WFDF)")) |
| 46.98 | 169.1 | fastest human: baseball pitch ([Aroldis Chapman](https://www.mlb.com/news/aroldis-chapman-throws-a-pitch-105-1-mph-c190404910 "Major League Baseball")) |
| 55 | 200 | terminal velocity of a typical skydiver |
| 70.8217 | 254.958 | fastest human: skiing ([Ivan Origone](http://www.kl-france.com/modules/edito/content.php?id=5 "France Ski de Vitesse")) |
| 73.06 | 263 | fastest human: tennis serve ([Sam Groth](https://www.atptour.com/en/news/groth-fast-serve "Association of Tennis Professionals")) |
| 80 | 290 | peregrine falcon in a dive |
| 82 | 295 | [very fast golf ball](https://www.usga.org/workarea/linkit.aspx?linkidentifier=id&itemid=10682 "Experimental determination of the effects of clubhead speed on driver launch conditions and the effects on drive distance for balls used by the PGA tour. Steven J. Quintavalla. USGA Technical Report RB/cor2006-01 (19 April 2006).") |
| 82.211 | 296.00 | fastest human: cycling ([Denise Korenek Mueller](http://theprojectspeed.com "The Project Speed")) |
| 33-83 | 120-300 | hurricane, maximum sustained wind speed |
| 30-90 | 105-330 | tornado, maximum sustained wind speed |
| 100 | 360 | nerve impulses, myelinated cells |
| 113.2 | 407.5 | maximum surface wind gust ([Barrow Island, Australia](https://wmo.asu.edu/content/world-maximum-surface-wind-gust "World Meteorological Organization (WMO), Arizona State University (ASU) DEAD LINK")) |
| 118.3 | 426 | fastest human: badminton smash ([Mads Pieler Kolding](https://www.guinnessworldrecords.com/world-records/fastest-badminton-hit-in-competition-(male)/ "Guinness World Records")) |
| 124.22 | 447.19 | fastest street-legal car ([Koenigsegg Agera RS](https://dev.koenigsegg.com/koenigsegg-agera-rs-achieves-multiple-production-car-world-speed-records/ "Koenigsegg Agera RS Achieves Multiple Production Car World Speed Records")) |
| 142.89 | 511.11 | fastest ship ([Spirit of Australia](https://www.uim.sport/Records1.aspx "Union Internationale Motonautique")) |
| 159.7 | 574.8 | fastest train ([Train à Grande Vitesse](http://www.record2007.com/ "record2007.com was a Société Nationale des Chemins de fer Français (SNCF) website active from 13 June 2007 to 25 August 2008 DEAD LINK")) |
| 168.249 | 605.697 | fastest motorcycle ([Top 1 Ack Attack](http://top1ackattack.com/ "ACK ATTACK - World's Fastest Motorcycle DEAD LINK")) |
| 200 | 700 | tsunami |
| 250 | 900 | commercial jet airplane |
| 331 | 1,190 | speed of sound in air, STP |
| 340 | 1,225 | speed of sound in air, sea level |
| 341.4031 | 1,229.051 | fastest experimental car ([Thrust SSC](http://www.thrustssc.com/Runs_Database/Runs_Database.html "ThrustSSC Runs Database")) |
| 343 | 1,235 | speed of sound in air, room temperature |
| 377.1 | 1,357.6 | fastest human: skydiving ([Felix Baumgartner)](https://issuu.com/redbullstratos/docs/red_bull_stratos_summit_report_final_050213 "Findings of the Red Bull Stratos Scientific Summit. California Science Center, Los Angeles, California, USA. January 23, 2013.") |
| 980.433 | 3,529.56 | fastest airplane ([SR-71 Blackbird](https://www.sr-71.org/blackbird/records.php "SR-71 Online - Blackbird Records. This page was last modified on 2 October 2011.")) |
| 180-1,200 | 650-4,400 | bullets |
| 1,500 | 5,400 | speed of sound in water |
| 2,000 | 6,000 | seismic waves |
| 6,900 | 25,000 | detonation velocity of TNT |
| 8,000 | 29,000 | space shuttle in orbit |
| 11,094 | 39,938 | fastest manned spacecraft ([Apollo 10](https://www.hq.nasa.gov/alsj/a410/A10_MissionReport.pdf "Apollo 10 Mission Report page 6-13 TABLE 6-VII.- ENTRY TRAJECTORY PARAMETERS Maximum conditions Velocity, ft/sec 36 397 Acceleration, g 6.78")) |
| 11,180 | 40,250 | [escape velocity on the surface of the Earth](https://www.google.com/search?&q=sqrt((2*gravitational+constant*mass+of+earth)/radius+of+earth) "Google Calculator") |
| 13,790 | 49,600 | [New Horizons](http://pluto.jhuapl.edu/Mission/Where-is-New-Horizons.php "Where is New Horizons?") space probe |
| 15,400 | 55,400 | [Voyager 2](https://voyager.jpl.nasa.gov/mission/status/ "Voyager mission status. Jet Propulsion Laboratory. NASA") space probe |
| 17,000 | 61,200 | [Voyager 1](https://voyager.jpl.nasa.gov/mission/status/ "Voyager mission status. Jet Propulsion Laboratory. NASA") space probe |
| 29,790 | 107,200 | [Earth in orbit](https://www.google.com/search?q=2*pi*astronomical+unit/1+year "Google Calculator") |
| 201,000 | 724,000 | fastest unmanned spacecraft ([Parker Solar Probe](http://parkersolarprobe.jhuapl.edu/The-Mission/ "Parker Solar Probe: The Mission")) |
| 248,000 | 892,000 | [Sun moving through the Milky Way](https://doi.org/10.3847/1538-4357/ab76cd "The Proper Motion of Sagittarius A*. III. The Case for a Supermassive Black Hole. M.J. Reid and A. Brunthaler. Astrophysical Journal. Vol. 892 No 1 (2020): 39.") |
| 300,000 | 1,100,000 | [solar wind near earth](https://www.swpc.noaa.gov/products/ace-real-time-solar-wind "ACE Real-Time Solar Wind, NOAA/NWS Space Weather Prediction Center") |
| 370,000 | 1,330,000 | [Milky Way through the cosmic microwave background](https://doi.org/10.1051/0004-6361/201832909 "Planck 2018 results. III. High Frequency Instrument data processing and frequency maps. Planck Collaboration. Astronomy & Astrophysics. Vol. 641 No. A3 (2020): 50.") |
| 60,000,000 | 216,000,000 | [Project Starshot](https://breakthroughinitiatives.org/news/4 "Breakthrough Starshot is a $100 million research and engineering program aiming to demonstrate proof of concept for light-propelled nanocrafts. These could fly at 20 percent of light speed and capture images of possible planets and other scientific data in our nearest star system, Alpha Centauri, just over 20 years after their launch."), proposed interstellar space probe |
| 124,000,000 | 446,000,000 | speed of light in diamond |
| 225,000,000 | 810,000,000 | speed of light in water |
| 299,792,369 | 1,079,252,530 | protons and antiprotons in the [Tevatron](https://indico.fnal.gov/event/291/contributions/79161/attachments/49746/59674/FinalSISTPaper2006.doc "Installing Instrumentation for Horizontal Test Radio-Frequency Cryostat. Sirius Ben-Judah. Alabama Agricultural and Mechanical University."), Fermilab |
| 299,792,455 | 1,079,252,840 | protons in the [Large Hadron Collider](http://cds.cern.ch/record/1211582 "Longitudinal Schottky spectrum of the peak bunch amplitude signal. E. Shaposhnikova, T. Bohl and T. Linnecar. Proceedings of 23rd Particle Accelerator Conference (PAC09), Vancouver, BC, Canada (2009): TH5RFP038."), CERN |
| 299,792,458 | 1,079,252,850 | [speed of light in a vacuum](https://www.bipm.org/en/measurement-units/ "Bureau international des poids et mesures (BIPM). Measurement units.") | |
Acceleration | https://physics.info/acceleration/ | # Acceleration
### definition
When the velocity of an object changes it is said to be accelerating. Acceleration is the rate of change of velocity with time.
In everyday English, the word acceleration is often used to describe a state of increasing speed. For many Americans, their only experience with acceleration comes from car ads. When a commercial shouts "zero to sixty in six point seven seconds" what they're saying here is that this particular car takes 6.7 s to reach a speed of 60 mph starting from a complete stop. This example illustrates acceleration as it is commonly understood, but acceleration in physics is much more than just increasing speed.
Any change in the velocity of an object results in an acceleration: increasing speed (what people usually mean when they say acceleration), decreasing speed (also called deceleration or retardation), or changing direction (called centripetal acceleration). Yes, that's right, a change in the direction of motion results in an acceleration even if the moving object neither sped up nor slowed down. That's because acceleration depends on the change in velocity and velocity is a vector quantity - one with both magnitude and direction. Thus, a falling apple accelerates, a car stopping at a traffic light accelerates, and the moon in orbit around the Earth accelerates. Acceleration occurs anytime an object's speed increases or decreases, or it changes direction.
Much like velocity, there are two kinds of acceleration: average and instantaneous. Average acceleration is determined over a "long" time interval. The word long in this context means finite - something with a beginning and an end. The velocity at the beginning of this interval is called the initial velocity, represented by the symbol **v**0 (vee nought), and the velocity at the end is called the final velocity, represented by the symbol **v** (vee). Average acceleration is a quantity calculated from two velocity measurements.
| **a** = | ∆**v** | = | **v** − **v**0 |
| --- | --- | --- | --- |
| ∆*t* | ∆*t* |
In contrast, instantaneous acceleration is measured over a "short" time interval. The word short in this context means infinitely small or infinitesimal - having no duration or extent whatsoever. It's a mathematical ideal that can only be realized as a limit. The limit of a rate as the denominator approaches zero is called a derivative. Instantaneous acceleration is then the limit of average acceleration as the time interval approaches zero - or alternatively, acceleration is the derivative of velocity.
| **a** = | | lim | | --- | | ∆*t*→0 | | ∆**v** | = | *d***v** |
| --- | --- | --- | --- | --- | --- | --- |
| ∆*t* | *dt* |
Acceleration is the derivative of velocity with time, but velocity is itself the derivative of position with time. The derivative is a mathematical operation that can be applied multiple times to a pair of changing quantities. Doing it once gives you a first derivative. Doing it twice (the derivative of a derivative) gives you a second derivative. That makes acceleration the first derivative of velocity with time and the second derivative of position with time.
| **a** = | *d***v** | = | *d* | | *d***s** | = | *d*2**s** |
| --- | --- | --- | --- | --- | --- | --- | --- |
| *dt* | *dt* | *dt* | *dt*2 |
A word about notation. In formal mathematical writing, vectors are written in **boldface**. Scalars and the magnitudes of vectors are written in *italics*. Numbers, measurements, and units are written in roman (not italic, not bold, not oblique - ordinary text). For example...
| *a* = 9.8 m/s2, θ = −90° | or | **a** = 9.8 m/s2 at −90° |
(Design note: I think Greek letters don't look good on the screen when italicized so I have decided to ignore this rule for Greek letters until good looking Greek fonts are the norm on the web.)
### units
#### international units
Calculating acceleration involves dividing velocity by time - or in terms of SI units, dividing the meter per second [m/s] by the second [s]. Dividing distance by time twice is the same as dividing distance by the square of time. Thus the SI unit of acceleration is the meter per second squared.
| ⎡⎢⎣ | m | = | m/s | = | m | | 1 | ⎤⎥⎦ |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| s2 | s | s | s |
#### natural units
Another frequently used unit is the standard acceleration due to gravity - g. Since we are all familiar with the effects of gravity on ourselves and the objects around us it makes for a convenient standard for comparing accelerations. Everything feels normal at 1 g, twice as heavy at 2 g, and weightless at 0 g. This unit has a precisely defined value of [9.80665 m/s2](https://www.bipm.org/fr/committees/cg/cgpm/3-1901/resolution-2 "Le nombre adopté dans le Service international des Poids et Mesures pour la valeur de l'accélération normale de la pesanteur est 980,665 cm/sec², nombre sanctionné déjà par quelques législations. Déclaration relative à l'unité de masse et à la définition du poids; valeur conventionnelle de gn. Résolution 2 de la 3ᵉ CGPM (1901)."), but for everyday use 9.8 m/s2 is sufficient, and 10 m/s2 is convenient for quick estimates.
The unit called the standard acceleration due to gravity (represented by a roman g) is not the same as the natural phenomenon called acceleration due to gravity (represented by an italic *g*). The former has a defined value whereas the latter has to be measured. (More on this [later](../falling/).)
Although the term "g force" is often used, the g is a measure of acceleration, not force. (More on forces [later](../newton-first/).) Of particular concern to humans are the physiological effects of acceleration. To put things in perspective, all values are stated in g.
* In roller coaster design, speed is of the essence. Or, is it? If speed was all there was to designing a thrill ride, then the freeway would be pretty exciting. Most roller coaster rarely exceed 30 m/s (60 mph). Contrary to popular belief, it is the acceleration that makes the ride interesting. A well designed roller coaster will subject the rider to maximum accelerations of 3 to 4 g for brief periods. This is what gives the ride its dangerous feel.
* Despite the immense power of its engines, the acceleration of the Space Shuttle was kept below 3 g. Anything greater would put unnecessary stress on the astronauts, the payload, and the ship itself. Once in orbit, the whole system enters into an extended period of free fall, which provides the sensation of weightlessness. Such a "zero g" environment can also be simulated inside a specially piloted aircraft or a free fall drop tower. (More on this [later](../frames/).)
* Fighter pilots can experience accelerations of up to 8 g for brief periods during tactical maneuvers. If sustained for more than a few seconds, 4 to 6 g is sufficient to induce blackout. To prevent "g-force loss of consciousness" (G-LOC), fighter pilots wear special pressure suits that squeeze the legs and abdomen, forcing blood to remain in the head.
* Pilots and astronauts may also train in human centrifuges capable of up to 15 g. Exposure to such intense accelerations is kept brief for safety reasons. Humans are rarely subjected to anything higher than 8 g for longer than a few seconds.
* Acceleration is related to injury. This is why the most common sensor in a crash test dummy is the accelerometer. Extreme acceleration can lead to death. The acceleration during the crash that killed Diana, Princess of Wales, in 1997 was estimated to have been on the order of 70 to 100 g, which was intense enough to tear the pulmonary artery from her heart - an injury that is nearly impossible to survive. Had she been wearing a seat belt, the acceleration would have been something more like 30 or 35 g - enough to break a rib or two, but not nearly enough to kill most people.
#### Gaussian units
The precise measurement of the strength of gravity over the surface of the Earth or other celestial objects is called gravimetry. For historical reasons the preferred unit in this field is the centimeter per second squared also known as the gal. In symbolic form...
[Gal = cm/s2]
Yes, that's right. The name of the unit is written all in lowercase (gal) while the symbol is capitalized (Gal). The gal was named in honor of the Italian scientist [Galileo Galilei](https://en.wikipedia.org/wiki/Galileo_Galilei "Galileo Galilei (1564-1642) Italy") (1564-1642) who was the first scientist to study the acceleration due to gravity - and maybe was the first scientist of any sort. Since the acceleration due to gravity varies by only small amounts over the surface of most celestial objects, deviations in strength from idealized models (called gravitational anomalies) are measured in thousandths of a gal or milligals (mGal).
[1,000 mGal = 1 Gal]
The gal and milligal are part of a precursor to the International System of Units called the centimeter-gram-second system or [Gaussian system of units](../system-gaussian/). I may one day actually write something significant in that section of this book.
Here are some sample accelerations to end this section.
Acceleration of selected events (smallest to largest)
| *a* (m/s2) | device, event, phenomenon, process |
| --- | --- |
| 0 | stationary or moving at a constant velocity |
| [5 × 10−14](https://doi.org/10.1103/PhysRevLett.98.150801 "Laboratory Test of Newton's Second Law for Small Accelerations. J.H. Gundlach, S. Schlamminger, C.D. Spitzer, K.Y. Choi, B. A. Woodahl, J.J. Coy, and E. Fischbach. Physical Review Letters. Vol. 98 No. 15 (2007): 150801.") | smallest acceleration in a scientific experiment |
| [2.32 × 10−10](https://arxiv.org/abs/2012.02036 "Gaia Early Data Release 3: Acceleration of the solar system from Gaia astrometry. Gaia Collaboration (2020) arXiv: 2012.02036") | galactic acceleration at the Sun |
| [9 × 10−10](https://doi.org/10.1103/PhysRevD.65.082004 "Study of the anomalous acceleration of Pioneer 10 and 11. John D. Anderson, Philip A. Laing, Eunice L. Lau, Anthony S. Liu, Michael Martin Nieto, and Slava G. Turyshev. Physical Review D. Vol. 65 No. 8 (2002): 082004-082003.") | anomalous acceleration of Pioneer spacecraft |
| [0.5](https://hypertextbook.com/facts/2005/elevator.shtml "Acceleration of an Elevator, Hydraulic. Olga Strachna, Diana Kuruvilla, Dorothy Soo. The Physics Factbook (2002)") | elevator, hydraulic |
| [0.63](https://www.google.com/search?q=gravitational+constant*mass+of+pluto/radius+of+pluto^2 "Google Calculator") | free fall acceleration on Pluto |
| [1](https://hypertextbook.com/facts/2009/AmosBaptiste.shtml "Acceleration of an Elevator, Cable. Amos Baptiste. The Physics Factbook (2009).") | elevator, cable |
| [1.6](https://www.google.com/search?q=gravitational+constant*mass+of+moon/(radius+of+moon)^2 "Google Calculator") | free fall acceleration on the moon |
| [8.8](https://www.google.com/search?q=gravitational+constant*mass+of+earth/(radius+of+earth+%2B+350+km)^2 "Google Calculator") | International Space Station in orbit |
| [3.7](https://www.google.com/search?q=gravitational+constant*mass+of+mars/(radius+of+mars)^2 "Google Calculator") | free fall acceleration on Mars |
| 9.8 | free fall acceleration on Earth |
| [10-40](https://hypertextbook.com/facts/2000/JeffreyAnthony.shtml "Acceleration of a Manned Rocket. Jeffrey Anthony. The Physics Factbook (2000).") | manned rocket at launch |
| [20](https://hypertextbook.com/facts/2000/JeffreyAnthony.shtml "Acceleration of a Manned Rocket. Jeffrey Anthony. The Physics Factbook (2000).") | space shuttle, peak |
| [24.8](https://www.google.com/search?q=gravitational+constant*mass+of+jupiter/(radius+of+jupiter)^2 "Google Calculator") | free fall acceleration on Jupiter |
| [29.06](https://www.amzracing.ch/en/world-record "World Record. Academic Motorsports Club Zurich (AMZ) (2023).") | Fastest 0-100 km/h by an electric car, average, 2023 |
| [37.36](https://www.amzracing.ch/en/world-record "World Record. Academic Motorsports Club Zurich (AMZ) (2023).") | Fastest 0-100 km/h by an electric car, peak, 2023 |
| [20-50](https://hypertextbook.com/facts/2006/SaintedymWills.shtml "Acceleration of a Roller Coaster. Saintedym Wills. The Physics Factbook (2006).") | roller coaster |
| 80 | limit of sustained human tolerance |
| [0-150](https://hypertextbook.com/facts/2003/NikkieZanevsky.shtml "Acceleration in a Training Centrifuge. Nikkie Zanevsky. The Physics Factbook (2003).") | human training centrifuge |
| 100-200 | ejection seat |
| [270](https://www.google.com/search?q=gravitational+constant*mass+of+sun/(radius+of+sun)^2 "Google Calculator") | free fall acceleration on the Sun |
| [600](https://hypertextbook.com/facts/2003/MichelleYee.shtml "Acceleration That Would Deploy Car Airbags. Michelle Yee. The Physics Factbook (2003).") | airbags automatically deploy |
| [104-106](https://hypertextbook.com/facts/2008/ElinaSlobod.shtml "Acceleration of a Medical Centrifuge. Elina Slobod. The Physics Factbook (2008).") | medical centrifuge |
| [~106](https://hypertextbook.com/facts/2003/MichaelTse.shtml "Acceleration of a Bullet. Michael Tse. The Physics Factbook (2003).") | bullet in the barrel of a gun |
| [~106](https://www.google.com/search?&q=gravitational+constant*mass+of+sun/(radius+of+earth)^2 "Google Calculator") | free fall acceleration on a white dwarf star |
| [~1012](https://www.google.com/search?q=gravitational+constant*1.4*mass+of+sun/(10+km)^2 "Google Calculator") | free fall acceleration on a neutron star |
Automotive accelerations (g)
| | starting | braking | cornering |
| --- | --- | --- | --- |
| typical car | 0.3-0.5 | 0.8-1.0 | 0.7-0.9 |
| sports car | 0.5-0.9 | 1.0-1.3 | 0.9-1.0 |
| F-1 race car | 1.7 | 2 | 3 |
| large truck | <0.2 | ~0.6 | |
Acceleration and the human body
Primary source:[Acceleration perturbations of daily living, 1994](https://doi.org/10.1097/00007632-199405310-00017 "Acceleration perturbations of daily living. A comparison to 'whiplash'. Allen, Murray E.; Weir-Jones, Iain; Eng, P.; Motiuk, Darren R.; Flewin, Kevan R.; Goring, Ralph D.; Kobetitch, Robert; Broadhurst, Andrew. Spine. Vol. 19 No. 11 (1994): 1285-1290.")
| *a* (g) | event |
| --- | --- |
| 02.9 | sneeze |
| 03.5 | cough |
| 03.6 | crowd jostle |
| 04.1 | slap on back |
| 08.1 | hop off step |
| 10.1 | plop down in chair |
| 60 | chest acceleration during car crash at 48 km/h with airbag |
| [70-100](http://www.cnn.com/WORLD/9709/05/crash.analysis/ "Could a seat belt have saved Diana? CNN (1997).") | crash that killed Diana, Princess of Wales, 1997 |
| 150-200 | head acceleration limit during bicycle crash with helmet | |
Equations of Motion | https://physics.info/motion-equations/ | # Equations of Motion
### constant acceleration
For the sake of accuracy, this section should be entitled "One dimensional equations of motion for constant acceleration". Given that such a title would be a stylistic nightmare, let me begin this section with the following qualification. These equations of motion are valid only when acceleration is constant and motion is constrained to a straight line.
Given that we live in a three dimensional universe in which the only constant is change, you may be tempted to dismiss this section outright. It would be correct to say that no object has ever traveled in a straight line with a constant acceleration anywhere in the universe at any time - not today, not yesterday, not tomorrow, not five billion years ago, not thirty billion years in the future, never. This I can say with absolute metaphysical certainty.
So what good is this section then? Well, in many instances, it is useful to assume that an object did or will travel along a path that is essentially straight and with an acceleration that is nearly constant; that is, any deviation from the ideal motion can be essentially ignored. Motion along a curved path may be considered effectively one-dimensional if there is only one degree of freedom for the objects involved. A road might twist and turn and explore all sorts of directions, but the cars driving on it have only one degree of freedom - the freedom to drive in one direction or the opposite direction. (You can't drive diagonally on a road and hope to stay on it for long.) In this regard, it is not unlike motion restricted to a straight line. Approximating real situations with models based on ideal situations is not considered cheating. This is the way things get done in physics. It is such a useful technique that we will use it over and over again.
Our goal in this section then, is to derive new equations that can be used to describe the motion of an object in terms of its three kinematic variables: velocity (*v*), position (*s*), and time (*t*). There are three ways to pair them up: velocity-time, position-time, and velocity-position. In this order, they are also often called the first, second, and third equations of motion, but there is no compelling reason to learn these names.
Since we are dealing with motion in a straight line, direction will be indicated by sign - positive quantities point one way, while negative quantities point the opposite way. Determining which direction is positive and which is negative is entirely arbitrary. The laws of physics are isotropic; that is, they are independent of the orientation of the coordinate system. Some problems are easier to understand and solve, however, when one direction is chosen positive over another. As long as you are consistent within a problem, it doesn't matter.
### velocity-time
The relation between velocity and time is a simple one during uniformly accelerated, straight-line motion. The longer the acceleration, the greater the change in velocity. Change in velocity is directly proportional to time when acceleration is constant. If velocity increases by a certain amount in a certain time, it should increase by twice that amount in twice the time. If an object already started with a certain velocity, then its new velocity would be the old velocity plus this change. You ought to be able to see the equation in your mind's eye already.
This is the easiest of the three equations to derive using algebra. Start from the definition of acceleration.
| *a* = | ∆*v* |
| --- | --- |
| ∆*t* |
Expand ∆*v* to *v* − *v*0 and condense ∆*t* to *t*.
| *a* = | *v* − *v*0 |
| --- | --- |
| *t* |
Then solve for *v* as a function of *t*.
*v* = *v*0 + *at* [1]
This is the first equation of motion. It's written like a polynomial - a constant term (*v*0) followed by a first order term (*at*). Since the highest order is 1, it's more correct to call it a linear function.
The symbol *v*0 [vee nought] is called the initial velocity or the velocity a time *t* = 0. It is often thought of as the "first velocity" but this is a rather naive way to describe it. A better definition would be to say that an initial velocity is the velocity that a moving object has when it first becomes important in a problem. Say a meteor was spotted deep in space and the problem was to determine its trajectory, then the initial velocity would likely be the velocity it had when it was first observed. But if the problem was about this same meteor burning up on reentry, then the initial velocity likely be the velocity it had when it entered Earth's atmosphere. The answer to "What's the initial velocity?" is "It depends". This turns out to be the answer to a lot of questions.
The symbol *v* is the velocity some time *t* after the initial velocity. It is often called the final velocity but this does not make it an object's "last velocity". Take the case of the meteor. What velocity is represented by the symbol *v*? If you've been paying attention, then you should have anticipated the answer. It depends. It could be the velocity the meteor has as it passes by the moon, as it enters the Earth's atmosphere, or as it strikes the Earth's surface. It could also be the meteorite's velocity as it sits in the bottom of a crater. (In that case *v* = 0 m/s.) Are any of these the final velocity? Who knows. Someone could extract the meteorite from its hole in the ground and drive away with it. Is this relevant? Probably not, but it depends. There's no rule for this kind of thing. You have to parse the text of a problem for physical quantities and then assign meaning to mathematical symbols.
The last part of this equation *at* is the change in the velocity from the initial value. Recall that *a* is the rate of change of velocity and that *t* is the time after some initial event. Rate times time is change. Given an object accelerating at 10 m/s2, after 5 s it would be moving 50 m/s faster. If it started with a velocity of 15 m/s, then its velocity after 5 s would be...
15 m/s + 50 m/s = 65 m/s
### position-time
The displacement of a moving object is directly proportional to both velocity and time. Move faster. Go farther. Move longer (as in longer time). Go farther. Acceleration compounds this simple situation since velocity is now also directly proportional to time. Try saying this in words and it sounds ridiculous. "Displacement is directly proportional to time and directly proportional to velocity, which is directly proportional to time." Time is a factor twice, making displacement proportional to the square of time. A car accelerating for two seconds would cover four times the distance of a car accelerating for only one second (22 = 4). A car accelerating for three seconds would cover nine times the distance (32 = 9).
Would that it were so simple. This example only works when initial velocity is zero. Displacement is proportional to the square of time when acceleration is constant and initial velocity is zero. A true general statement would have to take into account any initial velocity and how the velocity was changing. This results in a terribly messy proportionality statement. Displacement is directly proportional to time and proportional to the square of time when acceleration is constant. A function that is both linear and square is said to be quadratic, which allows us to compact the previous statement considerably. Displacement is a quadratic function of time when acceleration is constant
Proportionality statements are useful, but not as general as equations. We still don't know what the constants of proportionality are for this problem. One way to figure them out is to use algebra.
Start with the definition of average velocity.
| *v* = | ∆*s* |
| --- | --- |
| ∆*t* |
Expand ∆*s* to *s* − *s*0 and condense ∆*t* to *t*.
| *v* = | *s* − *s*0 |
| --- | --- |
| *t* |
Solve for position.
*s* = *s*0 + *vt* [a]
To continue, we need to resort to a little trick known as the mean speed theorem or the Merton rule. I prefer the latter since the rule can be applied to any quantity that changes at a uniform rate - not just speed. The Merton rule was first published in 1335 at Merton College, Oxford by the English philosopher, mathematician, logician, and calculator [William Heytesbury](https://en.wikipedia.org/wiki/William_of_Heytesbury "William of Heytesbury a.k.a. Gugliemus Hentisberus (1313-1372) England") (1313-1372). When the rate of change of a quantity is constant, its average value is halfway between its final and initial values.
*v* = ½(*v* + *v*0) [4]
Substitute the first equation of motion [1] into this equation [4] and simplify with the intent of eliminating *v*.
| *v* = ½[(*v*0 + *at*) + *v*0]*v* = ½(2*v*0 + *at*)*v* = *v*0 + ½*at* [b] |
| --- |
Now substitute [b] into [a] to eliminate *v* [vee bar].
*s* = *s*0 + (*v*0 + ½*at*)*t*
And finally, solve for *s* as a function of *t*.
*s* = *s*0 + *v*0*t* + ½*at*2 [2]
This is the second equation of motion. It's written like a polynomial - a constant term (*s*0), followed by a first order term (*v*0*t* ), followed by a second order term (½*at*2). Since the highest order is 2, it's more correct to call it a quadratic.
The symbol *s*0 [ess nought] is often thought of as the initial position. The symbol *s* is the position some time *t* later. You could call it the final position if you wished. The change in position (∆*s*) is called the displacement or distance (depending on circumstances) and some people prefer writing the second equation of motion like this.
∆*s* = *v*0*t* + ½*at*2 [2]
### velocity-position
The first two equations of motion each describe one kinematic variable as a function of time. In essence...
1. Velocity is directly proportional to time when acceleration is constant (*v* ∝ *t*).
2. Displacement is proportional to time squared when acceleration is constant (∆*s* ∝ *t*2).
Combining these two statements gives rise to a third - one that is independent of time. By substitution, it should be apparent that...
3. Displacement is proportional to velocity squared when acceleration is constant (∆*s* ∝ *v*2).
This statement is particularly relevant to driving safety. When you double the speed of a car, it takes four times more distance to stop it. Triple the speed and you'll need nine times more distance. This is a good rule of thumb to remember.
The conceptual introduction is done. Time to derive the formal equation.
#### method 1
Combine the first two equations together in a manner that will eliminate time as a variable. The easiest way to do this is to start with the first equation of motion...
*v* = *v*0 + *at* [1]
solve it for time...
| *t* = | *v* − *v*0 |
| --- | --- |
| *a* |
and then substitute it into the second equation of motion...
*s* = *s*0 + *v*0*t* + ½*at*2 [2]
like this...
| *s* = | *s*0 + *v*0 | ⎛⎜⎝ | *v* − *v*0 | ⎞⎟⎠ | + ½*a* | ⎛⎜⎝ | *v* − *v*0 | ⎞2⎟⎠ |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| *a* | *a* |
| *s* − *s*0 = | *vv*0 − *v*02 | + | *v*2 − 2*vv*0 + *v*02 |
| --- | --- | --- | --- |
| *a* | 2*a* |
| 2*a*(*s* − *s*0) = 2(*vv*0 − *v*02) + (*v*2 − 2*vv*0 + *v*02) | |
| --- | --- |
| |
| 2*a*(*s* − *s*0) = *v*2 − *v*02 | |
| --- | --- |
| |
Make velocity squared the subject and we're done.
*v*2 = *v*02 + 2*a*(*s* − *s*0) [3]
This is the third equation of motion. Once again, the symbol *s*0 [ess nought] is the initial position and *s* is the position some time *t* later. If you prefer, you may write the equation using ∆*s* - the change in position, displacement, or distance as the situation merits.
*v*2 = *v*02 + 2*a*∆*s* [3]
#### method 2
The harder way to derive this equation is to start with the second equation of motion in this form...
∆*s* = *v*0*t* + ½*at*2 [2]
and solve it for time. This is not an easy job since the equation is quadratic. Rearrange terms like this...
½*at*2 + *v*0*t* − ∆*s* = 0
and compare it to the general form for a quadratic.
*ax*2 + *bx* + *c* = 0
The solutions to this are given by the famous equation...
| *x* = | −*b* ± √(*b*2 − 4*ac*) |
| --- | --- |
| 2*a* |
Replace the symbols in the general equation with the equivalent symbols from our rearranged second equation of motion...
| *t* = | −*v*0 ± √[*v*02 − 4(½*a*)(−∆*s*)] |
| --- | --- |
| 2(½*a*) |
clean it up a bit...
| *t* = | −*v*0 ± √(*v*02 + 2*a*∆*s*) |
| --- | --- |
| *a* |
and then substitute it back into the first equation of motion.
*v* = *v*0 + *at* [1]
| *v* = *v*0 + *a* | ⎛⎜⎝ | −*v*0 ± √(*v*02 + 2*a*∆*s*) | ⎞⎟⎠ |
| --- | --- | --- | --- |
| *a* |
Stuff cancels and we get this...
*v* = ±√(*v*02 + 2*a*∆*s*)
Square both sides and we're done.
*v*2 = *v*02 + 2*a*∆*s* [3]
That wasn't so bad now, was it?
### calculus derivations
Calculus is an advanced math topic, but it makes deriving two of the three equations of motion much simpler. By definition, acceleration is the first derivative of velocity with respect to time. Take the operation in that definition and reverse it. Instead of differentiating velocity to find acceleration, integrate acceleration to find velocity. This gives us the velocity-time equation. If we assume acceleration is constant, we get the so-called first equation of motion [1].
| *a* | = | | *dv* | | --- | | *dt* | | |
| --- | --- | --- | --- | --- | --- |
| *dv* | = | *a dt* | |
| |
| | *v* | | | --- | --- | | ⌠⌡ | *dv* | | *v*0 | | | = | | *t* | | | --- | --- | | ⌠⌡ | *a dt* | | 0 | | | |
| *v* − *v*0 | = | *at* | |
| |
| *v* | = | *v*0 + *at* [1] | |
Again by definition, velocity is the first derivative of position with respect to time. Reverse this operation. Instead of differentiating position to find velocity, integrate velocity to find position. This gives us the position-time equation for constant acceleration, also known as the second equation of motion [2].
| *v* | | = | | *ds* | | --- | | *dt* | | |
| --- | --- | --- | --- | --- | --- | --- |
| | *ds* | = | *v dt* | |
| |
| | *ds* | = | (*v*0 + *at*) *dt* | |
| |
| | *s* | | | --- | --- | | ⌠⌡ | *ds* | | *s*0 | | | | = | | *t* | | | --- | --- | | ⌠⌡ | (*v*0 + *at*) *dt* | | 0 | | | |
| *s* − *s*0 | | = | *v*0*t* + ½*at*2 | |
| |
| *s* | | = | *s*0 + *v*0*t* + ½*at*2 [2] | |
Unlike the first and second equations of motion, there is no obvious way to derive the third equation of motion (the one that relates velocity to position) using calculus. We can't just reverse engineer it from a definition. We need to play a rather sophisticated trick.
The first equation of motion relates velocity to time. We essentially derived it from this derivative...
| *dv* | = *a* |
| --- | --- |
| *dt* |
The second equation of motion relates position to time. It came from this derivative...
| *ds* | = *v* |
| --- | --- |
| *dt* |
The third equation of motion relates velocity to position. By logical extension, it should come from a derivative that looks like this...
| *dv* | = ? |
| --- | --- |
| *ds* |
But what does this equal? Well nothing by definition, but like all quantities it does equal itself. It also equals itself multiplied by 1. We'll use a special version of 1 (*dt**dt*) and a special version of algebra (algebra with infinitesimals). Look what happens when we do this. We get one derivative equal to acceleration (*dv**dt*) and another derivative equal to the inverse of velocity (*dt**ds*).
| *dv* | = | *dv* | | 1 |
| --- | --- | --- | --- | --- |
| *ds* | *ds* |
| *dv* | = | *dv* | | *dt* |
| *ds* | *ds* | *dt* |
| *dv* | = | *dv* | | *dt* |
| *ds* | *dt* | *ds* |
| *dv* | = | *a* | | 1 |
| *ds* | *v* |
Next step, separation of variables. Get things that are similar together and integrate them. Here's what we get when acceleration is constant...
| | *dv* | | --- | | *ds* | | | = | | *a* | 1 | | --- | --- | | *v* | | |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| *v dv* | | = | *a ds* | |
| |
| | *v* | | | --- | --- | | ⌠⌡ | *v dv* | | *v*0 | | | | = | | *s* | | | --- | --- | | ⌠⌡ | *a ds* | | *s*0 | | | |
| ½(*v*2 − *v*02) | | = | *a*(*s* − *s*0) | |
| |
| | *v*2 | = | *v*02 + 2*a*(*s* − *s*0) [3] | |
| |
Certainly a clever solution, and it wasn't all that more difficult than the first two derivations. However, it really only worked because acceleration was constant - constant in time and constant in space. If acceleration varied in any way, this method would be uncomfortably difficult. We'd be back to using algebra just to save our sanity. Not that there's anything wrong with that. Algebra works and sanity is worth saving.
| *v* = | *v*0 + *at* | [1] |
| --- | --- | --- |
| | | + |
| *s* = | *s*0 + *v*0*t* + ½*at*2 | [2] |
| | | = |
| *v*2 = | *v*02 + 2*a*(*s* − *s*0) | [3] | |
Free Fall | https://physics.info/falling/ | "# Free Fall\n\n### acceleration due to gravity\n\nWant to see an object accelerate?\n\n* Pick somet(...TRUNCATED) |
Graphs of Motion | https://physics.info/motion-graphs/ | "# Graphs of Motion\n\n### introduction\n\nModern mathematical notation is a highly compact way to e(...TRUNCATED) |
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Dataset Details
Dataset Description
Discussions from https://physics.info.
Citation
@misc{Elert,
title={The physics Hypertextbook},
url={https://physics.info/},
journal={The Physics Hypertextbook},
publisher={hypertextbook},
author={Elert, Glenn}
}
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