Talk:Angular velocity

message: Can anyone explain to me what the centered dot being used in the following expression stands for:
:This tensor W(t) will act as if it were a (\vec \omega \times) operator :
:: \vec \omega(t) \times \vec{r}(t) = W(t) \vec{r}(t) 
:Given the orientation matrix A(t) of a frame, we can obtain its instant angular velocity tensor W as follows. We know that:
:: \frac {d \vec r(t)} {dt} = W \cdot \vec{r}
Not to mention:
:Therefore R=e^{Wt} is a rotation matrix and in a time dt is an infinitesimal rotation matrix. Therefore it can be expanded as R = I + W\cdot dt + {1 \over 2} (W \cdot dt)^2 + ...
What really got me fired up was this bit:
:Because of W is the derivative of an orthogonal transformation, the
:: B(\mathbf{r},\mathbf{s}) = (W\mathbf{r}) \cdot \mathbf{s} 
:bilinear form is skew-symmetric. (Here \cdot stands for the scalar product).
I am inclined to think that outside of this last case, the centered dot either stands for matrix multiplication or for scalar multiplication. Whoever wrote these parts has no idea of the mathematical notation in use.
Moving to the big picture, I am in favor of a complete reorganisation and rewrite of the article. I humbly invite all who are interested to contact me on my talk page. Hayazin (talk) 22:33, 6 February 2015 (UTC)
thread_title: Confusing Tensor/Matrix multiplication notation! and a call to reorganisation

message: I don't have time to fix the article at the moment, but I just wanted to point out that it is fundamentally wrong to talk about a particle having angular velocity. Particles are infintesimally small and thus it is impossible for them to have an angular velocity. It is also very incorrect to declare that something has an angular velocity about a point. Angular velocity is point independent. The first section (that's all I've read) is propogating incorrect and misinformation. Any reputable dynamics text will verify this. Feel free to contact me for more details. Moorepants Jan 21, 2013  —Preceding undated comment added 07:00, 22 January 2013 (UTC)
thread_title: Angular Velcity of a Particle

message: I think the article should have something like the introduction I've given it. As I see it, Lie algebras provide the explanation of the reason the angular velocity vector behaves as it does. I wish I had found out about them a lot sooner. However, the definition I have given is not correct. I'm trying to think of the right words, but would anyone care to jump in and help?Buster79 09:00, 1 October 2005 (UTC)
thread_title: Help

message: I put a context tag on this page because the introduction launches right into formal mathematical functions without explaining what will happen in non-expert terms or mentioning (anywhere in the article, really) how angular velocity is used in the real world. --Craig Stuntz 20:25, 19 May 2006 (UTC)
replies: text: Your current revision is much improved; thanks. I think some high schoolers (and below) would still have a problem understanding it, but it's at least understandable to non-mathematics specialists now. Good work, Buster79! --Craig Stuntz 14:19, 2 August 2006 (UTC)
thread_title:  Context 

message: In my opinion, revolutions per minute is not a unit of angular velocity or angular frequency, but of frequency. 1 rpm equals 60 Hz.--84.159.248.246 17:06, 20 November 2006 (UTC)
replies: text: I think that's incorrect. All units used for vector quantities deal only with the magnitude of the measure in question, so "rpm" is a unit for both angular speed and angular velocity.  1 rpm is not the same as 1 Hz.  The units of rpm are angle over time.  The units of Hz are simply 1 over time, without reference to the angle. -- Slowmover 16:57, 22 November 2006 (UTC)
replies: text:  Where does "rpm" refer to angle? In my opiniion, "revolution" is not a measure of angle but is simply used to specify the kind of things that are counted. --84.159.238.199 17:07, 24 November 2006 (UTC)
replies: text:  One revolution is 360°, or 2π radians, which is a measurement of angle. It is not unit-less.  So, 1 rpm is equal to 2π radians per minute, which is possibly easier to recognize as units of angle over time.  1 radian per minute is 1/(2π) rpm, and so on.   It's important to see that a revolution is a divisible quantity, like meters or miles.  It is measured quantity which can have any real number value, not just integers. -- Slowmover 22:09, 28 November 2006 (UTC)

text:  One thing that just occurred to me is that this is really a semantic argument.  The same thing applies to frequency.  The units of angle are actually "dimension-less" units, whether radians or revolutions.  Circular motion is inherent in the definiton of frequency (since each tick of a clock or the frequency of sound refers to a cycling through a full "revolution" of the available motion). Thus, it probably makes no difference if you talk of angular frequency or angular velocity, except for the vector component. -- Slowmover 22:20, 28 November 2006 (UTC)
replies: text:  Just have a look at the article revolutions per minute. There they say "Revolutions per minute (abbreviated rpm, RPM, r/min, or min−1) is a unit of frequency, commonly used to measure rotational speed, in particular in the case of rotation around a fixed axis." The article about rotational speed says: "Rotational speed tells how many complete rotations there are per time unit, and it is measured in revolutions per second (1/s or Hertz) in the SI System. " (Neither of the articles has been written by me.) --84.159.251.122 09:43, 2 December 2006 (UTC)
replies: text:  This whole issue of units of angular velocity and differences between angular velocity and frequency is a common problem (and angular frequency, which we define for talking about oscillations only adds to the confusion).  First of all, although it's not how we normally think of it, a "revolution" is a unit of angle.  This is increasingly stated explicitly, for example, in introductory physics textbooks (see, for example, R. D. Knight, Physics for Scientists and Engineers: A Strategic Approach, 2nd ed., (2008)).  A revolution is just a unit of angle where once around the circle is defined as 1 unit (as opposed to 360 units for degrees, etc.).  So, a frequency stated in revolutions per minute is really an angle per unit time.  In this sense it is an angular velocity (rate of change of angle with respect to time).  So, in a very real sense when refering to circular motion, frequency and angular velocity are the same thing.  But in common usage by physicists (mathematicians may differ) the term "angular velocity" always refers to this quantity quoted in radians/second, and "frequency" is used for this same quantity quoted in Hz or rpm.  When another "oddball" unit (e.g. degrees per second, gradians per fortnight...) is used then this is, or should be, explicitly defined.  So, frequency and angular velocity are essentially the same thing, and the terms are used to clarify what units are being used. --GLeeDads (talk) 15:15, 12 November 2008 (UTC)
thread_title:  rpm 

message: \boldsymbol\omega = {\mathbf{r} \times \mathbf{v} \over |\mathbf{r}|^2} \qquad \qquad (1)
is not true in general but only if the motion of the partical is contained in a plane and if that plane contains the origin. In general, ω is neither orthogonal to the position vector r nor to the velocity vector v, so 
equation (5) is not true.
--84.159.248.246 17:24, 20 November 2006 (UTC)
thread_title:  Non-circular motion 

message: Are there three types of angular velocity? in motion on a ellipse, each corresponding to the time derivative of mean anomaly, true anomaly and eccentric anomaly?--188.26.22.131 (talk) 12:39, 2 October 2012 (UTC)
thread_title:  Time derivative of the anomalies 

message: While the article describes the direction of angular velocity as being the axis of spinning, it doesn't say anything about what this represents, and what difference it makes whether it is up/down. Perhaps a real world analogy like hula hooping could be used to describe the relevance of this vector. Richard001 06:35, 7 December 2006 (UTC)
thread_title: Right hand rule/direction of angular velocity

message: I have resectioned things to make clear the differences between the angular velocity of a particle and the spin angular velocity of a rigid body. Almost all of the contents of the previous page have been included, except the "derivation" section has been shortened. PAR 02:39, 22 January 2007 (UTC)
thread_title: Rewrite

message: Medical Physics Query: I am not a physicist, just one very curious how the heart works so well for so long. Discovery of Angular Velocity in a living organism was an unexpected find in reading of other areas in this pursuit.
1. Application of living physiology to Angular Velocity is perhaps better appreciated in time phases of a coiled snake readying and striking prey or perceived danger.
2. The snake is a compliant rudimentary tubular organism comprised of many layers of neuromuscle, connective tissue, bone and gas. To most effectively strike prey or respond to threat, the snake recoils itself into the smallest sphere possible.
3. Recoil of the snake enables increasingly favorable numbers of interfaces between the physiologic layers to impart maximum angular velocity towards the target in coil.
4. Sensory input from the snake allows expedient recoil when prey is sighted and suggests this is by no means a passive/relaxation phase. 
5. The smallest unit of the heart [muscle] is a [cell] called a [cardiomyocyte]. 
6. [Cardiomyocyte]s are decidedly not [particle]s but tend to exhibit some astonishingly similar behavior around a long and short axis. 
7. Theory in this area suggests divergent strings of living cardiomyocytes [myocardial muscle mass] grouped and electrically herded around a center liquid [mass] tidally pushed in and out.
8. String theory of myocardial tissue implies anchored and fixed vectors matched 180 degrees to the connective tissue of the heart, namely the heart valves, skeleton of the heart and central body of the heart.
9. Demand driven tidal forward and backward flow begins to describe the number of potential vectors arranged in superimposed angles in solid muscle mass opposed against a viscous, living blood mass.  
10. Posit that the [heart/myocardium/cardiac muscle mass] rotates on a long axis clockwise and counterclockwise in layers of muscular sheets arranged one on another from the internal/blood exposed surfaces [endocardium] to the outer/[pericardial space] surfaces [epicardium].
11. Posit that no single layer turns back or forth on the long axis more than 30 degrees, but all layers in summation turn at least 360 degrees in response to physiologic demand.
12. Thus understood, revolutions per minute around the long axis are readily posited as and extrapolated to time variables [heart rate].
13. Posit the distal muscular layers of the heart fold and unspread inward to expel blood [systole/pump/ejection fraction= End Systolic Volume/End Diastolic Volume]triggered by sequential concurrent electrical polarization.
14. Volumetric derivation of Systole is perhaps best mathematically stated as Ejection Fraction [EF].
15. EF is readily extrapolated to [Cardiac Output/CO], first defined by [Adolph Fick]. 
16. Posit the proximal muscular layers of the heart unfold and spread outward to impel blood [diastole/sump/] as defined by [Arthur Guyton] guided by sequential electrical depolarization.
17. Posit that superimposed muscular layers engage one another on a plurality of angles around a well defined (mostly plasma) long axis suggesting shear and countershear of angular velocity. 
18. Suggest most pragmatic (inexpensive and noninvasive) readily imaged solid long axis definition as Cardiac Apex (south myocardial pole)-Central Body of the Heart [collagen]-(Left AV collagen ring)/ (Right PV collagen ring).
19. Long axis performance physics of the heart are best and first attributed to Robert Hooke.
20. Short axis determinants are most expediently attributed to muscle mass with scarce influence of blood mass. Short axis performance physics of the heart are best and first attributed to Pierre LaPlace.
21. Posit that myocardial layering back and forth of available subsets of cardiomyocytes illustrates principles of shear and subsequent torque generation at work impelling and expelling blood in and out 60-80 times/minute for 60-80 years.
22. Crossing/uncrossing of multiple muscular bands suggests that Francisco Torrent-Guasp was looking ahead and further implies a force multiplier such as Angular Velocity at work within  bands of a dedicated systolic heart and a dedicated diastolic heart.--Lbeben (talk) 03:00, 27 May 2008 (UTC)
thread_title: Physics/Medicine Perspective

message: From the article, section Two dimensions:
The equation
:\boldsymbol\omega=\frac{\mathbf{r}\times\mathbf{v}}{|\mathrm{\mathbf{r}}|^2}
allows the angular velocity to be found.
...
I'm a bit surprised in omega being written in bold (TeX \boldsymbol). As the article cross product states: «The cross product is not defined except in three-dimensions [...]»
? --Abdull (talk) 09:41, 28 June 2008 (UTC)
thread_title:  Angular velocity a vector in two dimensions? 

message: What is the relation of this quantity to peripheral speed on an elliptic trajectory?  —Preceding unsigned comment added by 84.232.141.36 (talk) 17:35, 2 September 2010 (UTC)
thread_title:  Relation to linear velocity 

message: Just a comment about some recent changes about vectors and pseudovectors.
A vector is a member of a vector space, and the definition of a vector space is vector space definition.
Therefore, as an algebraic structure, a pseudovector is a vector.
Hence is not necessary to speak about "angular velocity pseudovectors". To say "angular velocity vector" is equally correct.
:--Juansempere (talk) 17:45, 12 February 2011 (UTC)
thread_title:  Pseudovectors are vectors 

message: In the beginning of the article, in the first line, the link to angular speed redirects to the angular velocity article (so it's a loop). Quite unhelpful, I'd take away the link but maybe someone has a better proposal for rewording. L.livnev (talk) 15:33, 19 June 2011 (UTC)
replies: text: An editor changed the redirect recently without explanation from angular frequency, which is a far more appropriate target so I've change it back.--JohnBlackburnewordsdeeds 16:08, 19 June 2011 (UTC)
thread_title:  Link loop in first line 

message: The angular velocity, as its name indicates, has to do with angles. Its magnitude is therefore measured in rad/s. 
But a few line after it is said, that "It is sometimes also called the rotational velocity and its magnitude the rotational speed, typically measured in cycles or rotations per unit time"... 
Stricly speeking, it can not be the same object. There is : the angular velocity, which magnitude is in rad/s, and another vector, the rotational speed, highly related to the first one but nevertheless different, with unit cycle/s.
roy.nico 2011.10.19 16:30
: It is the same. E.g. a rotational speed of 10 cycles/second is the same as angular velocity wit 62.8 rad/s. It's no different to using inches, centimetres or miles to measure distance. It's still the same distance.
: It's important as rotational speeds are often given in such units; "RPM" or revolutions per minute for example. But it's easier to do many calculations if rad/s are used instead.--JohnBlackburnewordsdeeds 15:07, 19 October 2011 (UTC)
thread_title:  Inconsistency in the introduction  

message: "To prove it we start tarivative of \mathcal{R}\mathcal{R}^t being R(t) a rotation matrix:"
what is "tarivative"?  — Preceding unsigned comment added by 121.127.209.142 (talk) 13:15, 29 November 2012 (UTC)
replies: text: vandalism...  --Steve (talk) 02:40, 30 November 2012 (UTC)
thread_title:  "Tarivative" 

message: Why is the term 'velocity' used repeatedly instead of 'speed' when referring to a scalar  e.g.
"In two dimensions the angular velocity ω is given by" ...  — Preceding unsigned comment added by 46.59.253.143 (talk) 11:12, 23 April 2016 (UTC)
thread_title:  speed vs velocity 

message: Substituted at 07:50, 29 April 2016 (UTC)
thread_title: Assessment comment

message: The so-called short description of this article is currently: "physical quantity, the rate of change of angular position, and if regarded as a vector, the direction is the axis of rotation". This is 125 characters long — the recommended length is a maximum of 90 characters, and even that's pretty long (about 40 is recommended). The short description is not supposed to fully summarize the article, it's just meant as a concise subtitle to give context at a glance for an article, especially on mobile. I modified it to just "physical quantity" but that got reverted without any explanation. Based on this line, "The short description should focus on distinguishing the subject from similar ones rather than precisely defining it.", the edit I made seemed appropriate. Other similar articles like velocity and angular momentum aren't as wordy in their short descriptions, but those too could use some paring down. Thoughts? --CrocodilesAreForWimps (talk) 03:36, 16 September 2019 (UTC)
replies: text: @Crocodilesareforwimps It's currently a ridiculously technical version that starts with "pseudovector representing . . . ", which I'm not sure is even accurate (surely it's the actual quantity represented, not its mathematical representation). I'm about to change it to something shortish mentioning rotation. Musiconeologist (talk) 10:00, 18 April 2024 (UTC)
replies: text: I went with "Rate and direction of rotation". Maybe that's still a bit too close to attempting a definition, but at least it might have a chance of fitting on one line and meaning something to people who haven't learnt any physics or applied maths. Musiconeologist (talk) 10:10, 18 April 2024 (UTC)
thread_title:  Short description 

message: An editor has asked for a discussion to address the redirect Orders of magnitude (angular speed). Please participate in the redirect discussion if you wish to do so.  signed, Rosguill talk 17:23, 8 April 2020 (UTC)
thread_title:  "Orders of magnitude (angular speed)" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: Can anyone explain to me how a rigid body rotates about point?
I think it is clear how a rigid body can rotate about an axis, but about a point?
I believe all of this is nonsense.
If it is not, then a clear picture of a rigid body rotating about point (but not about an axis) should be added.  — Preceding unsigned comment added by 181.228.151.129 (talk) 04:27, 21 June 2020 (UTC)
thread_title:  Rigid body rotating about point