# FHSST Physics/Momentum

**Momentum** is the product of the mass and velocity of an object. In
general the momentum of an object can be conceptually thought of as the
tendency for an object to continue in its current state of motion, speed
and direction.

As such, it is a natural consequence of Newtons first law.

Momentum is a conserved quantity, meaning that the total momentum of any
closed system cannot be changed.

## Momentum in classical mechanics

If an object is moving in any reference frame, then it has momentum *in
that frame*. It is important to note that momentum is frame dependent.
That is, the same object may have a certain momentum in one frame of
reference, but a different amount in another frame.

The amount of momentum that an object has depends on two physical
quantities: the mass and the velocity of the moving object in the frame
of reference. In physics, the symbol for momentum is usually denoted by
$\vec p$ , so this can be written:

:   `<font size=5>`{=html}$\vec p=m\vec v$`</font size=5>`{=html}

where

$$\vec p$$ is the momentum,

$$m$$ is the mass, and

$$\vec v$$ is the velocity.

The velocity of an object is given by its speed and its direction.
Because momentum depends on velocity, it too has a magnitude and a
direction and is a vector quantity. For example the momentum of a $5kg$
bowling ball would have to be described by the statement that it was
moving westward at $2\frac{m}{s}$ . It is insufficient to say that the
ball has $10kg\cdot\frac{m}{s}$ of momentum because momentum is not
fully described unless its direction is given.

## Conservation of momentum

As far as we know, momentum is a conserved quantity. **Conservation of
momentum** (sometimes also **conservation of impulse**) states that the
total amount of momentum of all the things in the universe will never
change. One of the consequences of this is that the center of mass of
any system of objects will always continue with the same velocity unless
acted on by a force outside the system.

Conservation of momentum is a consequence of the homogeneity of space.

In an isolated system (one where external forces are absent) the total
momentum will be constant: this is implied by Newton\'s first law of
motion. Newton\'s third law of motion, the law of reciprocal actions,
which dictates that the forces acting between systems are equal in
magnitude, but opposite in sign, is due to the conservation of momentum.

Since momentum is a vector quantity it has direction. Thus when a gun is
fired, although overall movement has increased compared to before the
shot was fired, the momentum of the bullet in one direction is equal in
magnitude, but opposite in sign, to the momentum of the gun in the other
direction. These then sum to zero which is equal to the zero momentum
that was present before either the gun or the bullet was moving.


# FHSST Physics/Newtonian Gravitation

# Newtonian Gravitation

!Sir Isaac
Newton All
objects on Earth are pulled downward, towards the ground. This
phenomenon is called **gravity**. Every object falls just as fast as any
other object (unless the air slows it down like a feather, or pushes it
up like a balloon), as first shown by
Galileo. In 1687 Isaac
Newton stated that gravity
is not restricted to the Earth, but instead, there is gravity everywhere
in the universe. Newton explained that planets, moons, and comets move
in orbits because of the effect of gravity.


# FHSST Physics/Pressure

**Essay 3: Pressure and Forces**

Author: Asogan Moodaly

Asogan Moodaly received his Bachelor of Science degree (with honours) in
Mechanical Engineering from the University of Natal, Durban in South
Africa. For his final year design project he worked on a 3-axis filament
winding machine for composite (Glass re-enforced plastic in this case)
piping. He worked in Vereeniging, Gauteng at Mine Support Products (a
subsidiary of Dorbyl Heavy Engineering) as the design engineer once he
graduated. He currently lives in the Vaal Triangle area and is working
for Sasol Technology Engineering as a mechanical engineer, ensuring the
safety and integrity of equipment installed during projects.

# Pressure and Forces

In the mining industry, the roof (hangingwall) tends to drop as the face
of the tunnel (stope) is excavated for rock containing gold.

As one can imagine, a roof falling on one\'s head is not a nice
prospect! Therefore the roof needs to be supported.

![](Fhsst_press1.png "Fhsst_press1.png"){width="363"}

The roof is not one big uniform chunk of rock. Rather it is broken up
into smaller chunks. It is assumed that the biggest chunk of rock in the
roof has a mass of less than 20 000 kg therefore each support has to be
designed to resist a force related to that mass. The strength of the
material (either wood or steel) making up the support is taken into
account when working out the minimum required size and thickness of the
parts to withstand the force of the roof.

![](Fhsst_press2.png "Fhsst_press2.png"){width="363"}

Sometimes the design of the support is such that the support needs to
withstand the rock mass without the force breaking the roof..

Therefore hydraulic supports (hydro = water) use the principles of force
and pressure such that as a force is exerted on the support, the water
pressure increases. A pressure relief valve then squirts out water when
the pressure (and thus the force) gets too large. Imagine a very large,
modified doctor\'s syringe.

![](Fhsst_press3.png "Fhsst_press3.png"){width="363"}

In the petrochemical industry, there are many vessels and pipes that are
under high pressures. A vessel is a containment unit (Imagine a pot
without handles, that has the lid welded to the pot that would be a
small vessel) where chemicals mix and react to form other chemicals,
amongst other uses.

![](Fhsst_press4.png "Fhsst_press4.png"){width="335"}

The end product chemicals are sold to companies that use these chemicals
to make shampoo, dishwashing liquid, plastic containers, fertilizer,
etc. Anyway, some of these chemical reactions require high temperatures
and pressures in order to work. These pressures result in forces being
applied to the insides of the vessels and pipes. Therefore the minimum
thickness of the pipe and vessels walls must be determined using
calculations, to withstand these forces. These calculations take into
account the strength of the material (typically steel, plastic or
composite), the diameter and of course the pressure inside the
equipment.


# FHSST Physics/Electrostatics

# Electrostatics

The study of the effects of static charges. These charges are produced
by too many or too few electrons. Electrons, in turn, are the most
movable charge forms, and are found spread around the positive charge in
the nucleus of the atom. If there are too few electrons, a positive
charge will appear. If there are too many, a negative charge will
appear. If the charges are in balance, then no charge is detected. The
electron is a fundamental particle, and has interesting characteristics,
besides the charge, it spins, and this spin gives rise to a magnetic
field, much like an electric motor.

The decision to call some charges positive and others negative was
*arbitrary*. This gives rise to a potential misunderstanding when
charges are moving in a circuit. This will be deferred to a later
section, on electricity.

The fundamental study of these charges in isolation can best be observed
by experiment. If we generate a charge by friction, say fur on hard
rubber, or silk on glass, we can transfer the charge to a small ball
coated with aluminum foil. This ball is held up by a thin thread. Nylon
or silk work well.

If however the air is damp, the charge will leak off the metal balls.

Two such balls, charged by the same static source will repel each other.
If we use two different sources, they will attract each other. Maybe.

We can measure the amount of attraction or repulsion by a simple means.
If we measure the weight of these balls, then we know that they are
attracted by the earth. Other forces on these balls will cause them to
swing away from hanging straight down.

By measuring the movement, or the angle, we can figure out what tiny
force is pushing the ball away from the vertical. The tangent function
is the perfect candidate to resolve this problem. ((add more text and
diagrams here))

It would be nice to find out what happens when some charge is removed.
It turns out, that if we use a third ball, of the same size as the other
two, we can exactly halve the charge.

From this we can see that we can measure the effects of increasing
distance, and decreasing charge.


# FHSST Physics/Electricity

# Electricity

>   -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
>   *Warning*: We believe in experimenting and learning about physics at every opportunity, BUT playing with electricity can be **EXTREMELY DANGEROUS!** Do not try to build home made circuits without someone who knows if what you are doing is safe. Normal electrical outlets are dangerous. Treat electricity with respect in your everyday life.
>   You will encounter electricity every day for the rest of your life and to make sure you are able to make wise decisions we have included an entire chapter on electrical safety. Please read it - not only will it make you safer but it will show the applications of many of the ideas you will learn in this chapter.
>   -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------


# FHSST Physics/Atomic Nucleus

# Inside atomic nucleus

Amazingly enough, the human mind that is contained inside a couple of
liters of human\'s brain, is able to deal with extremely large as well
as extremely small objects such as the whole universe and its smallest
building blocks. So, what are these building blocks? As we already know,
the universe consists of galaxies, which consist of stars with planets
moving around. The planets are made of molecules, which are bound groups
(chemical compounds) of atoms.

There are more than stars in the universe. Currently, scientists know
over 12 million chemical compounds i.e. 12 million different molecules.
All this variety of molecules is made of only a hundred of different
atoms. For those who believe in beauty and harmony of nature, this
number is still too large. They would expect to have just few different
things from which all other substances are made. In this chapter, we are
going to find out what these elementary things are.


# Physics Study Guide/Purpose

## Purpose of Physics

The aim of the study of physics is to understand the natural world, in
its broadest and most fundamental sense. By understanding it, we hope to
be able to explain and predict (typically through the mathematics that
are developed) and ultimately modify (oftentimes through resulting
technology) events that occur. Physics deals with everything that
happens in this Universe, tries to understand it and provides the root
cause for the same in a logical manner.


# Physics Study Guide/Scientific Method

## Scientific Method

In order to uncover these \'laws of nature\', physics (like all science)
relies on a *deliberately-structured process* of

-   observe a natural phenomenon, (for example thanks to an
    experimentation)
-   creating a theory or model,
-   testing the theory or model,
-   adjusting the theory or model based on the results of the test,
-   and repeating the above process with the adjusted theory or model.

This process is known as the \'scientific method\'. Most curriculums
thus incorporate elements of both theory (principally, what laws others
have found in the past) and practical (how to undertake experiments and
observations).


# Physics Study Guide/Normal Force and Friction

## The Normal Force

Why is it that we stay steady in our chairs when we sit down? According
to the first law of motion, if an object is translationally in
equilibrium (velocity is constant), the sum of all the forces acting on
the object must be equal to zero. For a person sitting on a chair, it
can thus be postulated that a **normal force** is present balancing the
**gravitational force** that pulls the sitting person down. However, it
should be noted that only some of the normal force can cancel the other
forces to zero like in the case of a sitting person. In Physics, the
term **normal** as a modifier of the **force** implies that this force
is acting perpendicular to the surface at the point of contact of the
two objects in question. Imagine a person leaning on a vertical wall.
Since the person does not stumble or fall, he/she must be in
equilibrium. Thus, the component of his/her weight along the horizontal
is balanced or countered (opposite direction) by an equal amount of
force \-- this force is the *normal force* on the wall. So, on a slope,
the normal force would not point upwards as on a horizontal surface but
rather perpendicular to the slope surface.

The normal force can be provided by any one of the four fundamental
forces, but is typically provided by electromagnetism since
microscopically, it is the repulsion of electrons that enables
interaction between surfaces of matter. There is no easy way to
calculate the normal force, other than by assuming first that there is a
normal force acting on a body in contact with a surface (direction
perpendicular to the surface). If the object is not accelerating (for
the case of uniform circular motion, the object is accelerating) then
somehow, the magnitude of the normal force can be solved. In most cases,
the magnitude of the normal force can be solved together with other
unknowns in a given problem.

Sometimes, the problem does not warrant the knowledge of the normal
force(s). It is in this regard that other formalisms (e.g. Lagrange
method of undetermined coefficients) can be used to eventually *solve*
the physical problem.

## Friction

When there is relative motion between two surfaces, there is a
resistance to the motion. This force is called friction. Friction is the
reason why people may have trouble accepting Newton\'s first law of
Motion, that an object tends to keep its state of motion. Friction acts
opposite to the direction of the original force **The frictional force**
is equal to the **frictional coefficient** times the **normal force**

In order to set a body into a state of motion, the forward force or the
thrust force exerted upon the body must be greater in magnitude than the
maximum frictional value encountered upon the surface with which the
body is in contact with. If the thrust force does not exceed in
magnitude over the maximum frictional value or limiting value of motion
then the body shall not be set into motion.

Friction is caused due to attractive forces between the molecules near
the surfaces of the objects. If two steel plates are made really flat
and polished and cleaned and made to touch in a vacuum, it bonds
together. It would look as if the steel was just one piece.The bonds are
formed as in a normal steel piece. This is called cold welding. And this
is the main cause of friction.

The above equation is an empirical one --- in general, the frictional
coefficient is not constant. However, for a large variety of contact
surfaces, there is a well characterized value. This kind of friction is
called Coulomb friction. There is a separate coefficient for both static
and kinetic friction. This is because once an object is pushed on, it
will suddenly jerk once you apply enough force and it begins to move.

Also, the frictional coefficient varies greatly depending on what two
substances are in contact, and the temperature and smoothness of the two
substances. For example, the frictional coefficients of glass on glass
are very high. When you have similar materials, in most cases you don\'t
have Coulomb friction.

For **static friction**, the force of friction actually increases
proportionally to the force applied, keeping the body immobile. Once,
however, the force exceeds the maximum frictional force, the body will
begin to move. The maximum frictional force is calculated as follows:

**The static frictional force** is less than or equal to the
**coefficient of static friction** times the **normal force**. Once the
frictional force equals the coefficient of static friction times the
normal force, the object will break away and begin to move.

Once it is moving, the frictional force then obeys:

**The kinetic frictional force** is equal to the **coefficient of
kinetic friction** times the **normal force**. As stated before, this
always opposes the direction of motion.

## Variables

  Symbol        Units           Definition
  ------------- --------------- -------------------------
  $\vec{F}_f$   $\mathrm{N}\$   Force of friction
  $\mu\$        none            Coefficient of friction

```{=html}
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Definition of Terms

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**Normal force (N):** The force on an object perpendicular to the
surface it rests on utilized in order to account for the body\'s lack of
movement. Units: newtons (N)\
\
**Force of friction (F~f~):** The force placed on a moving object
opposite its direction of motion due to the inherent roughness of all
surfaces. Units: newtons (N)\
\
**Coefficient of friction (**μ**):** The coefficient that determines the
amount of friction. This varies tremendously based on the surfaces in
contact. There are no units for the coefficient of either static or
kinetic friction\

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It\'s important to note that in real life we often have to deal with
viscous and turbulent friction - they appear when you move the body
through the matter.

Viscous friction is proportional to velocity and takes place at
approximately low speeds. Turbulent friction is proportional to $V^2$
and takes place at higher velocities.


# Physics Study Guide/Circular Motion

## Uniform Circular Motion

### Speed and frequency

!A two dimensional polar co-ordinate system. The point $M$ can be
located in 2D plane as $(a,b)$ in Cartesian coordinate
system or $(r,\theta)$ in
polar coordinate
system in Cartesian coordinate system or (r,\theta) in polar coordinate system")

Uniform circular motion assumes that an object is moving (1) in circular
motion, and (2) at constant speed $v$; then

where $r$ is the radius of the circular path, and $T$ is the time period
for one revolution.

Any object travelling on a circle will return to its original starting
point in the period of one revolution, $T$. At this point the object has
travelled a distance $2\pi r$. If $T$ is the time that it takes to
travel distance $2\pi r$ then the object\'s speed is

where $f=\frac1T$

### Angular frequency

Uniform circular motion can be explicitly described in terms of polar
coordinates through angular frequency, $\omega$ :

where $\theta$ is the angular coordinate of the object (see the diagram
on the right-hand side for reference).

Since the speed in uniform circular motion is constant, it follows that

From that fact, a number of useful relations follow:

The equations that relate how $\theta$ changes with time are analogous
to those of linear motion at constant speed. In particular,

The angle at $t=0$, $\theta_0$, is commonly referred to as *phase*.

### Velocity, centripetal acceleration and force

The position of an object in a plane can be converted from polar to
cartesian coordinates through the equations

Expressing $\theta$ as a function of time gives equations for the
cartesian coordinates as a function of time in uniform circular motion:

Differentiation with respect to time gives the components of the
velocity vector:

Velocity in circular motion is a vector tangential to the trajectory of
the object. Furthermore, even though the speed is constant the velocity
vector changes direction over time. Further differentiation leads to the
components of the acceleration (which are just the rate of change of the
velocity components):

The acceleration vector is perpendicular to the velocity and oriented
towards the centre of the circular trajectory. For that reason,
acceleration in circular motion is referred to as *centripetal
acceleration*.

The absolute value of centripetal acceleration may be readily obtained
by

For centripetal acceleration, and therefore circular motion, to be
maintained a *centripetal force* must act on the object. From Newton\'s
Second Law it follows directly that the force will be given by

the components being

and the absolute value

thumbtime=5:44\|middle\|720px\|Example of finding the centripetal
acceleration of moon in
orbit.\'\'


# Physics Study Guide/Torque

## Torque and Circular Motion

Circular motion is the motion of a particle at a set distance (called
radius) from a point. For circular motion, there needs to be a force
that makes the particle turn. This force is called the \'centripetal
force.\' Please note that the centripetal force is *not* a new type of
force-it is just a force causing rotational motion. To make this
clearer, let us study the following examples:

1.  If Stone ties a piece of thread to a small pebble and rotates it in
    a horizontal circle above his head, the circular motion of the
    pebble is caused by the tension force in the thread.
2.  In the case of the motion of the planets around the sun (which is
    roughly circular), the force is provided by the gravitational force
    exerted by the sun on the planets.

Thus, we see that the centripetal force acting on a body is always
provided by some other type of force \-- centripetal force, thus, is
simply a name to indicate the force that provides this circular motion.
This centripetal force is *always* acting inward toward the center. You
will know this if you swing an object in a circular motion. If you
notice carefully, you will see that you have to continuously pull
inward. We know that an opposite force should exist for this centripetal
force(by Newton\'s 3rd Law of Motion). This is the centrifugal force,
which exists only if we study the body from a non-inertial frame of
reference(an accelerating frame of reference, such as in circular
motion). This is a so-called \'pseudo-force\', which is used to make the
Newton\'s law applicable to the person who is inside a non-inertial
frame. e.g. If a driver suddenly turns the car to the left, you go
towards the right side of the car because of centrifugal force. The
centrifugal force is equal and opposite to the centripetal force. It is
caused due to inertia of a body.

$$\omega_{\text{avg}}=\frac{\omega+\omega_f}{2}=\frac{\theta}{t}$$

**Average angular velocity** is equal to one-half of the sum of
**initial** and **final angular velocities** assuming constant
acceleration, and is also equal to the **angle gone through** divided by
the **time taken**.

------------------------------------------------------------------------

$$\alpha=\frac{\Delta\omega}{t}$$

**Angular acceleration** is equal to**change in angular velocity**
divided by **time taken**.

### Angular momentum

**Angular momentum** of an object revolving around an external axis $O$
is equal to the cross-product of the **position vector** with respect to
$O$ and its **linear momentum**.

**Angular momentum** of a rotating object is equal to the **moment of
inertia** times **angular velocity**.

$$L=I\omega$$

------------------------------------------------------------------------

$$\tau=I\alpha=\frac{\Delta L}{t}$$\>

**Rotational Kinetic Energy** is equal to one-half of the product of
**moment of inertia** and the **angular velocity** squared.

IT IS USEFUL TO NOTE THAT

The equations for rotational motion are analogous to those for linear
motion-just look at those listed above. When studying rotational
dynamics, remember:

-   the place of force is taken by torque

```{=html}
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```
-   the place of mass is taken by moment of inertia

```{=html}
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```
-   the place of displacement is taken by angle

```{=html}
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```
-   the place of linear velocity, momentum, acceleration, etc. is taken
    by their angular counterparts.

### Definition of terms

+----------------------------------------------------------------------+
| **Torque** ($\vec\tau$): Force times distance. A vector.             |
| $N\!\cdot\!m$                                                        |
|                                                                      |
| **Moment of inertia** ($I$): Describes the object\'s resistance to   |
| torque --- the rotational analog to inertial mass. $kg\!\cdot\!m^2$  |
|                                                                      |
| **Angular momentum** ($\vec L$): $kg\!\cdot\!\frac{m^2}{s}$          |
|                                                                      |
| **Angular velocity** ($\vec\omega$): $\frac{\text{rad}}{s}$          |
|                                                                      |
| **Angular acceleration** ($\vec\alpha$): $\frac{\text{rad}}{s^2}$    |
|                                                                      |
| **Rotational kinetic energy** ($K_r$):                               |
| $J=kg\!\cdot\!\left(\frac{m}{s}\right)^2$                            |
|                                                                      |
| **Time** ($t$): $s$                                                  |
+----------------------------------------------------------------------+


# Physics Study Guide/Waves

# Waves

Wave is defined as the movement of any periodic motion like a spring, a
pendulum, a water wave, an electric wave, a sound wave, a light wave,
etc.

!A wave with constant
amplitude.{width="400"}
Any periodic wave that has amplitude varied with time, phase
sinusoidally can be expressed mathematically as

:; R(t , θ) = R Sin (ωt + θ)

-   Minimum wave height (trough) at angle 0, π, 2π, \...

:; F(R,t,θ) = 0 at θ = nπ

-   Maximum wave height (peak or crest) at π/2, 3π/2, \...

:; F(R,t,θ) = R at θ = (2n+1)π/2

-   Wavelength (distance between two crests) λ = 2π.

:   λ = 2π - A circle or a wave
:   2λ = 2(2π) - Two circles or two waves
:   kλ = k2π - Circle k or k amount of waves

-   Wave Number,

:; k

-   Velocity (or Angular Velocity),

:; ω = 2πf

-   Time Frequency,

:; f = 1 / t

-   Time

:; t = 1 / f

**Wave speed** is equal to the **frequency** times the **wavelength**.
It can be understood as how frequently a certain distance (the
wavelength in this case) is traversed.

**Frequency** is equal to **speed** divided by **wavelength**.

**Period** is equal to the inverse of **frequency**.

```{=html}
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```
Variables

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\

+-------------------------------+
| **λ:** wavelength (m)\        |
| **v:** wave speed (m/s)\      |
| **f:** frequency (1/s), (Hz)\ |
| **T:** period (s)             |
+-------------------------------+

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Definition of terms

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+----------------------------------------------------------------------+
| **Wavelength (*λ*)**: The length of one wave, or the distance from a |
| point on one wave to the same point on the next wave. Units: meters  |
| (m). In light, *λ* tells us the color.\                              |
| \                                                                    |
| **Wave speed (v)**: the speed at which the wave pattern moves.       |
| Units: meters per second, (m/s)\                                     |
| \                                                                    |
| **Frequency of oscillation (*f*)** (or just **frequency**): the      |
| number of times the wave pattern repeats itself in one second.       |
| Units: seconds^-1^ = (1/s) = hertz (Hz) In sound, *f* tells us the   |
| pitch. The inverse of frequecy is the period of oscillation.\        |
| \                                                                    |
| **Period of oscillation (*T*)** (or just **period**): duration of    |
| time between one wave and the next one passing the same spot. Units: |
| seconds (s). The inverse of the period is frequency. Use a capital,  |
| italic *T* and not a lowercase one, which is used for time.\         |
| \                                                                    |
| **Amplitude (*A*)**: the maximum height of the wave measured from    |
| the average height of the wave (the wave's center). Unit: meters (m) |
+----------------------------------------------------------------------+

Image here

The wave's extremes, its peaks and valleys, are called **antinodes**. At
the middle of the wave are points that do not move, called **nodes**.

*Examples of waves:* Water waves, sound waves, light waves, seismic
waves, shock waves, electromagnetic waves ...

## Oscillation

A wave is said to oscillate, which means to move back and forth in a
regular, repeating way. This fluctuation can be between extremes of
position, force, or quantity. Different types of waves have different
types of oscillations.

**Longitudinal waves:** Oscillation is parallel to the direction of the
wave. Examples: sound waves, waves in a spring.

**Transverse waves:** Oscillation is perpendicular to direction of the
wave. Example: light

## Interference

When waves overlap each other it is called **interference**. This is
divided into **constructive** and **destructive** interference.

**Constructive interference:** the waves line up perfectly and add to
each others' strength.

**Destructive interference:** the two waves cancel each other out,
resulting in no wave.This happens when angle between them is 180degrees.

## Resonance

In real life, waves usually give a mishmash of constructive and
destructive interference and quickly die out. However, at certain
wavelengths standing waves form, resulting in **resonance**. These are
waves that bounce back into themselves in a strengthening way, reaching
maximum amplitude.

*Resonance is a special case of forced vibration when the frequency of
the impressed periodic force is equal to the natural frequency of the
body so that it vibrates with increased amplitude, spontaneously.*


# Physics Study Guide/Standing waves

------------------------------------------------------------------------

# Standing waves

  ----------------------------------------------
   $\|\vec{v}\|=\sqrt{\frac{\|\vec{T}\|}{\mu}}$
  ----------------------------------------------

**Wave speed** is equal to the square root of **tension** divided by the
**linear density** of the string.

+-------------------------------------------------+
| ```{=html}                                      |
| <div style="text-align: center;">               |
| ```                                             |
| `<big>`{=html}***μ* = *m*/*L*** `</big>`{=html} |
|                                                 |
| ```{=html}                                      |
| </div>                                          |
| ```                                             |
+-------------------------------------------------+

**Linear density** of the string is equal to the **mass** divided by the
**length** of the string.

+---------------------------------------------------+
| ```{=html}                                        |
| <div style="text-align: center;">                 |
| ```                                               |
| `<big>`{=html}***λ*~max~ = 2*L*** `</big>`{=html} |
|                                                   |
| ```{=html}                                        |
| </div>                                            |
| ```                                               |
+---------------------------------------------------+

The **fundamental wavelength** is equal to two times the **length** of
the string.

```{=html}
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Variables

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\

+---------------------------------------+
| *λ:* wavelength (m)\                  |
| *λ~max~:* fundamental wavelength (m)\ |
| *μ:* linear density (g/m)\            |
| *v:* wave speed (m/s)\                |
| *F:* force (N)\                       |
| *m:* mass (kg)\                       |
| *L:* length of the string (m)\        |
| *l:* meters (m)                       |
+---------------------------------------+

```{=html}
<H2>
```
Definition of terms

```{=html}
</H2>
```
+----------------------------------------------------------------------+
| **Tension (*F*):** (not frequency) in the string (*t* is used for    |
| time in these equations). Units: newtons (N)\                        |
| \                                                                    |
| **Linear density (*μ*):** of the string, Greek mu. Units: grams per  |
| meter (g/m)\                                                         |
| \                                                                    |
| **Velocity (*v*)** of the wave (m/s)\                                |
| \                                                                    |
| **Mass (*m*)**: Units: grams (g). (We would use kilograms but they   |
| are too big for most strings).\                                      |
| \                                                                    |
| **Length of the string (*L*):** Units: meters (m)                    |
+----------------------------------------------------------------------+

Fundamental frequency: the frequency when the wavelength is the longest
allowed, this gives us the lowest sound that we can get from the system.

In a string, the length of the string is half of the largest wavelength
that can create a standing wave, called its fundamental wavelength.


# Physics Study Guide/Sound

Sound is defined as mechanical sinosodial vibratory longitudinal impulse
waves which oscillate the pressure of a transmitting medium by means of
adiabatic compression and decompression consequently resulting in the
increase in the angular momentum and hence rotational kinetic energy of
the particles present within the transmitting medium producing
frequencies audible within hearing range, that is between the threshold
of audibility and the threshold of pain on a Fletchford Munson equal
loudness contour diagram.

## Intro

When two glasses collide, we hear a sound. When we pluck a guitar
string, we hear a sound.

Different sounds are generated from different sources. Generally
speaking, the collision of two objects results in a sound.

Sound does not exist in a vacuum; it travels through the materials of a
medium. Sound is a longitudinal wave in which the mechanical vibration
constituting the wave occurs along the direction of the wave\'s
propagation.

The velocity of sound waves depends on the temperature and the pressure
of the medium. For example, sound travels at different speeds in air and
water. We can therefore define sound as a mechanical disturbance
produced by the collision of two or more physical quantities from a
state of equilibrium that propagates through an elastic material medium.

# Sound

```{=html}
<table width=75%>
```
```{=html}
<tr>
```
```{=html}
<td style="background-color: white; border:1px solid #D6D6FF; padding:1em;" valign=top >
```
```{=html}
<center>
```
`<big>`{=html}**$decibel(\mathrm{dB}) = 10\cdot \log\left(\frac{I_1}{I_0}\right)$**`</big>`{=html}

```{=html}
</center>
```
```{=html}
</td>
```
```{=html}
</table>
```
thumb\|400px\|right\|Fig. 1: The Fletcher-Munson equal-loudness
contours. Phons are labelled in
blue. The amplitude is the
magnitude of sound pressure change within a sound wave.
Sound amplitude can be measured in pascals (Pa),
though its more common to refer to the *sound (pressure) level* as
Sound intensity(dB,dBSPL,dB(SPL)), and
the *perceived sound level* as Loudness(dBA,
dB(A)). **Sound intensity** is flow of sound energy per unit time
through a fixed area. It has units of watts per square meter. The
reference Intensity is defined as the minimum Intensity that is audible
to the human ear, it is equal to 10^-12^ W/m^2^, or one picowatt per
square meter. When the intensity is quoted in decibels this reference
value is used. **Loudness** is sound intensity altered according to the
frequency response of the human ear and is measured in a unit called the
A-weighted decibel (dB(A) "wikilink"), also used to be called
phon).

## The Decibel

The decibel is not, as is commonly believed, the unit of sound. Sound is
measured in terms of pressure. However, the decibel is used to express
the pressure as very large variations of pressure are commonly
encountered. The decibel is a dimensionless quantity and is used to
express the ratio of one power quantity to another. The definition of
the decibel is $10\cdot \log_{10}\left(\frac{x}{x_0}\right)$, where x is
a squared quantity, ie pressure squared, volts squared etc. The decibel
is useful to define relative changes. For instance, the required sound
decrease for new cars might be 3 dB, this means, compared to the old car
the new car must be 3 dB quieter. The absolute level of the car, in this
case, does not matter.

+-------------------------------------------------------------------------+
| ```{=html}                                                              |
| <center>                                                                |
| ```                                                                     |
| `<big>`{=html}**$I_0 = 10^{-12} \mbox{ W}/\mbox{m}^2$** `</big>`{=html} |
|                                                                         |
| ```{=html}                                                              |
| </center>                                                               |
| ```                                                                     |
+-------------------------------------------------------------------------+

## Definition of terms

+----------------------------------------------------------------------+
| **Intensity (I):** the amount of energy transferred through 1 m^2^   |
| each second. Units: watts per square meter\                          |
| \                                                                    |
+----------------------------------------------------------------------+

+----------------------------------------------------------------------+
| **Lowest audible sound:** I = 0 dB = 10^-12^ W/m^2^ (A sound with dB |
| \< 0 is inaudible to a human.)\                                      |
| \                                                                    |
| **Threshold of pain:** I = 120 dB = 10 W/m^2^                        |
+----------------------------------------------------------------------+

*Sample equation:* **Change in sound intensity**\
Δβ = β~2~ - β~1~\
= 10 log(*I*~2~/*I*~0~) - 10 log(*I*~1~/*I*~0~)\
= 10 \[log(*I*~2~/*I*~0~) - log(*I*~1~/*I*~0~)\]\
= 10 log\[(*I*~2~/*I*~0~)/(*I*~1~/*I*~0~)\]\
= 10 log(*I*~2~/*I*~1~)\
where log is the base-10 logarithm.

## Doppler effect

+------------------------------------------------------------------------+
| ```{=html}                                                             |
| <center>                                                               |
| ```                                                                    |
| `<big>`{=html} $f' = f \, \frac{v \pm v_0}{v \mp v_s}$ `</big>`{=html} |
|                                                                        |
| ```{=html}                                                             |
| </center>                                                              |
| ```                                                                    |
+------------------------------------------------------------------------+

\
f\' is the observed frequency, f is the actual frequency, v is the speed
of sound ($v=336+0.6T$), T is temperature in degrees Celsius $v_0$ is
the speed of the observer, and $v_s$ is the speed of the source. If the
observer is approaching the source, use the top operator (the +) in the
numerator, and if the source is approaching the observer, use the top
operator (the -) in the denominator. If the observer is moving away from
the source, use the bottom operator (the -) in the numerator, and if the
source is moving away from the observer, use the bottom operator (the +)
in the denominator.

### Example problems

A. An ambulance, which is emitting a 400 Hz siren, is moving at a speed
of 30 m/s towards a stationary observer. The speed of sound in this case
is 339 m/s.

$f' = 400\,\mathrm{Hz} \left( \frac{339 + 0}{339 - 30} \right)$

B. An M551 Sheridan, moving at 10 m/s is following a Renault FT-17 which
is moving in the same direction at 5 m/s and emitting a 30 Hz tone. The
speed of sound in this case is 342 m/s.

$f' = 30\,\mathrm{Hz} \left( \frac{342 + 10}{342 + 5} \right)$


# Physics Study Guide/Fluids

## Buoyancy

**Buoyancy** is the force due to pressure differences on the top and
bottom of an object under a fluid (gas or liquid).

Net force = buoyant force - force due to gravity on the object

## Bernoulli\'s Principle

Fluid flow is a complex phenomenon. An ideal fluid may be described as:

-   The fluid flow is **steady** i.e its velocity at each point is
    constant with time.
-   The fluid is **incompressible**. This condition applies well to
    liquids and in certain circumstances to gases.
-   The fluid flow is **non-viscous**. Internal friction is neglected.
    An object moving through this fluid does not experience a retarding
    force. We relax this condition in the discussion of **Stokes\'
    Law**.
-   The fluid flow is **irrotational**. There is no angular momentum of
    the fluid about any point. A very small wheel placed at an arbitrary
    point in the fluid does not rotate about its center. Note that if
    turbulence is present, the wheel would most likely rotate and its
    flow is then not irrotational.

As the fluid moves through a pipe of varying cross-section and
elevation, the pressure will change along the pipe. The Swiss physicist
Daniel Bernoulli
(1700-1782) first derived an
expression relating the pressure to fluid speed and height. This result
is a consequence of conservation of energy and applies to ideal fluids
as described above.

\'\'Consider an ideal fluid flowing in a pipe of varying cross-section.
A fluid in a section of length $\Delta x_1$ moves to the section of
length $\Delta x_2$ in time $\Delta t$ . The relation given by Bernoulli
is:

where:

$$P$$ is pressure at cross-section

$$h$$ is height of cross-section

$$\rho$$ is density

$$v$$ is velocity of fluid at cross-section

In words, the Bernoulli relation may be stated as: *As we move along a
streamline the sum of the pressure ($P$), the kinetic energy per unit
volume and the potential energy per unit volume remains a constant.*

------------------------------------------------------------------------

*(To be concluded)*


# Physics Study Guide/Fields

# Fields

A field is one of the more difficult concepts to grasp in physics. A
field is an area or region in which an influence or force is effective
regardless of the presence or absence of a material medium. Simply put,
a **field** is a collection of vectors often representing the force an
object *would* feel if it were placed at any particular point in space.
With gravity, the field is measured in newtons, as it depends solely on
the mass of an object, but with electricity, it is measured in newtons
per coulomb, as the force on an electrical charge depends on the amount
of that charge. Typically these fields are calculated based on canceling
out the effect of a body in the point in space that the field is
desired. As a result, a field is a vector, and as such, it can (and
should) be added when calculating the field created by TWO objects at
one point in space.

Fields are typically illustrated through the use of what are called
**field lines** or **lines of force**. Given a source that exerts a
force on points around it, sample lines are drawn representing the
direction of the field at points in space around the force-exerting
source.

There are three major categories of fields:

1.  **Uniform fields** are fields that have the same value at any point
    in space. As a result, the lines of force are parallel.
2.  **Spherical fields** are fields that have an origin at a particular
    point in space and vary at varying distances from that point.
3.  **Complex fields** are fields that are difficult to work with
    mathematically (except under simple cases, such as fields created by
    two point object), but field lines can still typically be drawn.
    **Dipoles** are a specific kind of complex field.

Magnetism also has a field, measured in Tesla, and it also has **field
lines**, but its use is more complicated than simple \"force\" fields.
Secondly, it also only appears in a two-pole form, and as such, is
difficult to calculate easily.

The particles that form these magnetic fields and lines of force are
called electrons and not magnetons. A magneton is a quantity in
magnetism.

## Definition of terms

+----------------------------------------------------------------------+
| **Field:** A collection of vectors that often represents the force   |
| that an object *would* feel if it were placed in any point in        |
| space.\                                                              |
| \                                                                    |
| **Field Lines:** A method of diagramming fields by drawing several   |
| sample lines showing direction of the field through several points   |
| in space.\                                                           |
| \                                                                    |
+----------------------------------------------------------------------+


# Physics Study Guide/Thermodynamics

# Introduction

Thermodynamics deals with the movement of heat and its conversion to
mechanical and electrical energy among others.

# Laws of Thermodynamics

### First Law

The `<b>`{=html}First Law`</b>`{=html} is a statement of conservation of
energy law:

+----------------------------------+
| ```{=html}                       |
| <center>                         |
| ```                              |
| `<big>`{=html}$\Delta U = Q - W$ |
+----------------------------------+

The `<b>`{=html}First Law`</b>`{=html} can be expressed as the change in
internal energy of a system ($\Delta U$) equals the amount of energy
added to a system (Q), such as heat, minus the work expended by the
system on its surroundings (W).

If Q is positive, the system has *gained* energy (by heating).

If W is positive, the system has *lost* energy from doing work on its
surroundings.

As written the equations have a problem in that neither Q or W are
`<b>`{=html}state functions`</b>`{=html} or quantities which can be
known by direct measurement without knowing the history of the system.

In a gas, the first law can be written in terms of state functions as

+----------------------------------+
| ```{=html}                       |
| <center>                         |
| ```                              |
| `<big>`{=html}$dU = T ds - p dV$ |
+----------------------------------+

### Zero-th Law

After the first law of Thermodynamics had been named, physicists
realised that there was another more fundamental law, which they termed
the \'zero-th\'.

This is that:

  --------------------------------------------------------------------------------------------
  *If two bodies are at the same temperature, there is no resultant heat flow between them.*
  --------------------------------------------------------------------------------------------

An alternate form of the \'zero-th\' law can be described:

  ----------------------------------------------------------------------------------------------------------
  *If two bodies are in thermal equilibrium with a third, all are in thermal equilibrium with each other.*
  ----------------------------------------------------------------------------------------------------------

This second statement, in turn, gives rise to a definition of
Temperature (T):

  ---------------------------------------------------------------------------------------------------------------------------------------
  *Temperature is the only thing that is the same between two otherwise unlike bodies that are in thermal equilibrium with each other.*
  ---------------------------------------------------------------------------------------------------------------------------------------

### Second Law

This law states that heat will never flow from a cold object to a hot
object.

$S = k_B \cdot ln(\Omega)$

where $k_B$ is the Boltzmann constant
($k_B = 1.380658 \cdot 10^{-23}  \mbox{ kg m}^2 \mbox{ s}^{-2} \mbox{ K}^{-1}$)
and $\Omega$ is the partition function, i. e. the number of all possible
states in the system.

This was the statistical definition of entropy, there is also a
\"macroscopic\" definition:

$S = \int  \frac{\mathrm{d}Q}{T}$

where *T* is the temperature and d*Q* is the increment in energy of the
system.

### Third Law

The third law states that a temperature of absolute zero cannot be
reached.

# Temperature Scales

There are several different scales used to measure temperature. Those
you will most often come across in physics are degrees Celsius and
kelvins.

Celsius temperatures use the symbol **Θ**. The symbol for degrees
Celsius is **°C**. Kelvin temperatures use the symbol **T**. The symbol
for kelvins is **K**.

### The Celsius Scale

The Celsius scale is based on the melting and boiling points of water.

The temperature for freezing water is 0 °C. This is called the *freezing
point*

The temperature of boiling water is 100 °C. This is called the *steam
point*.

The Celsius scale is sometimes known as \'Centigrade\', but the CGPM
chose *degrees Celsius* from among the three names then in use way back
in 1948, and centesimal and centigrade should no longer be used. See
Wikipedia for more details.

### The Kelvin Scale

The Kelvin scale is based on a more fundamental temperature than the
melting point of ice. This is absolute zero (equivalent to −273.15 °C),
the lowest possible temperature anything could be cooled to---where the
kinetic energy of *any* system is at its minimum. The Kelvin scale was
developed from an observation on how the pressure and volume of a sample
of gas changes with temperature- PV/T is a constant. If the temperature
( T)was reduced, then the pressure ( P) exerted by Volume (V) the Gas
would also reduce, in direct proportion. This is a simple experiment and
can be carried out in most school labs. Gases were assumed to exert no
pressure at -273 degree Celsius. ( In fact all gases will have condensed
into liquids or solids at a somewhat higher temperature)

Although the Kelvin scale starts at a different point to Celsius, its
units are of exactly the same size.

Therefore:

  ---------------------------------------------------------------------------------
  *Temperature in kelvins (*K*) = Temperature in degrees Celsius (*°C*) + 273.15*
  ---------------------------------------------------------------------------------

# Specific Latent Heat

Energy is needed to break bonds when a substance changes state. This
energy is sometimes called the *latent heat*. Temperature remains
constant during changes of state.

To calculate the energy needed for a change of state, the following
equation is used:

  ---------------------------------------------------------------------------------------------
  *Heat transferred, ΔQ (*J*) = Mass, m (*kg*) x specific latent heat capacity,*L*(*J*/*kg*)*
  ---------------------------------------------------------------------------------------------

The specific latent heat, *L*, is the energy needed to change the state
of 1 kg of the substance without changing the temperature.

The latent heat of *fusion* refers to melting. The latent heat of
*vapourisation* refers to boiling.

# Specific Heat Capacity

The specific heat capacity is the energy needed to raise the temperature
of a given mass by a certain temperature.

The change in temperature of a substance being heated or cooled depends
on the mass of the substance and on how much energy is put in. However,
it also depends on the properties of that given substance. How this
affects temperature variation is expressed by the substance\'s *specific
heat capacity* (*c*). This is measured in J/(kg·K) in SI units.

  ------------------------------------------------------------------------------------------------------------------------------------
  *Change in internal energy,*Δ*U (*J*) = mass, m (*kg*) x specific heat capacity, c (*J*/*(kg·K)*) x temperature change,*Δ*T (*K*)*
  ------------------------------------------------------------------------------------------------------------------------------------


# Physics Study Guide/Theories of Electricity

## Intro

All atoms are made of charged particles called electrons, neutrons and
protons. At the center of each atom is a nucleus of neutrons and
protons, which is surrounded by electrons orbiting it on circular paths.

## Charged Particles

The three main subatomic particles have very different properties, the
most important of which are:

  Particle   Charge           Mass (kg)
  ---------- ---------------- ----------------
  Electron   negative ( - )   9.11 x 10^-31^
  Proton     positive ( + )   1.67 x 10^-27^
  Neutron    zero ( 0 )       1.67 x 10^-27^

## Charge

Most objects are electrically neutral, i.e. the sum of their electric
charges equal to zero. However, when an object loses or gains electrons
it will become positively or negatively charged, respectively:

:;object + electron → negatively charged object

:;object - electron → positively charged object

A positively charged object has a quantity of charge *+Q* and electric
field lines radiate outward. A negatively charged object has a quantity
of charge *-Q* and electric field lines radiate inward.

**Like charges will repel each other and opposite charges will
attract**, i.e. negatively charged objects attract positively charged
objects and vice versa.

## Electrostatic/Coulomb Force

The force between 2 stationary charges is called the electrostatic force
or Coulomb force.

If two charges, *Q~1~* and *Q~2~*, are at a distance *r* from each
other, they will interact with a force:

:; $F = k_e \frac{Q_1 Q_2}{r^2}$ ,

where *k~e~* is Coulomb\'s constant (*k~e~* = 8.99 × 10^9^ N m^2^
C^−2^). The force of interaction between the charges is attractive if
the charges are opposite signed and repulsive if like signed.

The electrostatic force from a charge will be experienced by any other
charge around it, and the strength and direction of this force at all
positions around the charge is known as the electric field E. The
electric field is directly proportional to the force:

:   $E = \frac {F}{Q}$

## Electromotive Force

When a moving charge passes through a magnetic field, perpendicular to
the field lines,that has direction from left to right. The magnetic
field exerts a force on the charge to make it go up or down. Positive
charge goes up, Negative charge goes down.

:   $\mathbf{F_B} = Q(\mathbf{v} \times \mathbf{B})$

## Electromagnetic Force

For a moving charge the sum of Electrostatic Force and the Electromotive
Force gives Electromagnetic Force acting on the charge

:   F~EB~ = Q E + Q V B = Q (E + V B)

Electrostatic Force is the force generates Current going from left to
right . Electromotive Force is the force generates Current going
perpendicular to current of electrostatic

Electromagnetic Force generates an Electric Field going from left to
right and a magnetic Field perpendicular to Electric Fields

Electromagnetic force may be carried out by Electromagnetic induction
which is the inducing of current using electricity

## Electricity and Conductors

In all conductors, charges move freely in any direction. If there is an
Electric Force

:; F~E~ = Q E

Electric Force will exert a pressure F~E~ / A that force charges in
conductor to move in a straight line. This action generates a current of
charge moving in a straight line.

The Pressure from the Electric Force is called Voltage and the straight
line of moving charges is called Current.

If Voltage is V and Current is I, then the ratio of Current over Voltage
gives the Conductance of the Conductor and the ratio of Voltage over
Current gives the Resistance of the conductor.

:; $G = \frac{I}{V}$\

:; $Z = \frac{V}{I}$

Therefore, *All conductors have a Resistance and a Conductance*

If there exists a straight line conductor of length l, that has surface
area A with conductivity ρ then the Conductance of the conductor

:;G = ρ $\frac{l}{A}$

From above,

$$G = \frac{I}{V}$$ = ρ $\frac{l}{A}$

Therefore, the conduction of all material can be calculated by

:;ρ = $\frac{I}{V} \frac{A}{l}$

## Resistor

If there exists a straight line conductor. As shown above, every
conductor has a Resistance R equal to the ratio of Voltage over Current

$$R = \frac {V}{I}$$

:;$I_R = \frac{V}{R}$

A straight line conductor has a capability of reducing current. This can
be used in an electric circuit to reduce current. In an electric
circuit, straight line conductor has a symbol \--\^\^\^\-- with a
resistance R measured in Ohms Ώ and is called a resistor.

Resistance can be connected in series or in parallel to increase
Resistance or to decrease resistance.

If there are n resistors connected in a series, the total resistance is

:; $R_t = R_1 + R_2 + ... + R_n$

If there are n resistors connected in parallel, then the total
resistance is

:; $\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}$


# Physics Study Guide/Physics constants

# Commonly Used Physical Constants

  Name                                             Symbol                                                                 Value                                                         Units                                               Relative Uncertainty
  ------------------------------------------------ ---------------------------------------------------------------------- ------------------------------------------------------------- --------------------------------------------------- ----------------------
  Speed of light (in vacuum)                       $c$                                                                    $299\ 792\ 458$                                               $\mathrm{m}\ \mathrm{s}^{-1}$                       (exact)
  Magnetic Constant                                $\mu_0$                                                                $4\pi\times10^{-7}\approx12.566\ 370\ 6\times10^{-7}$         $\mathrm{N}\ \mathrm{A}^{-2}$                       (exact)
  Electric Constant                                $\varepsilon_0 = 1/\left( \mu_0c^2 \right)$                            $\approx8.854\ 187\ 817\times10^{-12}$                        $\mathrm{F}\ \mathrm{m}^{-1}$                       (exact)
  Newtonian Gravitaional Constant                  $G$                                                                    $6.674\ 2(10)\times10^{-11}$                                  $\mathrm{m}^3\ \mathrm{kg}^{-1}\ \mathrm{s}^{-2}$   $1.5\times10^{-4}$
  Plank\'s Constant                                $h$                                                                    $6.626\ 069\ 3(11)\times10^{-34}$                             $\mathrm{J}\ \mathrm{s}$                            $1.7\times10^{-7}$
  Elementary charge                                $e$                                                                    $1.602\ 176\ 53(14)\times10^{-19}$                            $\mathrm{C}$                                        $8.5\times10^{-8}$
  Mass of the electron                             $m_e$                                                                  $9.109\ 382\ 6(16)\times10^{-31}$                             $\mathrm{kg}$                                       $1.7\times10^{-7}$
  Mass of the proton                               $m_p$                                                                  $1.672\ 621\ 71(29)\times10^{-27}$                            $\mathrm{kg}$                                       $1.7\times10^{-7}$
  Fine structure constant                          $\alpha=\frac{e^2}{4 \pi \varepsilon_0 \hbar c}$                       $7.297\ 352\ 568(24)\times10^{-3}$                            dimensionless                                       $3.3\times10^{-9}$
  Molar gass constant                              $R$                                                                    $8.314\ 472(15)$                                              $\mathrm{J}\ \mathrm{mol}^{-1}\ \mathrm{K}^{-1}$    $1.7\times10^{-6}$
  Boltzmann\'s constant                            $k$                                                                    $1.380\ 650\ 5(24)\times10^{-23}$                             $\mathrm{J}\ \mathrm{K}^{-1}$                       $1.8\times10^{-6}$
  Avogadro\'s Number                               $N_{\text{A}}, L$                                                      $6.022\ 141\ 5(10)\times10^{23}$                              $\mathrm{mol}^{-1}$                                 $1.7\times10^{-7}$
  Rydberg constant                                 $R_\infty$                                                             $10\ 973\ 731.568\ 525(73)$                                   $\mathrm{m}^{-1}$                                   $6.6\times10^{-12}$
  Standard acceleration of gravity                 $g$                                                                    $9.806\ 65$                                                   $\mathrm{m}\ \mathrm{s}^{-2}$                       defined
  Atmospheric pressure                             $\mathrm{atm}$                                                         $101\ 325$                                                    $\mathrm{Pa}$                                       defined
  Bohr Radius                                      $a_0\$                                                                 $0.529\ 177\ 208\ 59(36)\times10^{-10}\$                      $\mathrm{m}\$                                       $6.8\times10^{-10}$
  Electron Volt                                    $eV$                                                                   $1.602\ 176\ 53(14)\times10^{-19}$                            $\mathrm{J}$                                        $8.7\times10^{-8}$
  Luminous efficacy of monochromatic radiation     $K_{cd}$                                                               $683$                                                         $\mathrm{lm/W}$                                     (exact)
  hyperfine transition frequency of Cs-133         $\Delta\nu_\text{Cs}$                                                  $9\ 192\ 631\ 770$                                            $\mathrm{Hz}$                                       (exact)
  Reduced Planck constant                          $\hbar = h/2\pi$                                                       $1.054\ 571\ 817\times{10}^{-34}$                             $\mathrm{J}\cdot \mathrm{s}$                        (exact)
  atomic mass of Carbon 12                         $m({}^{12}\text{C})$                                                   $1.992\ 646\ 879\ 92(60)\times {10}^{-26}$                    $\mathrm{kg}$
  molar mass of Carbon-12                          $M({}^{12}\text{C}) = N_{\text{A}} m({}^{12}\text{C})$                 $11.999\ 999\ 9958(36)\times{10}^{-3}$                        $\mathrm{kg\cdot {mol}^{-1}}$
  atomic mass constant                             $m_{\text{u}} = m({}^{12}\text{C}) / 12 = 1\,\text{Da}$                $1.660\ 539\ 066\ 60(50)\times{10}^{-27}$                     $\mathrm{kg}$
  molar mass constant                              $M_{\text{u}} = M({}^{12}\text{C}) / 12 = N_{\text{A}} m_{\text{u}}$   $0.999\ 999\ 999\ 65(30)\times{10}^{-3}$                      $\mathrm{kg\cdot {mol}^{-1}}$
  molar volume of silicon                          $V_{m}(\mathrm{Si})$                                                   $1.205\ 883\ 199(60)\times{10}^{-5}$                          $\mathrm{m^3\cdot {mol}^{-1}}$
  molar Planck constant                            $N_{\text{A}} h$                                                       $3.990\ 312\ 712\ldots{10}^{-10}$                             $\mathrm{J\cdot {Hz}^{-1}\cdot{mol}^{-1}}$
  Stefan-Boltzmann constant                        $\sigma = \pi^2 k_B^4 / 60 \hbar^3 c^2$                                $5.670\ 374\ 419\ldots \times {10}^{-8}$                      $\mathrm{W\cdot m^{-2}\cdot K^{-4}}$
  first radiation constant                         $c_1 = 2 \pi h c^2$                                                    $3.741\ 771\ 852\ldots{10}^{-16}$                             $\mathrm{W\cdot m^2}$
  first radiation constant for spectral radiance   $c_{\text{1L}} = 2 h c^2 / sr$[^1]                                     $1.191\ 042\ 972\ 397\ 188\ 414\ 079\ 4892\times{10}^{-16}$   $\mathrm{W\cdot m^2 {sr}^{-1}}$
  second radiation constant                        $c_2 = h c / k_B$                                                      $1.438\ 776\ 877\ldots\times{10}^{-2}$                        $\mathrm{m\cdot K}$
  Wien wavelength displacement constant            $b$                                                                    $2.897\ 771\ 955\ldots \times {10}^{-3}$                      $\mathrm{m\cdot K}$
  Wien frequency displacement constant             $b' = c / b$                                                           $5.878\ 925\ 757\ \times {10}^{10}$                           $\mathrm{Hz \cdot K^{-1}}$
  Wien entropy displacement constant               $b_\text{entropy}$                                                     $3.002\ 916\ 077\ldots \times {10}^{-3}$                      $\mathrm{m\cdot K}$
  Faraday constant                                 $F = N_{\text{A}} e$[^2]                                               $96\ 485.332\ 123\ 310\ 0184$                                 $\mathrm{C \cdot {mol}^{-1}}$

  : Uncertainty should be read as 1.234(56) =
  1.234$\pm$`<!-- -->`{=html}0.056

\_\_TOC\_\_

## To Be Merged Into Table

This list is prepared in the format

-   Constant (symbol) : value

------------------------------------------------------------------------

-   Coulomb\'s Law Constant (**k**) : 1/(4 π ε~0~) *=* 9.0 × 10^9^
    N·m^2^/C^2^
-   Faraday constant (**F**) : 96,485 C·mol^−1^
-   Mass of a neutron (**m~n~**) : 1.67495 × 10^−27^ kg
-   Mass of Earth : 5.98 × 10^24^ kg
-   Mass of the Moon : 7.35 × 10^22^ kg
-   Mean radius of Earth : 6.37 × 10^6^ m
-   Mean radius of the Moon : 1.74 × 10^6^ m
-   Dirac\'s Constant (**$\hbar$**) : $h/(2\pi)$ = 1.05457148 × 10^−34^
    J·s
-   Speed of sound in air at STP : 3.31 × 10^2^ m/s
-   Unified Atomic Mass Unit (**u**) : 1.66 × 10^−27^ kg

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# See Also

## Wiki-links

-    Wikipedia Article

## External Links

-   NIST Physics
    Lab

[^1]:

[^2]:


# Physics Study Guide/Frictional Coefficients

## Approximate Coefficients of Friction

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# Physics Study Guide/Greek alphabet

# About the *Common uses in Physics*

While these are indeed common usages, it should be pointed out that
there are many other usages and that other letters are used for the same
purpose. The reason is quite simple: there are only so many symbols in
the Greek and Latin alphabets, and scientists and mathematicians
generally do not use symbols from other languages. It is a common trap
to associate a symbol exclusively with some particular meaning, rather
than learning and understanding the physics and relations behind it.

+------------------+------------------+---------+------------------+
| Capital          | Lower case       | Name    | Common use in    |
|                  |                  |         | Physics          |
+==================+==================+=========+==================+
| ```{=mediawiki}  | ```{=mediawiki}  | alpha   | Angular          |
| {{math|          | {{math|          |         | acceleration\    |
| size=1.5em|<math | size=1.5em|<math |         | Linear           |
| >\Alpha</math>}} | >\alpha</math>}} |         | expansion\       |
| ```              | ```              |         | Coefficient\     |
|                  |                  |         | Alpha particle   |
|                  |                  |         | (helium          |
|                  |                  |         | nucleus)\        |
|                  |                  |         | Fine Structure   |
|                  |                  |         | Constant         |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | beta    | Beta particle    |
| {{math           | {{math           |         | --- high energy  |
| |size=1.5em|<mat | |size=1.5em|<mat |         | electron\        |
| h>\Beta</math>}} | h>\beta</math>}} |         | Sound intensity  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | gamma   | Gamma ray (high  |
| {{math|          | {{math|          |         | energy EM wave)\ |
| size=1.5em|<math | size=1.5em|<math |         | Ratio of heat    |
| >\Gamma</math>}} | >\gamma</math>}} |         | capacities (in   |
| ```              | ```              |         | an ideal gas)\   |
|                  |                  |         | Relativistic     |
|                  |                  |         | correction       |
|                  |                  |         | factor Shear     |
|                  |                  |         | strain           |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | delta   | Δ=\"Change in\"\ |
| {{math|          | {{math|          |         | δ                |
| size=1.5em|<math | size=1.5em|<math |         | =\"Infinitesimal |
| >\Delta</math>}} | >\delta</math>}} |         | change in (),    |
| ```              | ```              |         | also used to     |
|                  |                  |         | denote the Dirac |
|                  |                  |         | delta function   |
|                  |                  |         | (reference       |
|                  |                  |         | needed)\"        |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | epsilon | Emissivity\      |
| {{math|si        | {{math|si        |         | Strain (Direct   |
| ze=1.5em|<math>\ | ze=1.5em|<math>\ |         | e.g. tensile or  |
| Epsilon</math>}} | epsilon</math>}} |         | compression)\    |
| ```              | ```              |         | Permittivity\    |
|                  |                  |         | EMF              |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | zeta    | (no common use)  |
| {{math           | {{math           |         |                  |
| |size=1.5em|<mat | |size=1.5em|<mat |         |                  |
| h>\Zeta</math>}} | h>\zeta</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | eta     | Viscosity\       |
| {{mat            | {{mat            |         | Energy           |
| h|size=1.5em|<ma | h|size=1.5em|<ma |         | efficiency       |
| th>\Eta</math>}} | th>\eta</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | theta   | Angle (°, rad)\  |
| {{math|          | {{math|          |         | Temperature      |
| size=1.5em|<math | size=1.5em|<math |         |                  |
| >\Theta</math>}} | >\theta</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | iota    | The lower case   |
| {{math           | {{math           |         | $\iota\;$ is     |
| |size=1.5em|<mat | |size=1.5em|<mat |         | rarely used,     |
| h>\Iota</math>}} | h>\iota</math>}} |         | while $\Iota$ is |
| ```              | ```              |         | sometimes used   |
|                  |                  |         | for the identity |
|                  |                  |         | matrix or the    |
|                  |                  |         | moment of        |
|                  |                  |         | inertia. Note    |
|                  |                  |         | that $\iota$ is  |
|                  |                  |         | not to be        |
|                  |                  |         | confused with    |
|                  |                  |         | the Roman        |
|                  |                  |         | character $i$    |
|                  |                  |         | (which has a dot |
|                  |                  |         | and is much more |
|                  |                  |         | widely used in   |
|                  |                  |         | mathematics and  |
|                  |                  |         | physics).        |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | kappa   | Spring constant\ |
| {{math|          | {{math|          |         | Dielectric       |
| size=1.5em|<math | size=1.5em|<math |         | constant         |
| >\Kappa</math>}} | >\kappa</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | lambda  | Wavelength\      |
| {{math|s         | {{math|s         |         | Thermal          |
| ize=1.5em|<math> | ize=1.5em|<math> |         | conductivity\    |
| \Lambda</math>}} | \lambda</math>}} |         | Constant\        |
| ```              | ```              |         | Eigenvalue of a  |
|                  |                  |         | matrix\          |
|                  |                  |         | Linear density   |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | mu      | Coefficient of   |
| {{ma             | {{ma             |         | friction\        |
| th|size=1.5em|<m | th|size=1.5em|<m |         | Electrical       |
| ath>\Mu</math>}} | ath>\mu</math>}} |         | mobility\        |
| ```              | ```              |         | Reduced mass\    |
|                  |                  |         | Permeability     |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | nu      | Frequency        |
| {{ma             | {{ma             |         |                  |
| th|size=1.5em|<m | th|size=1.5em|<m |         |                  |
| ath>\Nu</math>}} | ath>\nu</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | xi      | Damping          |
| {{ma             | {{ma             |         | cofficient       |
| th|size=1.5em|<m | th|size=1.5em|<m |         |                  |
| ath>\Xi</math>}} | ath>\xi</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | omicron | (no common use)  |
| {{math|si        | {{math|si        |         |                  |
| ze=1.5em|<math>\ | ze=1.5em|<math>\ |         |                  |
| Omicron</math>}} | omicron</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | pi      | Product symbol   |
| {{ma             | {{ma             |         | $\Pi$\           |
| th|size=1.5em|<m | th|size=1.5em|<m |         | Circle number    |
| ath>\Pi</math>}} | ath>\pi</math>}} |         | $                |
| ```              | ```              |         | \pi:=3.14159...$ |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | rho     | Volume density\  |
| {{mat            | {{mat            |         | Resistivity      |
| h|size=1.5em|<ma | h|size=1.5em|<ma |         |                  |
| th>\Rho</math>}} | th>\rho</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | sigma   | Sum symbol\      |
| {{math|          | {{math|          |         | Boltzmann        |
| size=1.5em|<math | size=1.5em|<math |         | constant\        |
| >\Sigma</math>}} | >\sigma</math>}} |         | Electrical       |
| ```              | ```              |         | conductivity\    |
|                  |                  |         | Uncertainty\     |
|                  |                  |         | Stress (Direct   |
|                  |                  |         | e.g. tensile,    |
|                  |                  |         | compression)\    |
|                  |                  |         | Surface density  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | tau     | Torque\          |
| {{mat            | {{mat            |         | Tau particle (a  |
| h|size=1.5em|<ma | h|size=1.5em|<ma |         | lepton)\         |
| th>\Tau</math>}} | th>\tau</math>}} |         | Time constant    |
| ```              | ```              |         | Shear stress     |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | upsilon | mass to light    |
| {{math|si        | {{math|si        |         | ratio            |
| ze=1.5em|<math>\ | ze=1.5em|<math>\ |         |                  |
| Upsilon</math>}} | upsilon</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | phi     | M                |
| {{mat            | {{mat            |         | agnetic/electric |
| h|size=1.5em|<ma | h|size=1.5em|<ma |         | flux\            |
| th>\Phi</math>}} | th>\phi</math>}} |         | Angle (°, rad)   |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | chi     | Rabi frequency   |
| {{mat            | {{mat            |         | (lasers)\        |
| h|size=1.5em|<ma | h|size=1.5em|<ma |         | Susceptibility   |
| th>\Chi</math>}} | th>\chi</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | psi     | Wave function    |
| {{mat            | {{mat            |         |                  |
| h|size=1.5em|<ma | h|size=1.5em|<ma |         |                  |
| th>\Psi</math>}} | th>\psi</math>}} |         |                  |
| ```              | ```              |         |                  |
+------------------+------------------+---------+------------------+
| ```{=mediawiki}  | ```{=mediawiki}  | omega   | Ohms (unit of    |
| {{math|          | {{math|          |         | electrical       |
| size=1.5em|<math | size=1.5em|<math |         | resistance)\     |
| >\Omega</math>}} | >\omega</math>}} |         | ω Angular        |
| ```              | ```              |         | velocity         |
+------------------+------------------+---------+------------------+

: **Greek Alphabet**

# See Also

Greek alphabet on
Wikipedia

Greek letters used in mathematics, science, and
engineering


# Physics Study Guide/Vectors and scalars

**Vectors** are quantities that are characterized by having both a
numerical **quantity** (called the \"magnitude\" and denoted as \|*v*\|)
and a **direction**. Velocity is an example of a vector; it describes
the time rated change in position with a numerical quantity (meters per
second) as well as indicating the direction of movement.

The definition of a vector is any quantity that adds according to the
parallelogram law (there are some physical quantities that have
magnitude and direction that are not vectors).

**Scalars** are quantities in physics that have **no direction**. Mass
is a scalar; it can describe the quantity of matter with units
(kilograms) but does not describe any direction.

## Multiplying vectors and scalars

-   A **scalar** times a **scalar** gives a **scalar** result.
-   A **vector** scalar-multiplied by a **vector** gives a **scalar**
    result (called the dot-product).
-   A **vector** cross-multiplied by a **vector** gives a **vector**
    result (called the cross-product).
-   A **vector** times a **scalar** gives a **vector** result.

## Frequently Asked Questions about Vectors

##### When are scalar and vector compositions essentially the same?

**Answer:** when multiple vectors are in same direction then we can just
add the magnitudes.so, the scalar and vector composition will be same as
we do not add the directions.

##### What is a \"dot-product\"? (work when force not parallel to displacement)

!A Man walking up a
hill **Answer:**
Let\'s take gravity as our force. If you jump out of an airplane and
fall you will pick up speed. (for simplicity\'s sake, let\'s ignore air
drag). To work out the kinetic energy at any point you simply multiply
the *value* of the force caused by gravity by the *distance* moved in
the direction of the force. For example, a 180 N boy falling a distance
of 10 m will have 1800 J of extra kinetic energy. We say that the man
has had 1800 J of work done on him by the force of gravity.

Notice that energy is *not* a vector. It has a value but no direction.
Gravity and displacement are vectors. They have a value plus a
direction. (In this case, their directions are down and down
respectively) The reason we can get a scalar energy from vectors gravity
and displacement is because, in this case, they happen to point in the
same direction. Gravity acts downwards and displacement is also
downwards.

When two vectors point in the same direction, you can get the scalar
product by just multiplying the *value* of the two vectors together and
ignoring the direction.

But what happens if they don\'t point in the same direction?

Consider a man walking up a hill. Obviously it takes energy to do this
because you are going against the force of gravity. The steeper the
hill, the more energy it takes every step to climb it. This is something
we all know unless we live on a salt lake.

In a situation like this we can still work out the work done. In the
diagram, the green lines represent the displacement. To find out how
much work *against* gravity the man does, we work out the *projection*
of the displacement along the line of action of the force of gravity. In
this case it\'s just the y component of the man\'s displacement. This is
where the cos θ comes in. θ is merely the angle between the velocity
vector and the force vector.

If the two forces do not point in the same direction, you can still get
the scalar product by multiplying the projection of one force in the
direction of the other force. Thus:
`{{PSG/eq|<math>\vec{a}\cdot\vec{b}\equiv \|\vec{a}\|\ \|\vec{b}\|\ \cos\theta</math>}}`{=mediawiki}
There is another method of defining the dot product which relies on
components.

  --------------------------------------------------
   $\vec{a}\cdot\vec{b}\equiv a_xb_x+a_yb_y+a_zb_z$
  --------------------------------------------------

##### What is a \"cross-product\"? (Force on a charged particle in a magnetic field)

**Answer:** Suppose there is a charged particle moving in a constant
magnetic field. According to the laws of electromagnetism, the particle
is acted upon by a force called the Lorentz force. If this particle is
moving from left to right at 30 m/s and the field is 30 Tesla pointing
straight down perpendicular to the particle, the particle will actually
curve in a circle spiraling out of the plane of the two with an
acceleration of its charge in coulombs times 900 newtons per coulomb!
This is because the calculation of the Lorentz force involves a
cross-product.when cross product can replace the sin0 can take place
during multiplication. A cross product can be calculated simply using
the angle between the two vectors and your right hand. If the forces
point parallel or 180° from each other, it\'s simple: the cross-product
does not exist. If they are exactly perpendicular, the cross-product has
a magnitude of the product of the two magnitudes. For all others in
between however, the following formula is used:

  --------------------------------------------------------------------------------------------------
   $\left\|\vec{a}\times\vec{b}\right\| = \left\|\vec{a}\right\|\ \left\|\vec{b}\right\|\sin\theta$
  --------------------------------------------------------------------------------------------------

!The right-hand rule: point your index finger along the first vector
and your middle finger across the second; your thumb will point in the
direction of the resulting
vector
But if the result is a vector, then what is the direction? That too is
fairly simple, utilizing a method called the \"right-hand rule\".

The right-hand rule works as follows: Place your right-hand flat along
the first of the two vectors with the palm facing the second vector and
your thumb sticking out perpendicular to your hand. Then proceed to curl
your hand towards the second vector. The direction that your thumb
points is the direction that cross-product vector points! Though this
definition is easy to explain visually it is slightly more complicated
to calculate than the dot product.

  ---------------------------------------------------------------------------------------------
   $(a_x,\ a_y,\ a_z)\times(b_x,\ b_y,\ b_z) =(a_yb_z-a_zb_y\ ,a_xb_z-a_zb_x\ ,a_xb_y-a_yb_x)$
  ---------------------------------------------------------------------------------------------

##### How to draw vectors that are in or out of the plane of the page (or board)

!How to draw vectors in the plane of the
paper
!Standard symbols of a vector going into or out of a
page
**Answer:** Vectors in the plane of the page are drawn as arrows on the
page. A vector that goes into the plane of the screen is typically drawn
as circles with an inscribed X. A vector that comes out of the plane of
the screen is typically drawn as circles with dots at their centers. The
X is meant to represent the fletching on the back of an arrow or dart
while the dot is meant to represent the tip of the arrow.


# Physics Study Guide/Topics

1.  Displacement, velocity, and
    acceleration
    -   Vectors and
        scalars
2.  Force
3.  Ropes and
    tension
4.  Gravity
5.  Momentum and collision
    force
6.  Energy
    -   Kinetic energy
7.  Friction
8.  Periodic Motion
9.  Torque
10. Circular Motion
    -   Center of Mass
    -   Inertia and moment of
        inertia
11. Strengths of materials: Stress and
    strain
12. Thermodynamics
    -   Power
13. Gases
    -   Ideal gases
    -   Pressure and partial
        pressure
14. Fluids
15. Density
16. Laminar flow in ideal
    fluids
17. Energy density
18. Real liquids
19. Sheer thickening and thinning
    fluids


# Physics Study Guide/Style Guide

#### Equations

For uniformity in the book a template should be used for embeding
equations. View the template at
Template:PSG/eq use it as follows

`{{PSG/eq|<math>ax^2+bx+c=0</math>}}`

Which gives

#### Units

Units should be given using the \\mathrm{} command and small spaces \\,
between the units. Vectors should be bold and italicized if they are
variables with the \\boldsymbol{} command.

`{{PSG/eq|<math>\sum\Delta\boldsymbol{p}=0~\mathrm{kg\,m/s}</math>}}`

-   Barry N. Taylor (2004), Guide for the Use of the International
    System of Units (SI) (version 2.2).
    Available1. National Institute of
    Standards and Technology, Gaithersburg, MD.

## Global Style Guidelines

-   Wikibooks Manual of Style