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{{DISPLAYTITLE:<span style="font-size:35%">Wright State University Lake Campus/</span><span style="font-size:75%">University Physics Volume 1</span><span style="font-size:35%">/Equations</span>}}
{{:OpenStax equations/Guild/A}}
[[File:Homebuilt sailboats racing at WSU Lake Campus.JPG|300px|thumb| {{User:Guy vandegrift/T/Courses now}}]]
{{green|Material customized for the first semester course at}} [[Physics equations/Equations|WSU Lake]] {{green|in '''green'''}}
===Math===
[[File:Theta in radians minimalistic.svg|left|thumb|110px|radian&arclength]][[File:Vector components with unit vectors.svg|left|140px|unit vectors|thumb]] Metric prefixes on page 5.
{{clear}}
{{colbegin}}
&#9645;&nbsp;Arclength <math>s</math> &#9645;&nbsp; <math>r</math> radius<br>
&#9645;&nbsp;<math>\theta = s/r</math> (in radians)<br>
&#9645;&nbsp;<math>C_\odot = \,2\pi r</math> Circumference of circle<br>
&#9645;&nbsp;<math>A_\odot = \,\pi r^2</math> Area of circle<br>
&#9645;&nbsp;<math>A_\bigcirc = 4\pi r^2</math> Area of sphere<br>
&#9645;&nbsp;<math>V_\bigcirc = \frac{4}{3}\pi r^3</math> Volume of sphere<br>
&#9645;&nbsp;<math>\vec\mathcal F\cdot d\vec s </math><math>=\mathcal F_xdx+\mathcal F_ydy = \mathcal F_rdr+\mathcal F_\theta rd\theta</math><br>

{{colend}}

===Mechanics===
=====Symbols=====
{{colbegin}}
&#9645;&nbsp;<math>\vec r = x\hat i + y\hat j + z\hat k = x\hat x + y\hat y + z\hat z</math> Position<br>
&#9645;&nbsp;<math>\Delta\vec\ell, d\vec\ell, \Delta\vec s, d\vec s </math> Line element (better than <math>d\vec r</math>)</br>
&#9645;&nbsp;<math>\vec v =d\vec r/dt</math> Velocity [m/s]<br>
&#9645;&nbsp;<math>\vec a =d\vec v/dt</math> Acceleration [m/s]<br>
&#9645;&nbsp;<math>\vec F=m \vec a</math> Force [N], Mass [kg], Acceleration [m/s<sup>2</sup>]<br>
&#9645;&nbsp;<math>f</math> Friction force [N] ''or'' frequency [Hz=s<sup>&minus;1</sup>] <br>
&#9645;&nbsp;<math>\mu_{s,k}</math> (static, kinetic) coefficient of friction<br>
&#9645;&nbsp;<math>\vec N</math> normal force<br>
&#9645;&nbsp;<math>g</math> gravitational constant (Earth: ''9.8m/s<sup>2</sup>'')<br>
{{green|Universal gravitational constant}} G≈{{val|6.67|e=-11|u=m<sup>3</sup>·kg<sup>−1</sup>·s<sup>−2</sup>}} <br>
&#9645;&nbsp;<math>W</math> Work [J=Nm=kg(m/s)<sup>2</sup>]<br>
&#9645;&nbsp;<math>P</math> Power [W=J/s]<br>
&#9645;&nbsp;<math>\vec p</math> Momentum<br>
&#9645;&nbsp;<math>p</math> Pressure (N/m<sup>2</sup>)<br> 
&#9645;&nbsp;<math>KE (PE)</math> Kinetic (Potential) Energy [J=Nm=Ws]<br>
&#9645;&nbsp;<math>(U_g, U_s)</math> Potential energy (gravity, spring)<br>
&#9645;&nbsp;<math>F=-k_s x</math> defines spring constant [N/m]<br>
&#9645;&nbsp;<math>T</math> Tension [N] ''or'' period [s] ''or'' temperature [K]<br>
&#9645;&nbsp;<math>Q</math> Heat [J=Ws]<br>
&#9645;&nbsp;<math>\theta</math> Angle (radians)<br>
&#9645;&nbsp;<math>\omega=d\theta/dt</math> Angular velocity (speed) [s<sup>&minus;1</sup>]<br> 
&#9645;&nbsp;<math>\alpha=d\omega/dt</math> Angular acceleration [s<sup>&minus;2</sup>]<br> 
&#9645;&nbsp;<math>I=\Sigma m_ir_i^2</math> Moment of inertia<br>
&#9645;&nbsp;<math>\tau =I\alpha</math> Torque &#9645;<math>L=I\omega</math> Angular momentum<br>
{{colend}}
{{clear}}

<div style="page-break-before:always"></div><!--simple pagebreak-->

=====Kinematics=====
<!--{|class="wikitable floatright" style="text-align:center; font-size:90%;"-->
{|class="wikitable" style="text-align:center; font-size:90%;"
|-
! class="unsortable"|Linear motion
! class="unsortable"|Rotational motion
! class="unsortable"|Defining equation
|-
|-
| Displacement = <math> \mathbf{x} </math>
| Angular displacement = <math> \theta </math>
|<math> \theta = \mathbf{s}/\mathbf{r}</math>
|-
|-
| Velocity = <math> \mathbf{v} </math>
| Angular velocity = <math> \omega </math>
| <math> \omega= \mathbf{d}\theta /\mathbf{dt}=\mathbf{v}/\mathbf{r}</math>
|-
|-
| Acceleration = <math> \mathbf{a} </math>
| Angular acceleration = <math> \alpha </math>
| <math> \alpha= \mathbf{d}\omega / \mathbf{dt}=\mathbf{a_\mathbf{t}}/\mathbf{r}</math>
|-
|-
| Mass = <math> \mathbf{m} </math>
| Moment of Inertia = <math> \mathbf{I} </math>
| <math> \mathbf{I}=\sum \mathbf{m_j}\mathbf{r_j}^2 </math>
|-
|-
| Force = <math> \mathbf{F} = \mathbf{m} \mathbf{a} </math>
| Torque = <math> \tau = \mathbf{I} \alpha </math>
| <math> \tau = \sum\mathbf{r_j} \mathbf{F}_\perp\mathbf{_j}=\sum\mathbf{r_{\perp j}} \mathbf{F}_\mathbf{_j}</math>
|-
|-
| Momentum= <math> \mathbf{p} = \mathbf{m} \mathbf{v} </math>
| Angular momentum= <math> \mathbf L = \mathbf{I} \omega</math>
| <math> \mathbf L = \sum\mathbf{r_j}\mathbf{p}\mathbf{_j}</math>
|-
|-
| Kinetic energy = <math> \frac 1 2\mathbf{m} \mathbf{v}^2 </math>
| Kinetic energy = <math> \frac 1 2\mathbf{I} \omega^2</math>
| <math> \frac 1 2 \sum\mathbf{m_j}\mathbf{v_j}^2 = \frac 1 2 \sum\mathbf{m_j}\mathbf{r_j}^2\omega^2</math>
|-
|}
{| class="wikitable floatright"
|-
!Vector notation
!Component notation
|-
|<math>\vec r-\vec r_0 = \vec v_0 t + \frac {1} {2} \vec a t^2 </math>
|<math> \vec v_0 =\vec v_{0x}\hat i + \vec v_{0y}\hat j +\vec v_{0z}\hat k </math>
|-
|<math>v^2 = v_0^2 + 2 \vec a \cdot (\vec r -\vec r_0)\,</math>
|Free fall: <math>a_x=0,\; a_y=-g</math>
|}
{| class="wikitable floatleft"
|-
!Linear motion
!Angular motion
|-
|<math>x-x_0 = v_0 t + \frac {1} {2} a t^2 </math>
|<math> \theta-\theta_0 = \omega _0 t + \frac{1}{2} \alpha t^2</math>
|-
|<math>v = v_0+at \,</math>
|<math> \omega = \omega _0 + \alpha t \,</math>
|-
|<math>x-x_0 = \frac {1} {2}(v_0+v) t </math>
|<math> \theta-\theta_0 = \frac{1}{2}(\omega _0 + \omega )t</math>
|-
|<math>v^2 = v_0^2 + 2 a (x -x_0)\,</math>
|<math> \omega^2 = \omega _0^2 + 2\alpha(\theta-\theta_0)</math>
|}{{clear}}

=====Equations=====
{{colbegin}}
&#9645;&nbsp;<math>KE = \frac 1 2 m v^2\,</math>&nbsp;
&#9645;&nbsp;<math>U_g = mgy+\mathcal C</math>&nbsp; &#9645;&nbsp;<math>U_s = \frac 1 2 k_s x^2</math><br>
&#9645;&nbsp;<small><math>\sum KE_f + \sum PE_f = \sum KE_i + \sum PE_i -Q</math></small><br>
&#9645;&nbsp;<small><math>W = F \ell\cos\theta=\vec F\cdot\vec\ell\Rightarrow\sum \vec F\cdot\Delta\ell\Rightarrow\int \vec F\cdot\Delta\ell</math></small><br>
&#9645;&nbsp;<small><math>P=\frac{\vec F \cdot \vec\Delta \ell}{\Delta t}=\vec F\cdot\vec v</math></small> is power<br>
&#9645;&nbsp;<math>\vec p = m\vec v</math> Momentum<br>
&#9645;&nbsp;<small><math>\sum \vec p_f = \sum \vec p_f + \int \vec F_{ext} dt</math></small><br>
&#9645;&nbsp;<small><math>m_1v_1+m_2v_2=(m_1+m_2)v_f</math></small> Inelastic collision<br>
&#9645;&nbsp;<math>\omega T = 2\pi \Leftrightarrow fT=1</math> frequency-period<br> 
&#9645;&nbsp;<math>a=v^2/r=\omega v = \omega^2 r</math> centripetal acceleration<br>
&#9645;&nbsp;<math>\sum \vec F_j=0=\sum\vec \tau_j</math> <math>\tau=rF_\perp</math> statics<br>
&#9645;&nbsp;<math>f_s\le\mu_sN ,\; f_k=\mu_kN</math> friction<br>
&#9645;&nbsp;<math>\vec F_{12}=G\tfrac{m_1m_2}{r^2}\hat r_{12}</math> Newtonian gravity<br>
&#9645;&nbsp;<math>\vec F_{12}=G\tfrac{m_1m_2}{r^2}\hat r_{12}</math>Newtonian gravity<br>
&#9645;&nbsp;<math>g=G\tfrac{M}{r^2}</math> planet's surface gravity<br> 
{{colend}}

====Fluid_Mechanics====
[[File:Archimedes gv52.png|thumb|120px|Pressure is the weight per unit area of the fluid above a point.]]
&#9645; [[w:Mass density|Mass density]] <math>\rho=m/V\;</math>

&#9645; [[w:Pressure|Pressure]] <math>P=F/A\;</math> 


Buoyant force <math>B</math> equals weight of the displaced fluid.  If <math>W</math> is the weight of a cylindrical object, the displaced volume is <math>A\Delta h</math>

{{spaces|3}}&#9645; <math>B=\rho_{flu}(A\Delta h )g</math> and &#9645; <math>W = \rho_{obj}(A\Delta h )g = M_{obj}g</math>

&#9645; [[w:Vertical pressure variation|Pressure vs depth/height]] (constant density)<math>\,p=p_o+\rho gh \Leftarrow dp/dy = -\rho g</math> 

&#9645; [[w:Volumetric flow rate|Volume flow rate]] <math>Q=dV/dt\;</math> 

&#9645; [[w:Continuity equation|Continuity equation]] <math>\rho_1A_1v_1=\rho_2A_2v_2</math><math>\Rightarrow A_1v_1=A_2v_2\text{ if }\rho=const.\;</math> 

&#9645; [[w:Bernoulli%27s_principle#Incompressible_flow_equation|Bernoulli's principle]] <math>p_1+\tfrac 1 2 \rho v_1^2 + \rho gy_1=p_2+\tfrac 1 2 \rho v_2^2 + \rho gy_2</math>

====Oscillations====

&#9645;&nbsp;Simple harmonic motion <math>x(t)=A\cos(\omega t+\phi),\,
 </math> <math>v(t)=-A\omega\sin(\omega t+\phi),\,</math> <math>
  a(t)=-A\omega^2\cos(\omega t+\phi)</math> 

&#9645;&nbsp;<math>\,x_{max}=A,\;v_{max}=A\omega,\;a_{max}=A\omega^2 </math>, where <math>
  \omega=\sqrt{k/m};\,</math> and <math>k</math> is spring constant

&#9645;&nbsp;Energy <math>E_{Tot}=\tfrac 1 2 kx^2 + \tfrac 1 2 mv^2 = 
\tfrac 1 2 mv_{max}^2 = \tfrac 1 2 kx_{max}^2</math>

===={{Green|Physics of hearing (extracted from [[Physics equations]])}}====
*<math>v_s =\sqrt{   \frac{T}{273}    }\cdot 331 \text{m/s}</math> speed of sound (T in Kelvins). <math>v_s=\sqrt{\frac{\gamma k_B T}{m}}</math> where <math>\gamma \approx 1.4</math> 
*<math>v =\sqrt{   \frac{F}{\mu}    }</math> Speed of a stretched string wave: <math>F</math> is the tension and <math>\mu</math> is the linear mass density (kilograms per meter).
[[File:StandingWaves.png|right|180px]]
*<math>f\lambda =  v_p</math> relates the frequency, f, wavelength, &lambda;,and the the phase speed, v<sub>p</sub> of the wave (also written as v<sub>w</sub>)   This phase speed is the speed of individual crests, which for sound and light waves also equals the speed at which a [[w:wave packet|wave packet]] travels. 
*<math>L = \frac{n\lambda_n}{2}</math> describes the n-th normal mode vibrating wave on a string that is fixed at both ends (i.e. has a node at both ends).  The mode number, n = 1, 2, 3,..., as shown in the figure.
*Beat frequency: The frequency of beats heard if two closely space frequencies, <math>f_1</math> and <math>f_2</math>, are played is <math>\Delta f = |f_2-f_1|</math>.
*Musical acoustics: Frequency ratios of 2/1, 3/2, 4/3, 5/3, 5/4, 6/5, 8/5 are called the ([[w:Just intonation|just]]) "[[w:Octave|octave]]", "[[w:Perfect fifth|fifth]]",     "[[w:Perfect fourth|fourth]]", "[[w:Major sixth|major-sixth]]", "[[w:Major third|major-third]]", "[[w:Minor third|minor-third]]", and "[[w:Minor sixth|minor-sixth]]",  respectively.
===Thermodynamics===
====Constants and conversions====
*'''Boltzmann's constant''' = k<sub>B</sub>≈ {{nowrap|1.38 × 10<sup>-23</sup> [[w:Joule|J]] [[w:Kelvin|K]]<sup>−1</sup> }}, and the '''gas constant''' is R&nbsp;= {{nowrap|N<sub>A</sub>k<sub>B</sub>}}≈{{nowrap|8.314 [[w:Joule|J]]   [[w:Kelvin|K]]<sup>−1</sup>  [[w:Mole (unit)|mol]]<sup>−1</sup>}}, where N<sub>A</sub>≈ {{nowrap|6.02 × 10<sup>23</sup>}} is the Avogadro number.
*Boltzmann's constant can also be written in eV and Kelvins: k<sub>B</sub> ≈{{nowrap|8.6 × 10<sup>-5</sup> eV/deg}}, where {{nowrap begin}}1eV=1.602x10<sup>&minus;19</sup> Joules{{nowrap end}}
* <math>T_C=T_K-273.15</math> converts from Celsius to Kelvins, and <math>T_F=\frac 9 5 T_C+32</math> converts from Celsius to Fahrenheit.
* 1 amu =  1 u ≈ 1.66 × 10<sup>-27</sup> kg is the approximate mass of a proton or neutron.

====13-Temperature, Kinetic Theory, and Gas Laws====


* <math>PV=nRT=Nk_BT</math> is the '''[[w:ideal gas law|ideal gas law]]''', where P is pressure, V is volume, n is the number of moles and N is the number of atoms or molecules.  Temperature is in Kelvins.  

* <math>\frac 3 2 k_B T =\frac 1 2 mv_{rms}^2</math> is the average translational kinetic energy per "atom" of a 3-dimensional ideal gas. 
*<math>v_{rms}=\sqrt{\frac{3k_BT}{m}}=\sqrt{\overline{v^2}}</math> is the root-mean-square speed of atoms in an ideal gas.

===14-Heat and Heat Transfer===
<section begin=14-Heat_and_Heat_Transfer/>
Here it is convenient to define '''[[w:heat|heat]]''' as energy that passes between two objects of different temperature <math>Q</math> The SI unit is the Joule.  The rate of heat trasfer, <math>\Delta Q/\Delta t</math> or  <math>\dot Q</math> is "power": {{nowrap begin}}1 Watt = 1 W = 1J/s{{nowrap end}} 
* <math>Q = mc_S\Delta T</math> is the heat required to change the temperature of a substance of mass, m.  The change in temperature is &Delta;T.  The '''[[w:Heat capacity|specific heat]]''', c<sub>S</sub>, depends on the substance (and to some extent, its temperature and other factors such as pressure).  Heat is the transfer of energy, usually from a hotter object to a colder one.  The units of specfic heat are ''energy/mass/degree'', or {{nowrap begin}}J/(kg-degree){{nowrap end}}.
* <math>Q = mL</math> is the heat required to change the phase of a a mass, m, of a substance (with no change in temperature).  The '''[[w:latent heat|latent heat]]''', L, depends not only on the substance, but on the nature of the phase change for any given substance.  L<sub>F</sub> is called the latent heat of fusion, and refers to the melting or freezing of the substance.  L<sub>V</sub> is called the latent heat of vaporization, and refers to evaporation or condensation of a substance.
*<math>\dot Q= \frac{k_cA}{d}\Delta T</math> is rate of heat transfer for a material of area, A. The difference in temperature between two sides separated by a distance, d, is <math>\Delta T</math>.  The '''[[w:thermal conductivity|thermal conductivity]]''', k<sub>c</sub>, is a property of the substance used to insulate, or subdue, the flow of heat.

===15-Thermodynamics===
[[File:Piston gv52.png|thumb]]
* Here, Pressure (P), Energy (E), Volume (V), and Temperature (T) are the [[w:State_function|state functions]].
[[File:PdV work cycle.gif|right|130px]]
*The net work done per cycle is the area enclosed by the loop and equals the net heat flow into the system, <math>Q_{in} - Q_{out} </math> (valid only for closed loops).
* <math>\Delta W=-F\Delta x= ( -P\cdot\mathrm{Area} ) \left( \frac{\Delta V}{\mathrm{Area}} \right) = -P\Delta V</math> is the work done on a system of pressure P by a piston of voulume V.  If ΔV>0 the substance is expanding as it exerts an outward force, so that ΔW<0 and the substance is doing work on the universe; ΔW>0 whenever the universe is doing work on the system. 
* <math>\Delta Q</math> is the amount of heat (energy) that flows into a system. It is positive if the system is placed in a ''heat bath'' of higher temperature.  If this process is reversible, then the heat bath is at an infinitesimally higher temperature and a finite &Delta;Q takes an infinite amount of time.
* <math>\Delta E=\Delta Q-P\Delta V</math> is the change in energy ([[w:First Law of Thermodynamics|First Law of Thermodynamics]]).
*<math> -\int P \ dV</math> is work done ''on'' system. <math> \oint P \ dV = Q_{in} - Q_{out}</math> is work (out) per cycle.
<div style="page-break-before:always"></div>

==Original (long) formula sheet==
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Introduction}}
#{{green|The circumference of a circle is}} <math>C_\odot = \,2\pi r</math> and the circle's area is <math>A_\odot = \,\pi r^2</math> is its area.  
#The surface area of a sphere is <math>A_\bigcirc = 4\pi r^2</math> and sphere's volume is <math>V_\bigcirc = \frac{4}{3}\pi r^3</math> 
#{{green|1 kilometer}} = .621 miles and  1 MPH = 1 mi/hr ≈ .447 m/s
#{{green|Typical  air density}} is 1.2kg/m<sup>3</sup>, with pressure 10<sup>5</sup>Pa. The density of water is 1000kg/m<sup>3</sup>.
#{{green|Earth's mean radius ≈ 6371km, mass ≈ }}{{val|6|e=24|u=kg}} 
#{{green|Universal gravitational constant}} = G ≈ {{val|6.67|e=-11|u=m<sup>3</sup>·kg<sup>−1</sup>·s<sup>−2</sup>}} 
#{{green|Speed of sound ≈ 340m/s and the speed of light}} = c ≈ 3×10<sup>8</sup>m/s 
#{{green|One light-year ≈ 9.5×10<sup>15</sup>m ≈ 63240AU (Astronomical unit) }} 
#{{green|1 amu (or 1 u) ≈ 1.66 × 10<sup>-27</sup> kg is the approximate mass of a proton or neutron}}.... <small><These 8 equations were added for WSU-L exams</small>>

{{#lst:OpenStax University Physics Volume 1/Equations (master)|Units_and_Measurement}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Vectors}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Motion_Along_a_Straight_Line}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Motion_in_Two_and_Three_Dimensions}}

'''{{Green|This is a transclusion, added two days before Test 1}}'''

{|
|-
| <math>x=x_0+v_{0x}\Delta t+\frac{1}{2}a_x\Delta t^2</math>
||{{spaces|5}}<math>v_x=v_{0x}+a_x \Delta t</math>
||{{spaces|5}}<math>v_x^2=v_{x0}^2+ 2a_x\Delta x </math>
|-
| <math>y=y_0+v_{0y}\Delta t+\frac{1}{2}a_y\Delta t^2</math>
||{{spaces|5}}<math>v_y=v_{0y}+a_y \Delta t</math>
||{{spaces|5}}<math>v_y^2=v_{x0}^2+ 2a_y\Delta y </math>
|}
<math>v^2=v_0^2+ 2a_x\Delta x + 2a_y\Delta y</math> &nbsp; ...<small>in advanced notation this becomes</small>  <math>\Delta (v^2) = 2\vec a\cdot\Delta\vec\ell</math>.

In [[w:free fall|free fall]] we often set, ''a<sub>x</sub>=0''  and  ''a<sub>y</sub>= -g''.  If angle is measured with respect to the x axis:

<math> v_x =  v\cos\theta</math> {{spaces|6}}<math> v_y =  v\sin\theta</math> {{spaces|6}}<math> v_{x0} =  v_0\cos\theta_0</math> {{spaces|6}}<math> v_{y0} =  v_0\sin\theta_0</math>


{{#lst:OpenStax University Physics Volume 1/Equations (master)|Newton's_Laws_of_Motion}}
[[File:UniCircMot gv52.png|thumb|180px|{{green|Use for}} [[special:permalink/1411691|'''this quiz''']]]]
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Applications_of_Newton's_Laws}}
[[File:Threetensions.jpg|180px|right]]
{{Green|The x and y components of the three forces of tension on the small grey circle where the three "massless" ropes meet are:}}
:<math>T_{1x}=-T_1\cos\theta_1 </math> ,&nbsp;  &nbsp;  &nbsp;  &nbsp; <math> T_{1y}=T_1\sin\theta_1</math>
:<math>T_{2x}=0 </math> ,&nbsp; &nbsp;  &nbsp; &nbsp;  &nbsp; &nbsp;  &nbsp; &nbsp;  &nbsp; &nbsp; &nbsp;  &nbsp; &nbsp;  &nbsp;  &nbsp;<math>T_{2y}=-mg</math>
:<math>T_{3x}=T_3\cos\theta_3 </math> ,&nbsp;  &nbsp;  &nbsp;  &nbsp;  &nbsp; <math>T_{3y}=T_3\sin\theta_3</math>

{{Green|Also transcluded from [[Physics equations]]}}
* <math>2\pi\;rad=360\;deg=1\;rev</math> relates the radian, degree, and revolution.
*<math>f = \frac{\#\,\text{revs}}{\#\,\text{secs}}</math> is the number of revolutions per second, called '''[[w:frequency|frequency]]'''.
*<math>T = \frac{\#\,\text{secs}}{\#\,\text{revs}}</math> is the number of seconds per revolution, called '''[[w:period|period]]'''.  Obviously <math>fT = 1</math>.
*<math>\omega = \frac{\Delta\theta}{\Delta t}</math> is called '''[[w:angular frequency|angular frequency]]''' (ω is called omega, and &theta; is measured in radians).  Obviously <math>\omega T = 2\pi</math>
* <math>a=\frac{v^2}{r}=\omega v =\omega^2 r</math> is the acceleration of '''[[w:Circular_motion#Uniform|uniform circular motion]]''', where v is speed, and r is radius.
* <math>v=\omega r =2\pi r/T</math>, where T is period.

{{#lst:OpenStax University Physics Volume 1/Equations (master)|Work_and_Kinetic_Energy}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Potential_Energy_and_Conservation_of_Energy}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Linear_Momentum_and_Collisions}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Fixed-Axis_Rotation}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Angular_Momentum}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Static_Equilibrium_and_Elasticity}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Gravitation}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Fluid_Mechanics}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Oscillations}}
{{#lst:OpenStax University Physics Volume 1/Equations (master)|Waves}}
<!--{{#lst:OpenStax University Physics Volume 1/Equations (master)|Sound}}-->
===={{Green|Sound}}====
[[w:special:permalink/816047502#Mathematical_definition|Pressure]] and [[w:special:permalink/793294895|displacement]] fluctuations in a sound wave
<math>P=\Delta P_{max}\sin(kx\mp\omega t +\phi)</math> and <math>s=s_{max}\cos(kx\mp\omega t +\phi)</math>

<!--keep together-->
&#9645;&nbsp;[[w:special:permalink/817484953|Speed of sound]] in a fluid <math>v=f\lambda=\sqrt{\beta/\rho}</math>,
&#9645;&nbsp;in a solid <math>\sqrt{Y/\rho}</math>,
&#9645;&nbsp;in an idal gas <math>\sqrt{\gamma RT/M}</math>,
&#9645;&nbsp;in air <math>331\tfrac m s\sqrt{\tfrac{T_K}{273\,K}}=331\tfrac m s\sqrt{1+\tfrac{T_C}{273^oC}}</math>

====={{Green|Physics of hearing (extracted from [[Physics equations]])}}=====
{{#lst:Physics_equations/Equations|17-Physics_of_Hearing}}
[[File:StandingWaves.png|right|180px]]
*<math>f\lambda =  v_p</math> relates the frequency, f, wavelength, &lambda;,and the the phase speed, v<sub>p</sub> of the wave (also written as v<sub>w</sub>)   This phase speed is the speed of individual crests, which for sound and light waves also equals the speed at which a [[w:wave packet|wave packet]] travels. 
*<math>L = \frac{n\lambda_n}{2}</math> describes the n-th normal mode vibrating wave on a string that is fixed at both ends (i.e. has a node at both ends).  The mode number, n = 1, 2, 3,..., as shown in the figure.
*Beat frequency: The frequency of beats heard if two closely space frequencies, <math>f_1</math> and <math>f_2</math>, are played is <math>\Delta f = |f_2-f_1|</math>.
*Musical acoustics: Frequency ratios of 2/1, 3/2, 4/3, 5/3, 5/4, 6/5, 8/5 are called the ([[w:Just intonation|just]]) "[[w:Octave|octave]]", "[[w:Perfect fifth|fifth]]",     "[[w:Perfect fourth|fourth]]", "[[w:Major sixth|major-sixth]]", "[[w:Major third|major-third]]", "[[w:Minor third|minor-third]]", and "[[w:Minor sixth|minor-sixth]]",  respectively.

===={{Green|Kinetic theory of gasses}}====
* <math>T_C=T_K-273.15</math> converts from Celsius to Kelvins, and <math>T_F=\frac 9 5 T_C+32</math> converts from Celsius to Fahrenheit.
* <math>PV=nRT=Nk_BT</math> is the '''[[w:ideal gas law|ideal gas law]]''', where <math>P</math> is pressure, <math>V</math> is volume, <math>n</math> is the number of moles and <math>N</math> is the number of atoms or molecules.  Temperature must be measured on an absolute scale (e.g. Kelvins).  
*'''Boltzmann's constant''' = <math>k_B</math>≈ {{nowrap|1.38 × 10<sup>-23</sup> [[w:Joule|J]] [[w:Kelvin|K]]<sup>−1</sup> }}, and the '''gas constant''' is <math>R=N_Ak_B</math> ≈{{nowrap|8.314 [[w:Joule|J]]   [[w:Kelvin|K]]<sup>−1</sup>  [[w:Mole (unit)|mol]]<sup>−1</sup>}}, where <math>N_A</math>≈ {{nowrap|6.02 × 10<sup>23</sup>}} is the Avogadro number. Boltzmann's constant can also be written in eV and Kelvins: k<sub>B</sub> ≈{{nowrap|8.6 × 10<sup>-5</sup> eV/deg}}.
* <math>\frac 3 2 k_B T =\frac 1 2 mv_{rms}^2</math> is the average translational kinetic energy per "atom" of a 3-dimensional ideal gas. 
*<math>v_{rms}=\sqrt{\frac{3k_BT}{m}}=\sqrt{\overline{v^2}}</math> is the root-mean-square speed of atoms in an ideal gas.
* <math>E = \frac{\varpi}{2}Nk_BT</math> is the total energy of an ideal gas, where <math>\varpi=3\;</math> only if the gas is monatomic.

===={{Green|Thermodynamics}}====
{{#lst:Physics_equations/Equations|15-Thermodynamics}}



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[[Category:Quizbank/Equations]]