Generic Formulas

Kinematics

$v=v_0+at$

$\Delta x=\frac{v+v_0}{2}t$

$\Delta x=v_{0}t+\frac{1}{2}a{t}^2$

$v^2=v_0^2+2a\Delta x$

Rotational Kinematics

$\omega ={\omega }_0+\alpha t$

${\omega }^2={\omega }_0^2+2\alpha (\theta -{\theta }_0)$

$\theta -{\theta }_0=\frac{1}{2}({\omega }_0+\omega )t$

$\theta ={\theta }_0+{\omega }_{0}t+\frac{1}{2}\alpha t^2$

Linear to Rotational Motion

Displacement: $s=r\theta$

Velocity: $\omega r=v$

Acceleration: $a=r\alpha$

Energy

$k=\frac{1}{2}m{v}^2$

$k=\frac{1}{2}I{\omega }^2$

Momentum

Linear Momentum: $p=mv$ (in $\frac{kgm}{s}$)

Angular Momentum: $L=mvr$ or $L=I\omega$ (in $\frac{kg{m}^2}{s}$)

Summary of Basic Gas Processes

Process	Definition	Stays Constant	Work	Heat
Isochoric (Same volume)	$\Delta V=0$	$V$ and $\frac{p}{T}$	$W=0$	$Q=n{C}_V\Delta T$
Isobaric (Same pressure)	$\Delta p=0$	$p$ and $\frac{V}{T}$	$W=-p\Delta V$	$Q=n{C}_P\Delta T$
Isothermal (Same temp)	$\Delta T=0$	$T$ and $pV$	$W=-nRT\ln (\frac{V_f}{V_i})$	$\Delta E_{th}=0$
Adiabatic	$Q=0$	$p{V}^{\gamma }$	$W=\Delta E_{th}$	$Q=0$
All gas processes	First Law $\Delta E_{th}=W+Q=n{C}_V\Delta T$		Ideal-gas law $pV=nRT$

Gas	$C_P$	$C_V$	$C_P-C_V$
Monoatomic Gases
$He$	20.8	12.5	8.3
$Ne$	20.8	12.5	8.3
$Ar$	20.8	12.5	8.3
Diatomic Gases
$H_2$	28.7	20.4	8.3
$N_2$	29.1	20.8	8.3
$O_2$	29.2	20.9	8.3

Specific Heat Capacity: $Q=mc\Delta T$

Thermodynamics

$\Delta E_{th}=W+Q$

Inertias

Inertia about solid cylinder (disk): $I=\frac{1}{2}M{R}^2$

Inertia about hollow hoop: $I=M{R}^2$

Inertia in solid sphere: $I=\frac{2}{5}M{R}^2$

Inertia about spherical shell: $I=\frac{2}{3}M{R}^2$

Inertia of rod about center: $I=\frac{1}{12}M{L}^2$

Inertia of rod about end: $I=\frac{1}{3}M{L}^2$

Parallel Axis Theorem: $I=I_{cm}+m{d}^2$ where d is the perpendicular distance between the axes

Torque

Torque $=r\times F=|r||F|\sin (\theta )=\tau$

Constants and Conversions

$g=9.8\frac{m}{s^2}$

$G=6.6710-11N\frac{m^2}{k{g}^2}$ (gravitational constant) $R=8.314\frac{J}{molK}$ (ideal gas constant) $k=1.38\times 10^{-23}\frac{J}{K}$ (Boltzmann constant)

$1atm=101000Pa$ ($1Pa=1\frac{N}{m^2}$)

$0^{\circ }C=273.15K$

Specific heat capacity of liquid water = $4190\frac{J}{kgK}$

Specific heat capacity of water ice = $2100\frac{J}{kgK}$

Latent heat of fusion for water = $3.34\times 10^5\frac{J}{kg}$

Latent heat of vaporization for water = $2.26\times 10^6\frac{J}{kg}$