Physics Reference

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Kinematics

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

Equations
$x=x_0+v_{0}t+\frac{1}{2}a{t}^2$
$v=\frac{\Delta s}{t}$
$a=\frac{\Delta v}{t}$
$v=v_0+at$
$v^2=v_0^2+2a(x-x_0)$
$\vec{a}\cdot \vec{b}=|a|\times |b|\times cos\left(\theta \right)$
$\vec{a}\times \vec{b}=a_x{b}_x+a_y{b}_y$
$|\vec{a}|=\sqrt{a_x^2+a_y^2}$
$\Delta v=\frac{\Delta x}{t}$
$\Delta x=x_2-x_1$
$W=K_f-K_i$
$K=\frac{1}{2}m{v}^2$
$W_g=-mg\Delta y$

Electromagnetism

Constants
Vacuum permittivity	${\epsilon }_0=8.9875517873681764\times {10}^{-12}\frac{F}{m}$
Mass of electron	$9.10938356\times {10}^{-31}kg$
Mass of proton	$1.6726219\times {10}^{-27}kg$
Coulomb's constant	$k=8.9875517873681764\times {10}^9\frac{N{m}^2}{C^2}$
Elementary electric charge	$1.60217662\times {10}^{19}C$

Equations
$$F=ma=k\frac{q_1{q}_2}{r^2}=Eq$$
$$E=k\frac{q}{r^2}$$
$$\tau =rFsin\left(\theta \right)$$
$$E_{\text{ring}}=k\frac{qz}{{z^2+r^2}^{\frac{3}{2}}}$$
$$\lambda =\frac{q}{2\pi r}$$
$$\sigma =\frac{q}{\pi r^2}$$
$$E_{\text{disk}}=2\pi k\sigma \left(\frac{1-z}{\sqrt{z^2+r^2}}\right)$$
$$E_{\text{dipole}}=\frac{2kqd}{z^3}$$
$$\Phi =\frac{q_{\text{enc}}}{{\epsilon }_0}$$
$$E_{\text{inf. rod}}=\frac{1}{2\pi {\epsilon }_0}\frac{\lambda }{d}$$
$$E_{\text{inf. sheet}}=\frac{\sigma }{2{\epsilon }_0}$$

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