Physics Formula Sheet: Electromagnetism, Mechanics, and Waves

Vocabulary practice flashcards covering all base formulas and their algebraic rearrangements across Electromagnetism, Mechanics, and Waves.

$$E = \frac{V}{d}$$

Electromagnetism formula relating electric field, voltage, and distance; rearranges to $V = Ed$ and $d = \frac{V}{E}$.

$$F = Eq$$

Electromagnetism formula relating electric force, electric field, and charge; rearranges to $E = \frac{F}{q}$ and $q = \frac{F}{E}$.

$$\Delta E_p = Eqd$$

Electromagnetism formula for change in potential energy; rearranges to $E = \frac{\Delta E_p}{qd}$, $q = \frac{\Delta E_p}{Ed}$, and $d = \frac{\Delta E_p}{Eq}$.

$$E_k = \frac{1}{2}mv^2$$

Formula for kinetic energy; rearranges to $m = \frac{2E_k}{v^2}$ and $v = \sqrt{\frac{2E_k}{m}}$.

$$F = BIL$$

Electromagnetism formula for magnetic force on a current-carrying wire; rearranges to $B = \frac{F}{IL}$, $I = \frac{F}{BL}$, and $L = \frac{F}{BI}$.

$$F = Bqv$$

Electromagnetism formula for magnetic force on a moving charge; rearranges to $B = \frac{F}{qv}$, $q = \frac{F}{Bv}$, and $v = \frac{F}{Bq}$.

$$I = \frac{q}{t}$$

Electromagnetism formula for electric current; rearranges to $q = It$ and $t = \frac{q}{I}$.

$$V = \frac{\Delta E}{q}$$

Electromagnetism formula relating electric potential difference to energy and charge; rearranges to $\Delta E = Vq$ and $q = \frac{\Delta E}{V}$.

$$V = IR$$

Electromagnetism formula relating voltage, current, and resistance; rearranges to $I = \frac{V}{R}$ and $R = \frac{V}{I}$.

$$V = BvL$$

Electromagnetism formula for induced voltage; rearranges to $B = \frac{V}{vL}$, $v = \frac{V}{BL}$, and $L = \frac{V}{Bv}$.

$$P = IV$$

Electromagnetism formula for electric power; rearranges to $I = \frac{P}{V}$ and $V = \frac{P}{I}$.

$$P = \frac{\Delta E}{t}$$

Formula for power in terms of energy transferred over time; rearranges to $\Delta E = Pt$ and $t = \frac{\Delta E}{P}$.

$$R_T = R_1 + R_2 + \dots$$

Electromagnetism formula for total resistance in series; rearranges to $R_1 = R_T - R_2 - \dots$.

$$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$$

Electromagnetism formula for total resistance in parallel; rearranges to $R_T = \left(\frac{1}{R_1} + \frac{1}{R_2} + \dots\right)^{-1}$.

$$v = \frac{\Delta d}{\Delta t}$$

Mechanics formula for average velocity; rearranges to $\Delta d = v\Delta t$ and $\Delta t = \frac{\Delta d}{v}$.

$$a = \frac{\Delta v}{\Delta t}$$

Mechanics formula for acceleration; rearranges to $\Delta v = a\Delta t$ and $\Delta t = \frac{\Delta v}{a}$.

$$v_f = v_i + at$$

Mechanics kinematic formula relating final velocity, initial velocity, acceleration, and time; rearranges to $v_i = v_f - at$, $a = \frac{v_f - v_i}{t}$, and $t = \frac{v_f - v_i}{a}$.

$$d = v_it + \frac{1}{2}at^2$$

Mechanics kinematic formula for displacement; rearranges to $v_i = \frac{d - \frac{1}{2}at^2}{t}$ and $a = \frac{2(d - v_it)}{t^2}$.

$$d = \frac{v_i + v_f}{2}t$$

Mechanics kinematic formula for displacement using average velocity; rearranges to $v_i = \frac{2d}{t} - v_f$, $v_f = \frac{2d}{t} - v_i$, and $t = \frac{2d}{v_i + v_f}$.

$$v_f^2 = v_i^2 + 2ad$$

Mechanics kinematic formula relating velocities, acceleration, and displacement; rearranges to $v_i = \sqrt{v_f^2 - 2ad}$, $a = \frac{v_f^2 - v_i^2}{2d}$, and $d = \frac{v_f^2 - v_i^2}{2a}$.

$$a_c = \frac{v^2}{r}$$

Mechanics formula for centripetal acceleration; rearranges to $v = \sqrt{a_cr}$ and $r = \frac{v^2}{a_c}$.

$$p = mv$$

Mechanics formula for momentum; rearranges to $m = \frac{p}{v}$ and $v = \frac{p}{m}$.

$$\Delta p = F\Delta t$$

Mechanics formula relating impulse to change in momentum; rearranges to $F = \frac{\Delta p}{\Delta t}$ and $\Delta t = \frac{\Delta p}{F}$.

$$E_p = mg\Delta h$$

Mechanics formula for gravitational potential energy; rearranges to $m = \frac{E_p}{g\Delta h}$ and $\Delta h = \frac{E_p}{mg}$.

$$E_p = \frac{1}{2}kx^2$$

Mechanics formula for elastic potential energy; rearranges to $k = \frac{2E_p}{x^2}$ and $x = \sqrt{\frac{2E_p}{k}}$.

$$W = Fd$$

Mechanics formula for work done; rearranges to $F = \frac{W}{d}$ and $d = \frac{W}{F}$.

$$P = \frac{W}{t}$$

Mechanics formula for power in terms of work done over time; rearranges to $W = Pt$ and $t = \frac{W}{P}$.

$$F = ma$$

Mechanics formula for force; rearranges to $m = \frac{F}{a}$ and $a = \frac{F}{m}$.

$$\tau = Fd$$

Mechanics formula for torque; rearranges to $F = \frac{\tau}{d}$ and $d = \frac{\tau}{F}$.

$$F = -kx$$

Mechanics formula for restoring force in a spring; rearranges to $k = -\frac{F}{x}$ and $x = -\frac{F}{k}$.

$$F_c = \frac{mv^2}{r}$$

Mechanics formula for centripetal force; rearranges to $m = \frac{F_cr}{v^2}$, $v = \sqrt{\frac{F_cr}{m}}$, and $r = \frac{mv^2}{F_c}$.

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$

Waves formula for focal length, object distance, and image distance; rearranges to $f = \left(\frac{1}{d_o} + \frac{1}{d_i}\right)^{-1}$, $d_o = \left(\frac{1}{f} - \frac{1}{d_i}\right)^{-1}$, and $d_i = \left(\frac{1}{f} - \frac{1}{d_o}\right)^{-1}$.

$$s_is_o = f^2$$

Waves optics formula relating extra-focal distances to focal length; rearranges to $s_i = \frac{f^2}{s_o}$, $s_o = \frac{f^2}{s_i}$, and $f = \sqrt{s_is_o}$.

$$m = \frac{d_i}{d_o}$$

Waves formula for magnification using image distance and object distance; rearranges to $d_i = md_o$ and $d_o = \frac{d_i}{m}$.

$$m = \frac{h_i}{h_o}$$

Waves formula for magnification using image height and object height; rearranges to $h_i = mh_o$ and $h_o = \frac{h_i}{m}$.

$$m = \frac{f}{s_o}$$

Waves formula for magnification using focal length and $s_o$; rearranges to $f = ms_o$ and $s_o = \frac{f}{m}$.

$$m = \frac{s_i}{f}$$

Waves formula for magnification using focal length and $s_i$; rearranges to $s_i = mf$ and $f = \frac{s_i}{m}$.

$$n_1\sin(\theta_1) = n_2\sin(\theta_2)$$

Waves formula for refraction; rearranges to $n_1 = \frac{n_2\sin(\theta_2)}{\sin(\theta_1)}$, $\sin(\theta_1) = \frac{n_2\sin(\theta_2)}{n_1}$, $n_2 = \frac{n_1\sin(\theta_1)}{\sin(\theta_2)}$, and $\sin(\theta_2) = \frac{n_1\sin(\theta_1)}{n_2}$.

$$\frac{n_1}{n_2} = \frac{v_2}{v_1}$$

Waves formula relating indices of refraction and wave velocities; rearranges to $n_1 = n_2\left(\frac{v_2}{v_1}\right)$ and $v_1 = v_2\left(\frac{n_2}{n_1}\right)$.

$$\frac{v_2}{v_1} = \frac{\lambda_2}{\lambda_1}$$

Waves formula relating wave velocities and wavelengths; rearranges to $v_2 = v_1\left(\frac{\lambda_2}{\lambda_1}\right)$ and $\lambda_1 = \lambda_2\left(\frac{v_1}{v_2}\right)$.

$$v = f\lambda$$

Waves wave equation; rearranges to $f = \frac{v}{\lambda}$ and $\lambda = \frac{v}{f}$.

$$f = \frac{1}{T}$$

Waves formula relating frequency and period; rearranges to $T = \frac{1}{f}$.

$$v = \frac{d}{t}$$

Waves formula relating speed, distance, and time; rearranges to $d = vt$ and $t = \frac{d}{v}$.