$$ v = u + at $$ $$ s = ut + \frac{1}{2}at^2 $$ $$ v^2 = u^2 + 2as $$ $$ s_n = u + \frac{a}{2}(2n – 1) $$

$$ \vec{F}_{\text{net}} = \frac{d\vec{p}}{dt} = m\vec{a} $$ $$ \vec{p} = m\vec{v} $$ $$ \vec{J} = \Delta \vec{p} = \int \vec{F}\,dt = \vec{F}_{\text{avg}}\Delta t $$

$$ f_s \le \mu_s N, \quad f_k = \mu_k N $$ $$ a_c = \frac{v^2}{r} = \omega^2 r $$ $$ v_{\text{banked}} = \sqrt{r g \left(\frac{\mu + \tan\theta}{1 – \mu\tan\theta}\right)} $$

$$ W = \int \vec{F} \cdot d\vec{r} = F d \cos\theta $$ $$ K = \frac{1}{2}m v^2 = \frac{p^2}{2m} $$ $$ U_g = mgh, \quad U_s = \frac{1}{2}kx^2 $$ $$ P = \frac{dW}{dt} = \vec{F}\cdot\vec{v} $$

$$ \tau = \vec{r} \times \vec{F} = I\alpha $$ $$ L = \vec{r} \times \vec{p} = I\omega $$ $$ K_{\text{rot}} = \frac{1}{2}I\omega^2 $$ $$ I_{\text{parallel}} = I_{\text{cm}} + M d^2 $$

$$ F = G\frac{m_1 m_2}{r^2}, \quad g = \frac{GM}{R^2} $$ $$ U_g = -\frac{GMm}{r}, \quad v_e = \sqrt{\frac{2GM}{R}} $$ $$ v_o = \sqrt{\frac{GM}{r}}, \quad T^2 = \left(\frac{4\pi^2}{GM}\right)r^3 $$

$$ P = P_0 + \rho g h $$ $$ A_1 v_1 = A_2 v_2 $$ $$ P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant} $$ $$ F_v = 6\pi\eta r v \quad (\text{Stokes’ Law}) $$

$$ \Delta L = L_0 \alpha \Delta T, \quad \Delta V = V_0 \gamma \Delta T $$ $$ Q = mc\Delta T = mL $$ $$ \frac{dQ}{dt} = -kA\frac{dT}{dx} = \sigma e A (T^4 – T_0^4) $$

$$ PV = nRT = N k_B T $$ $$ v_{\text{rms}} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3k_B T}{m}} $$ $$ \Delta Q = \Delta U + W, \quad W_{\text{iso}} = nRT\ln\left(\frac{V_f}{V_i}\right) $$ $$ \eta = 1 – \frac{Q_C}{Q_H} = 1 – \frac{T_C}{T_H} \quad (\text{Carnot}) $$

$$ \frac{d^2x}{dt^2} + \omega^2 x = 0 \implies x(t) = A\sin(\omega t + \phi) $$ $$ T_{\text{spring}} = 2\pi\sqrt{\frac{m}{k}}, \quad T_{\text{pendulum}} = 2\pi\sqrt{\frac{L}{g}} $$ $$ E_{\text{total}} = \frac{1}{2}kA^2 = \frac{1}{2}m\omega^2 A^2 $$

$$ y(x,t) = A\sin(kx – \omega t), \quad v = \frac{\omega}{k} = f\lambda $$ $$ v_{\text{string}} = \sqrt{\frac{T}{\mu}}, \quad v_{\text{sound}} = \sqrt{\frac{\gamma P}{\rho}} $$ $$ f’ = f\left(\frac{v \pm v_o}{v \mp v_s}\right) \quad (\text{Doppler Effect}) $$

$$ \vec{F} = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2}\hat{r} $$ $$ \Phi_E = \oint \vec{E}\cdot d\vec{A} = \frac{q_{\text{enclosed}}}{\varepsilon_0} $$ $$ V = \frac{1}{4\pi\varepsilon_0}\frac{q}{r}, \quad \vec{E} = -\vec{\nabla}V $$

$$ C = \frac{Q}{V} = \frac{\kappa\varepsilon_0 A}{d} $$ $$ U_C = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{1}{2}QV $$ $$ C_{\text{parallel}} = \sum C_i, \quad \frac{1}{C_{\text{series}}} = \sum \frac{1}{C_i} $$

$$ I = \frac{dQ}{dt} = n e A v_d, \quad V = IR $$ $$ R = \rho\frac{L}{A}, \quad P = VI = I^2 R = \frac{V^2}{R} $$ $$ \sum I_{\text{node}} = 0, \quad \sum \Delta V_{\text{loop}} = 0 $$

$$ \vec{F}_B = q(\vec{v}\times\vec{B}), \quad \vec{F}_I = I(\vec{L}\times\vec{B}) $$ $$ d\vec{B} = \frac{\mu_0 I}{4\pi}\frac{d\vec{l}\times\hat{r}}{r^2} $$ $$ \oint \vec{B}\cdot d\vec{l} = \mu_0 I_{\text{enclosed}} $$

$$ \Phi_B = \int \vec{B}\cdot d\vec{A} $$ $$ \mathcal{E} = -\frac{d\Phi_B}{dt} = (\vec{v}\times\vec{B})\cdot\vec{L} $$ $$ U_L = \frac{1}{2}L I^2, \quad \mathcal{E}_L = -L\frac{dI}{dt} $$

$$ X_L = \omega L, \quad X_C = \frac{1}{\omega C} $$ $$ Z = \sqrt{R^2 + (X_L – X_C)^2} $$ $$ \omega_0 = \frac{1}{\sqrt{LC}}, \quad P_{\text{avg}} = V_{\text{rms}}I_{\text{rms}}\cos\phi $$

$$ \frac{1}{f} = \frac{1}{v} + \frac{1}{u}, \quad \frac{1}{f} = (\mu – 1)\left(\frac{1}{R_1} – \frac{1}{R_2}\right) $$ $$ n_1 \sin\theta_1 = n_2 \sin\theta_2, \quad \beta = \frac{\lambda D}{d} $$

$$ E = hf = \frac{hc}{\lambda}, \quad hf = \Phi_0 + K_{\text{max}} $$ $$ E_n = -\frac{13.6\,\text{eV}}{n^2}Z^2, \quad \lambda_{\text{dB}} = \frac{h}{p} $$ $$ N(t) = N_0 e^{-\lambda t}, \quad T_{1/2} = \frac{\ln 2}{\lambda} $$