AP Physics Formula Cheat Sheet

Physics can sometimes feel overwhelming, but having a well-organized cheat sheet can make a huge difference. Below, you'll find a collection of essential formulas grouped by topic to help you tackle AP Physics problems.

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Kinematics Equations

$$ v_x = v_{x0} + a_x t $$

$$ x = x_0 + v_{x0} t + \frac{1}{2} a_x t^2 $$

$$ v_x^2 = v_{x0}^2 + 2 a_x (x - x_0) $$

Center of Mass

$$ \vec{x}_{\mathrm{cm}} = \frac{\sum m_i \vec{x}_i}{\sum m_i} $$

Newton's Second Law

$$ \vec{a}_{\mathrm{sys}} = \frac{\sum \vec{F}_{\mathrm{sys}}}{m_{\mathrm{sys}}} = \frac{\vec{F}_{\mathrm{net}}}{m_{\mathrm{sys}}} $$

Gravitational Force

$$ |\vec{F}_g| = G \frac{m_1 m_2}{r^2} $$

Friction Force

$$ |\vec{F}_f| \leq |\mu \vec{F}_n| $$

Spring Force

$$ \vec{F}_s = -k \Delta \vec{x} $$

Centripetal Acceleration

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

Kinetic Energy

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

Work

$$ W = F_{\|} d = F d \cos (\theta) $$

Work-Energy Theorem

$$ \Delta K = \sum W_i = \sum F_{\|,i} d_i $$

Spring Potential Energy

$$ \Delta U_s = \frac{1}{2} k (\Delta x)^2 $$

Gravitational Potential Energy

$$ U_G = - \frac{G m_1 m_2}{r} $$

$$ \Delta U_g = m g \Delta y $$

Power

$$ P_{\text{avg}} = \frac{W}{\Delta t} = \frac{\Delta E}{\Delta t} $$

$$ P_{\text{inst}} = F_{\|} v = F v \cos(\theta) $$

Momentum and Impulse

$$ \vec{p} = m \vec{v} $$

$$ \vec{F}_{\text{net}} = \frac{\Delta \vec{p}}{\Delta t} = m \frac{\Delta \vec{v}}{\Delta t} = m \vec{a} $$

$$ \vec{J} = \vec{F}_{\text{avg}} \Delta t = \Delta \vec{p} $$

$$ \vec{v}_{\text{cm}} = \frac{\sum \vec{p}_i}{\sum m_i} = \frac{\sum m_i \vec{v}_i}{\sum m_i} $$

Rotational Kinematics

$$ \omega = \omega_0 + \alpha t $$

$$ \theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 $$

$$ \omega^2 = \omega_0^2 + 2 \alpha (\theta - \theta_0) $$

$$ v = r \omega $$

$$ a_T = r \alpha $$

Torque

$$ \tau = r_{\perp} F = r F \sin (\theta) $$

Moment of Inertia

$$ I = \sum m_i r_i^2 $$

$$ I' = I_{\text{cm}} + M d^2 $$

Rotational Acceleration (System-Wide)

\(\alpha_{\text{sys}} = \frac{\Sigma \tau}{I_{\text{sys}}} = \frac{\tau_{\text{net}}}{I_{\text{sys}}}\)

Rotational Power and Work

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

$$ W = \tau \Delta \theta $$

Angular Momentum

$$ L = I \omega $$

$$ L = r m v \sin \theta $$

$$ \Delta L = \tau \Delta t $$

$$ \Delta x_{\text{cm}} = r \Delta \theta $$

Oscillations

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

$$ T_s = 2 \pi \sqrt{\frac{m}{k}} $$

$$ T_p = 2 \pi \sqrt{\frac{\ell}{g}} $$

$$ x = A \cos (2 \pi f t) $$

$$ x = A \sin (2 \pi f t) $$

Fluid Mechanics

$$ \rho = \frac{m}{V} $$

$$ P = \frac{F_{\perp}}{A} $$

$$ P = P_0 + \rho g h $$

$$ P_{\text{gauge}} = \rho g h $$

$$ F_b = \rho V g $$

Continuity Equation

$$ A_1 v_1 = A_2 v_2 $$

Bernoulli's Equation

$$ P_1 + \rho g y_1 + \frac{1}{2} \rho v_1^2 = P_2 + \rho g y_2 + \frac{1}{2} \rho v_2^2 $$

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