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

$$v_x=v_{x0}+a_{x}t$$

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

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

Center of Mass

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

Newton's Second Law

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

Gravitational Force

$$|{\overrightarrow{F}}_g|=G\frac{m_1{m}_2}{r^2}$$

Friction Force

$$|{\overrightarrow{F}}_f|\le |\mu {\overrightarrow{F}}_n|$$

Spring Force

$${\overrightarrow{F}}_s=-k\mathrm{\Delta }\overrightarrow{x}$$

Centripetal Acceleration

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

Kinetic Energy

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

Work

$$W=F_{\Vert }d=Fd\cos (\theta )$$

Work-Energy Theorem

$$\mathrm{\Delta }K=\sum W_i=\sum F_{\Vert ,i}{d}_i$$

Spring Potential Energy

$$\mathrm{\Delta }{U}_s=\frac{1}{2}k(\mathrm{\Delta }x{)}^2$$

Gravitational Potential Energy

$$U_G=-\frac{G{m}_1{m}_2}{r}$$

$$\mathrm{\Delta }{U}_g=mg\mathrm{\Delta }y$$

Power

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

$$P_{\text{inst}}=F_{\Vert }v=Fv\cos (\theta )$$

Momentum and Impulse

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

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

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

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

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

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

Moment of Inertia

$$I=\sum m_i{r}_i^2$$

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

Rotational Acceleration (System-Wide)

${\alpha }_{\text{sys}}=\frac{\mathrm{\Sigma }\tau }{I_{\text{sys}}}=\frac{{\tau }_{\text{net}}}{I_{\text{sys}}}$

Rotational Power and Work

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

$$W=\tau \mathrm{\Delta }\theta$$

Angular Momentum

$$L=I\omega$$

$$L=rmv\sin \theta$$

$$\mathrm{\Delta }L=\tau \mathrm{\Delta }t$$

$$\mathrm{\Delta }{x}_{\text{cm}}=r\mathrm{\Delta }\theta$$

Oscillations

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

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

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

$$x=A\cos (2\pi ft)$$

$$x=A\sin (2\pi ft)$$

Fluid Mechanics

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

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

$$P=P_0+\rho gh$$

$$P_{\text{gauge}}=\rho gh$$

$$F_b=\rho Vg$$

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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