Formula Sheet

Official-style AP reference. Hover a formula to copy its LaTeX.

Kinematics

v = v_0 + at

Velocity with constant acceleration

x = x_0 + v_0 t + \tfrac{1}{2}at^2

Position with constant acceleration

v^2 = v_0^2 + 2a(x - x_0)

Velocity squared without time

\vec{F}_{net} = m\vec{a}

Newton's second law

F_f \le \mu N

Friction force

F_g = \frac{Gm_1 m_2}{r^2}

Newton's law of gravitation

K = \tfrac{1}{2}mv^2

Kinetic energy

U_g = mgh

Gravitational potential energy

p = mv

Linear momentum

J = F\Delta t = \Delta p

Impulse-momentum theorem

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

Centripetal acceleration

\tau = rF\sin\theta

Torque

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

Period of a mass-spring oscillator

T_p = 2\pi\sqrt{\frac{L}{g}}

Period of a simple pendulum

v = f\lambda

Wave speed

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

Electric current

V = IR

Ohm's law

P = IV

Electrical power