Formula Sheet

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

Kinematics (Calculus)

v(t) = \frac{dx}{dt}

Velocity as the derivative of position

a(t) = \frac{dv}{dt} = \frac{d^2x}{dt^2}

Acceleration as the derivative of velocity

x = x_0 + \int v\, dt

Position from integrating velocity

\vec{F} = \frac{d\vec{p}}{dt}

Newton's second law (momentum form)

W = \int \vec{F}\cdot d\vec{r}

Work done by a variable force

P = \vec{F}\cdot\vec{v}

Instantaneous power

\tau = I\alpha

Rotational form of Newton's second law

L = I\omega

Angular momentum

x(t) = A\cos(\omega t + \phi)

Simple harmonic motion position

U_g = -\frac{Gm_1 m_2}{r}

Gravitational potential energy

v_{esc} = \sqrt{\frac{2GM}{r}}

Escape speed