AP Physics 1 Equation Sheet Annotated Cheat Sheet

Key Facts

• For constant acceleration in one dimension, use $v = v_0 + at$, $\Delta x = v_0t + \frac{1}{2}at^2$, and $v^2 = v_0^2 + 2a\Delta x$.
• Newton’s second law is $\sum \vec{F} = m\vec{a}$, so acceleration points in the direction of the net force.
• Linear momentum is $\vec{p} = m\vec{v}$, and impulse changes momentum according to $\vec{J} = \Delta \vec{p} = \vec{F}_{\text{avg}}\Delta t$.
• Mechanical energy is conserved when only conservative forces do work, so $K_i + U_i = K_f + U_f$.
• Work is $W = Fd\cos\theta$, kinetic energy is $K = \frac{1}{2}mv^2$, and gravitational potential energy near Earth is $U_g = mgh$.
• For rotation, torque is $\tau = rF\sin\theta$, rotational inertia connects to angular acceleration through $\sum \tau = I\alpha$, and angular momentum is $L = I\omega$.
• For simple harmonic motion, the spring period is $T = 2\pi\sqrt{\frac{m}{k}}$ and the pendulum period for small angles is $T = 2\pi\sqrt{\frac{L}{g}}$.
• For DC circuits, Ohm’s law is $V = IR$, electric power is $P = IV = I^2R = \frac{V^2}{R}$, and series resistors add as $R_{\text{eq}} = R_1 + R_2 + \cdots$.

Vocabulary

Net force

The vector sum of all forces acting on an object, written as $\sum \vec{F}$.

Impulse

The change in momentum caused by a force acting over time, written as $\vec{J} = \Delta \vec{p}$.

Mechanical energy

The total energy from motion and position, usually written as $E = K + U$.

Torque

The rotational effect of a force, calculated by $\tau = rF\sin\theta$.

Angular velocity

The rate at which an object rotates, written as $\omega = \frac{\Delta \theta}{\Delta t}$.

Equivalent resistance

A single resistance value that has the same effect as a group of resistors in a circuit, written as $R_{\text{eq}}$.