AP Physics C Mechanics Formula Sheet Cheat Sheet

Key Facts

• Linear kinematics connects position, velocity, and acceleration by $v = \frac{dx}{dt}$, $a = \frac{dv}{dt}$, and $\Delta x = \int_{t_1}^{t_2} v\,dt$.
• Newton's second law is $\sum \vec{F} = m\vec{a}$ for constant mass, and equilibrium requires $\sum \vec{F} = \vec{0}$.
• Work and energy are connected by $W = \int \vec{F}\cdot d\vec{r}$ and $W_{\text{net}} = \Delta K$, where $K = \frac{1}{2}mv^2$.
• Linear momentum is $\vec{p} = m\vec{v}$, impulse is $\vec{J} = \int \vec{F}\,dt = \Delta \vec{p}$, and total momentum is conserved when external impulse is zero.
• Rotational motion uses $\omega = \frac{d\theta}{dt}$, $\alpha = \frac{d\omega}{dt}$, $\tau = I\alpha$, and $K_{\text{rot}} = \frac{1}{2}I\omega^2$.
• Angular momentum is $\vec{L} = I\vec{\omega}$ for rotation about a fixed axis, and $\vec{L}$ is conserved when the net external torque is zero.
• Newtonian gravitation uses $F_g = \frac{Gm_1m_2}{r^2}$, $U_g = -\frac{GMm}{r}$, and circular orbit speed $v = \sqrt{\frac{GM}{r}}$.
• Simple harmonic motion satisfies $a = -\omega^2x$, with spring angular frequency $\omega = \sqrt{\frac{k}{m}}$ and period $T = 2\pi\sqrt{\frac{m}{k}}$.

Vocabulary

Derivative

A derivative gives an instantaneous rate of change, such as $v = \frac{dx}{dt}$ for velocity.

Integral

An integral accumulates a changing quantity, such as $W = \int \vec{F}\cdot d\vec{r}$ for work.

Net Force

Net force is the vector sum of all forces acting on an object, written as $\sum \vec{F}$.

Torque

Torque measures the rotational effect of a force and is given by $\vec{\tau} = \vec{r}\times \vec{F}$.

Moment of Inertia

Moment of inertia $I$ measures how mass is distributed relative to an axis of rotation.

Conservative Force

A conservative force has path-independent work and can be described by potential energy with $\vec{F} = -\nabla U$.