Rotational Kinematics Worked Examples Cheat Sheet

Key Facts

• Angular displacement is measured by $\theta = \frac{s}{r}$, where $s$ is arc length and $r$ is radius.
• Average angular velocity is $\omega_{avg} = \frac{\Delta \theta}{\Delta t}$.
• Average angular acceleration is $\alpha_{avg} = \frac{\Delta \omega}{\Delta t}$.
• For constant angular acceleration, angular velocity is found with $\omega_f = \omega_i + \alpha t$.
• For constant angular acceleration, angular displacement is found with $\theta = \omega_i t + \frac{1}{2}\alpha t^2$.
• A useful equation without time is $\omega_f^2 = \omega_i^2 + 2\alpha \theta$.
• Tangential speed and angular speed are related by $v = r\omega$.
• Tangential acceleration and angular acceleration are related by $a_t = r\alpha$.

Vocabulary

Angular displacement

Angular displacement $\theta$ is the angle through which an object rotates, usually measured in radians.

Angular velocity

Angular velocity $\omega$ is the rate at which angular position changes with time.

Angular acceleration

Angular acceleration $\alpha$ is the rate at which angular velocity changes with time.

Radian

A radian is an angle measure defined by $\theta = \frac{s}{r}$, where the arc length equals the radius for $1$ radian.

Tangential speed

Tangential speed $v$ is the linear speed of a point moving along the circular path, given by $v = r\omega$.

Constant angular acceleration

Constant angular acceleration means $\alpha$ does not change, so the standard rotational kinematics equations can be used.