Table of Contents
What Is Angular Acceleration?
Angular acceleration is the rate of change of angular velocity over time, measured in radians per second squared (rad/s²). It is the rotational analog of linear acceleration. When a spinning object speeds up or slows down its rotation, it experiences angular acceleration.
This concept is fundamental to rotational dynamics and appears in everything from electric motors and turbines to figure skating and planetary motion. Newton second law for rotation states that the net torque on an object equals its moment of inertia times its angular acceleration.
Angular Acceleration Formulas
Where alpha is angular acceleration, omega is angular velocity, t is time, theta is angular displacement, tau is torque, and I is the moment of inertia.
Angular Acceleration Examples
| Object | Angular Acceleration |
|---|---|
| CD drive spinning up | ~100 rad/s² |
| Car wheel accelerating | ~10 rad/s² |
| Washing machine spin | ~15 rad/s² |
| Turbine startup | ~50 rad/s² |
| Flywheel braking | ~-5 rad/s² |
FAQ
How is angular acceleration related to linear acceleration?
The tangential linear acceleration of a point on a rotating object equals angular acceleration times the radius: a = alpha * r. Points farther from the axis have greater linear acceleration for the same angular acceleration.
What is moment of inertia?
Moment of inertia is the rotational equivalent of mass. It depends on both the object mass and how that mass is distributed relative to the rotation axis. Objects with mass concentrated far from the axis have higher moment of inertia and resist angular acceleration more.
Can angular acceleration be negative?
Yes. Negative angular acceleration means the rotational speed is decreasing in the positive direction (decelerating). A spinning wheel slowing down due to friction has negative angular acceleration. The sign convention follows the right-hand rule or the chosen positive direction.