Home / Topics / Kinematics
Angular acceleration
Intermediate
Rate of change of angular velocity.
α = dω/dtAngular acceleration α = dω/dt is the rate of change of angular velocity and relates to tangential acceleration by at = αr. A spinning-up wheel has constant α under constant torque.
A wheel from 0 to 20 rad/s in 4 s has α = 5 rad/s².
rad/s² is not the same unit as m/s².
In more detail
Angular acceleration is the rate of change of angular velocity, α = dω/dt. It is the rotational analogue of linear acceleration.
Real-world uses
- A motor speeding up a fan has angular acceleration.
- Brakes on bicycle wheels produce negative angular acceleration.
- A spinning drill speeding up from rest has an angular acceleration that tells engineers how quickly its speed rises.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What units are used?
Radians per second squared.
How does it relate to linear acceleration?
The tangential acceleration equals the angular acceleration times the radius.
What units does angular acceleration use?
Radians per second squared, rad/s², which is the same as s⁻² because radians are dimensionless.
Related topics in Kinematics
Period and frequency · Centripetal acceleration · Non-uniform circular motion · Rotational kinematics equations · Motion in polar coordinates · Motion in three dimensions