Angular acceleration

Beginner

Rate of change of angular velocity.

Key relationα = dω/dt

α = dω/dt changes the spin. With constant α the angular equations mirror the linear ones.

Worked example

Speeding up from 0 to 30 rad/s in 6 s: α = 5 rad/s².

Common mistake

rad/s² not m/s².

In more detail

Angular acceleration is the rate of change of angular velocity, α = dω/dt. It describes how quickly a rotating body speeds up or slows down.

A motor speeding up a turbine produces angular acceleration.
Brakes on bicycle wheels cause negative angular acceleration.
A drill bit speeding up when switched on has an angular acceleration that determines how quickly it reaches full speed.

What units are used?

Radians per second squared.

Does it need a torque?

Yes. A net torque produces angular acceleration, just as a net force produces linear acceleration.

What units is angular acceleration measured in?

Radians per second squared. Since radians are dimensionless, it is equivalent to inverse seconds squared.