Angular velocity

Beginner

Rate of change of angle.

Key relationω = dθ/dt

ω = dθ/dt in rad/s; it is the same for all points in a rigid body. Direction along the axis by the right-hand rule.

Worked example

1200 rpm = 125.7 rad/s.

Common mistake

Convert rpm using 2π/60.

In more detail

Angular velocity is the rate of change of angular displacement, ω = dθ/dt. It is measured in radians per second and gives how fast a body rotates.

Engines are rated by their angular velocity in revolutions per minute.
Hard disk drives spin at a set angular velocity to read data.
A washing machine motor is rated in revolutions per minute, which can be converted to angular velocity in radians per second.

How is angular velocity related to speed?

For a point on a rotating body, linear speed equals ω times the distance from the axis.

Can it be negative?

Yes. The sign shows the direction of rotation.

How do I convert rpm to rad/s?

Multiply the revolutions per minute by 2π and divide by 60.