Conservation of angular momentum

Intermediate

Torque-free systems keep L constant.

Key relationL = Iω

If the net torque is zero, L stays constant. Changing the radius or the moment of inertia changes the angular speed.

Worked example

A diver tucks to spin faster.

Common mistake

Torque from gravity about the centre of mass is zero for free-falling bodies.

In more detail

Angular momentum is conserved when no net external torque acts on a system. Changing the moment of inertia then changes the angular velocity.

Figure skaters spin faster when they pull in their arms.
Neutron stars spin rapidly because their collapsed cores conserve angular momentum.
A figure skater who pulls in their arms spins faster because the angular momentum is conserved while the moment of inertia falls.

Does energy stay constant too?

Not necessarily. When the skater pulls in, the rotational kinetic energy increases because the muscles do work.

What is the condition for conservation?

No net external torque acting about the axis.

Can a system change its angular momentum with no torque?

No. Without an external torque, the total angular momentum of the system stays constant.