Conservation of angular momentum

Intermediate

No external torque keeps L constant.

Key relationI₁ω₁ = I₂ω₂

With no net external torque, L stays constant: I₁ω₁ = I₂ω₂. It explains spinning skaters, divers, pulsars and the Moon's recession.

Worked example

A star collapsing spins faster.

Common mistake

Check torque about the chosen point is zero.

In more detail

If no net external torque acts on a system, its total angular momentum is conserved. A change in moment of inertia then changes the angular velocity.

Figure skaters and divers change spin rate by changing body shape.
Neutron stars spin up when their cores collapse.
A diver tucking in during a somersault spins faster, because the angular momentum is conserved as the moment of inertia falls.

Why does a spinning skater speed up?

Because the moment of inertia falls as the arms come in, so the angular velocity must rise.

Is energy conserved too?

No. Work done by muscles changes the rotational kinetic energy.

Can a diver change their spin without touching anything?

Yes. Moving the arms and legs changes the moment of inertia, which changes the spin rate even with no external torque.