A spinning object has angular momentum, represented by l or L.

Four fast facts about angular momentum

1. L = Iω
   
   
2. Angular momentum is a vector, pointing in the direction of the angular velocity.
   
   
3. If there is no net torque acting on a system, the system's angular momentum is conserved.
   
   
4. A net torque produces a change in angular momentum that is equal to the torque multiplied by the time interval during which the torque was applied.

In a rotational situation, impulse is the product of a torque and the time interval over which the torque acts.

Work (a torque acting over an angle) produces a change in kinetic energy. An impulse (a torque acting over a time interval) produces a change in angular momentum.

τ = Iα

τ

=

I

dω dt

=

dL dt

Expressed as an integral, this becomes:

ΔL = ∫ τ dt

The impulse is the area under the torque vs. time graph.

If the torque is constant: ΔL = τ Δt

The Law of Conservation of Angular Momentum states that, when no external torques act on a system, the angular momentum of the system is conserved.

Always remember that angular momentum is a vector when applying this law.

A person standing on a turntable while holding a bicycle wheel is an excellent place to observe angular momentum conservation in action. The person is initially not rotating on the turntable, and the bicycle wheel is rotating about a horizontal axis.

The initial angular momentum about a vertical axis is zero.

If the person re-positions the bicycle wheel so its rotation axis is vertical, the wheel exerts a torque on the person during the re-positioning that makes the person spin in the opposite direction as the wheel. The angular momenta cancel, so that L = 0 at all times about a vertical axis.

As long as the rotating platform is well-balanced and there are no net external torques acting, re-positioning the bike wheel so its rotation axis is horizontal again should stop the person's rotation. Flipping the bike wheel over so that its rotation axis is again vertical but reversed will make the person spin in the opposite direction.