As in linear motion, we can write Newton's second law in a differential form:

Στ

=

Iα

=

I

dω dt

=

d(Iω) dt

The last step is valid only when the rotational inertia is constant.

This equation expresses the fact that the net torque produces a change in quantity Iω. We call Iω the angular momentum, and give it the symbol L.

General form of Newton's Second Law:

Στ

=

dL dt

=

d(Iω) dt

= I

dω dt

+ ω

dI dt

Integrating the general equation, we get:   ∫ ∑ τ dt = ΔL

The net torque acting over a time interval is the angular impulse.

• The angular impulse is the product of the torque and the time interval over which the torque acts.
• The angular impulse is equal to the change in angular momentum.
• The angular impulse equals the area under the net torque vs. time graph.
• If the torque is constant: ΔL = (∑ τ) Δt