As we did for straight-line motion, we can write Newton's second law in a different form:

Στ

=

Iα

=

I

dω dt

=

d(Iω) dt

That is true if the rotational inertia is constant.

Our equation has the quantity Iω in it - a net torque on an object produces a change in this quantity.

Can you think of a good name for this quantity, Iω, that is so directly tied to the net torque?

We call Iω 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

Turning the general equation around, expressing it as an integral, we get:

∫ τ dt = ΔL

Let's call a net torque acting over a time interval an angular impulse.
The angular impulse is the product of the torque and the time interval over which the net torque acts.
The angular impulse is equal to the change in angular momentum.
The angular impulse is the area under the net torque vs. time graph.

If the torque is constant: ΔL = τ Δt