Basic Facts About Angular Momentum:

• For one particle moving in a circular orbit, the angular momentum is L = r x p → m r² ω.
• For a continuous mass distribution, L = ∫ dm r² ω = Iω
• Angular momentum is a vector that is parallel to the angular velocity.
• If there is no net torque acting on a system, the system's angular momentum is conserved.
• A net torque produces a change in angular momentum that is equal to the torque multiplied by the time interval over which the torque is applied.

Torque and Impulse

Newton's second law for rotational motion in differential form:

Στ

=

dL dt

=

d(Iω) dt

= I

dω dt

+ ω

dI dt

→  I

dα dt

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

The net torque equals the rate of change of the angular momentum!

Integrating the general equation gives:   ∫ ∑ τ dt = ΔL

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