# Angular Momentum

Earlier we defined the angular momentum for rotation about a fixed axis as

L = I

Now we will investigate angular momentum in more detain -- for more general cases.

The angular momentum L of a particle is defined as

L = r x p

The particle is located at position r (relative to some origin -- so this means our angular momentum L is defined relative to that origin as well). p is the linear momentum of the particle.

We can start with our basic definition of torque,

If there are several forces acting on one particle, we can sum these forces and their associated torques,

What is this r x (dp/dt) term?

This means that if the net torque is zero, the angular momentum is conserved.

Lfinal = Linitial

For a rigid body (and that is all we will consider) we can also write the angular momentum as

L = I

or

This means angular momentum is a vector that points in the same direction as the angular velocity.

 Torque Conservation of Angular Momentum Return to ToC, Ch11, Rolling Motion