Angular Momentum

Angular momentum is the rotational analog of linear momentum. It is also conserved in rotational collisions which we'll elaborate on in just a second. Angular momentum has two main mathematical definitions that we can use. The first one is the rotational analogous definition. Since linear momentum is the product of mass and velocity, angular momentum is the product of the moment of inertia and angular velocity.

Keep in mind that moment of inertia is also dependent on the radius at which the object is from its relative axis of rotation. Thus, it's safer to say that the angular momentum of a system is the angular momentum of the system relative to its pivot.

Recall that angular velocity is related to linear velocity through:

and the moment of inertia is given by:

Using the two equations above along with the first equation for the angular momentum at the top of this page, we can then derive the following relation: