Conservation of Angular Momentum

Angular momentum, defined byis conserved in all processes, if no external forces act, just as ordinary linear momentum is conserved. In fact, angular and linear momentum are conserved independently.

Suppose that a disc of massand radiusis rotating about an axis through the edge of the disc, perpendicular to the plane of the disc. The moment of inertia of the disc about an axis through its centre, perpendicular to the plane of the disc isThe parallel axis theorem gives the moment of inertia about the pivot point on the circumference as

The disc is rotating at two revolutions per second (so that), and is hit by a particle of masstravelling with a speedwhich strikes the disc a perpendicular distancefrom the centre.

The angular momentum of the disc isand the angular momentum of the particle about the pivot isThe total angular momentum is

The moment of inertia of disc plus particle isso if the angular velocity of particle plus disc after the collision isthen