## Conservation of Angular Momentum

Angular momentum, defined by is 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 mass and radius is 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 is The 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 mass travelling with a speed which strikes the disc a perpendicular distance from the centre. The angular momentum of the disc is and the angular momentum of the particle about the pivot is The total angular momentum is The moment of inertia of disc plus particle is so if the angular velocity of particle plus disc after the collision is then  