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