To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies.

(figure 1) consider a turntable to be a circular disk of moment of inertia it rotating at a constant angular velocity ? i around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry"). the axis of the disk is vertical and the disk is supported by frictionless bearings. the motor of the turntable is off, so there is no external torque being applied to the axis.
another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). the moment of inertia of the record is ir. the initial angular velocity of the second disk is zero.

there is friction between the two disks.