Consider a turntable to be a circular disk of moment of inertia rotating at a co

Question

Consider a turntable to be a circular disk of moment of inertia rotating at a constant angular velocity 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 . The initial angular velocity of the second disk is zero. There is friction between the two disks. After this "rotational collision," the disks will eventually rotate with the same angular velocity. What is the final angular velocity of the two disks? *I'm looking for an equation here http://session.masteringphysics.com/problemAsset/1016274/12/MAD_cl_3_r1.jpg

Explanation / Answer

The initial angular momentum of the system is L = ( It ) ( ?i ) The final angular momentum is L = ( It + Ir ) ( ?f ) where ?f is the final angular velocity of the system. Since the two angular momenta are equal, we see that ( It ) ( ?i ) = ( It + Ir ) ( ?f ) so ?f = [ ( It ) / ( It + Ir ) ] ?i

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