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Question

A nonrotating cylindrical disk of moment of inertia I is dropped onto an identical disk rotating at angular speed ω.

Assuming no external torques, what is the final common angular speed of the two disks?

Answer 1

Angular momentum , where is the moment of inertia and is the angular velocity.

The initial momentum of disk 1 is .

The initial momentum of disk 2(Non-rotating disk) .

If the 2 disks are combined then , where is the final velocity.

Law of conservative of angular momentum:

Angular momentum before the two disks get combined is equal to the angular momentum after the two disks are combined.

The two disks are identical then .

Final angular speed of the two disks is