Two disks of identical mass but different radii (r and 2r) are spinning on frict

Question

Two disks of identical mass but different radii (r and 2r) are spinning on frictionless bearings at the same angular speed ?0, but in opposite directions. The two disks are brought slowly together. The resulting frictional force between the surfaces eventually brings them to a common angular velocity.
-What is the change in rotational kinetic energy of the system? (Use the following as necessary: K as the initial kinetic energy.)
You need to substitute in K for the initial kinetic energy. Thanks!
Btw the magnitude of the final angular velocity in terms of ?0 : 3/5 ?0.

Thanks !

Explanation / Answer

moment of inertia r disk : I1=1/2*m*r2 2r disk I2=1/2*m*4*r2=2*m*r2 conservation of momentum -I1*?0+I2*?0=(I1+I2)*? =>?=3/5*?0 (b) the change in rotational kinetic energy of thesystem K-K2=1/2*(I1+I2)*?02-1/2*(I1+I2)*?2 =4/5*m*r2*?02 ,reduced if count on direction : change = -4/5*m*r2*?02

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