Two discs of radii `R and 2R` are pressed against each other. Initially, disc with radius `R` is rotating with angular velocity `omega` and other disc is stationary. Both discs are hinged at their respective centres and are free to rotate about them. Moment of inertia of smaller disc is `I` and of bigger disc is `2I` about their respective axis of rotation. Find the angular velocity of bigger disc after long time.

Explanation

The only force which is producing any torque about the centre of first disk is friciton.
Let the disc rotates with angular velocity `omega_(1)` and `omega_(2)` as shown.
Now `omega_(1)R=omega_(2)2R` as the point in contact should have same velocity after slipping stops.
`impliesomega_(2)=(omega_(1))/(2)`
Now, total angular impulse provided by the friciton is equal to change in angular momentum of the disc
`intfRdt=l(omega-omega_(1))`
`intf2Rdt=2lomega_(2)`
`implies2l(omega-omega_(1))=2lomega_(2)`
`omega_(1)+omega_(2)=omega`
`2omega_(2)+omega_(2)=omega`
`omega_(2)=(omega)/(3)`