Two discs of radii `R and 2R` are pressed against eachother. Initially, disc wit 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 inertiaof 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

As the discs are pressed against eachother, an equal and opposite frictional force will act on both the discs, till the time rolling starts and hence the linear speed of the circumference of the two discs becomes the same.
Let `omega_(1) =` angular velocity of smaller disc after long time `t`
`omega_(2) =` angular velocity of bigger disc after long time `t`
`f =` force of friction between the two discs when rolling starts,
`upsilon_(1) = upsilon_(2)`
`omega_(1)R = omega_(2)(2R) :. omega_(1) = 2omega_(2)`
For smaller disc, `tau = f xx R = (I (omega - omega_(1)))/(t)` ..(i)
For bigger disc, `tau_(2) = fxx 2R = (2I(omega_(2) - 0))/(t)`
or `f xx R = (I omega_(2))/(t)` ..(ii)
From (i) and (ii), `omega - omega_(1) = omega_(2)`
or `omega - 2 omega_(2) = omega_(2)`
`omega = 2 omega_(2)`
or `omega = omega//3`