Question

A kid of mass M stands at the edge of a platform of radius R which can be freely rotated about its axis. The moment of inertia of the platform is I.The system is at rest when a friend throws a ball of mass m and the kid catches it. If the velocity of the ball is v horizontally along the tangent to edge of the platform when it was caught by the kid, find the angular speed of the platform after the event.

Answer 1

A kid of mass $M$ stands at the edge of a platform of radius $R$ Which has a moment of inertia $I$.

A ball of $m$ thrown to him and horizontal velocity of the ball $v$ when he catches it.
Therefore if we take the total bodies as a system
Therefore

$mvR=\{I+(M+m\left)R^2\right\}\omega$

The moment of inertia of the kid and ball about the axis $=(M+m)R^2$)

$\Rightarrow \omega =\frac{mVR}{(M+m)R^2}$.