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 the edge of the platform when it was caught by the kid, find the angular speed of the platform after the event.

Answer 1

Given,

A kid of mass M stands at the edge of the platform of a radius R which has a moment of inertia I. A ball is thrown to him and with a horizontal velocity of the ball v when he catches it. Therefore, if we take the total bodies as a system, then no external torque acts on it, therefore the angular momentum will be conserved.

$L_i=L_f$

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

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

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

Hence the angular speed is $\Rightarrow \omega =\frac{mvR}{I+(M+m)R^2}$.