Question

Suppose in the previous problem, the child stays at rest on the platform and one of his friend throws a ball of mass $m_1$ towards him with a velocity of $v$ from a direction tangential to the platform and the child on the platform catches the ball. Find the angular velocity of the platform after he catches the ball.

Answer 1

New moment of inertia of system about center of platform$=I+m{R}^2+m_1{R}^2=I+(m+m_1)R^2$ (after ball is caught)

Again using conservation of angular momentum

$m_1.v.R=(I+(m+m_1)R^2){\omega }_0$

$\Rightarrow {\omega }_0=\frac{m_{1}vR}{I+(m+m_1)R^2}$