Question:
Suppose the platform of the previous problem is brought to rest with the ball in hand of the kid standing on the rim. The kid throws the ball horizontally to his friend in a direction tangential to the rim with a speed $v$ as seen by friend. Find the angular velocity with which the platform will start rotating.
Solution:
Considering ball, boy and platform as system
$L_{i}=L_{f}$
$0+0+0=m v R+l(-w)+\left(M^{R^{2}}\right)(-w)$
$\omega=\frac{m v R}{\left(I+M R^{2}\right)}$