Question

The rotating assembly eventually assumes constant angular speed ${\omega }^{\ast }$ . Write ${\omega }^{\ast }$ in terms of $v$ and $r$ . Argue how a constant $\omega$ does not violate energy conservation.

Answer 1

${\omega }^{\ast }=\frac{v}{r}$
Argument : Initially ${\omega }_i$ increases until it reaches a value $v={\omega }^{\ast }r$ , i.e. the speed of the falling ball. Thereafter the ball merely touches the sphere and does not impart it any momentum.