Question

A thin circular ring of mass $M$ and radius ${}^{\prime }{r}^{\prime }$ is rotating about its axis with a constant angular velocity $\omega$. Four object each of mass $m$, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be-

Answer 1

Using conservation of angular momentum

Initial angular momentum = Final angular momentum

$M{r}^2\times \omega =(M{r}^2+4m{r}^2){\omega }^{\prime }$

${\omega }^{\prime }=\frac{Mw}{(M+4m)}$

${\omega }^{\prime }$ is the new angular velocity.