Physics - Rotation Question with Solution | TestHub

Initial moment of inertia of the ring is $I_1=M{r}^2$.

Initial angular velocity is ${\omega }_1=\omega$.

When four objects, each of mass $M/2$, are placed at the ends of two perpendicular diameters, the new moment of inertia of the system becomes:

$I_2=I_1+4\times \left(\frac{M}{2}\right)r^2=M{r}^2+2M{r}^2=3M{r}^2$

Since no external torque acts on the system, angular momentum is conserved:

$I_1{\omega }_1=I_2{\omega }_2$

$M{r}^2\omega =3M{r}^2{\omega }_2$

${\omega }_2=\frac{\omega }{3}$

Answer: $\omega /3$