Question

A circular disc rotates freely about a vertical axis through its centre with angular velocity ${\omega }_1$. A ring having the same mass and radius as the disc, is placed on the disc, and the system now rotates with an angular velocity ${\omega }_2$ about the same vertical axis. Then ${\omega }_2/{\omega }_1$ is:

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{3}{2}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{1}{3}$

In this case, since no net torque exist on the disc + ring system, angular momentum about center will remain conserved.

$I_1{\omega }_1=(I_1+I_2){\omega }_2$

$\frac{m{r}^2}{2}{\omega }_1=(\frac{m{r}^2}{2}+m{r}^2){\omega }_2$

$\frac{m{r}^2}{2}{\omega }_1=\frac{3m{r}^2}{2}{\omega }_2$

Hence, $\frac{{\omega }_2}{{\omega }_1}=\frac{1}{3}$