Question

A hoop of radius r and mass m rotating with an angular velocity ${\omega }_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

• A. $\frac{r{\omega }_0}{3}$
• B. $\frac{r{\omega }_0}{2}$
• C. $r{\omega }_0$
• D. $\frac{r{\omega }_0}{4}$

Answer 1

The correct option is B $\frac{r{\omega }_0}{2}$


From conservation of angular momentum about any fix point on the surface.Applying conservation at point of contact,
$m{r}^2{\omega }_0=mvr+m{r}^2\omega =mvr+m{r}^2\left(\frac{v}{r}\right)$
$\Rightarrow m{r}^2{\omega }_0=mvr+mvr=2mvr$
or $v=\frac{r{\omega }_0}{2}$