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 ceaes to slip?

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

Answer 1

Answer: (C)

$\frac{r{\omega }_0}{2}$

conservation of angular momentum about $a$ point ${}^{\prime }{A}^{\prime }$

$I{w}_0=Iw+mvr$

And $v=wr$ $($ rolling starts $)$

$m{r}^2{w}_0=m{r}^2\frac{v}{r}+mvr$

$v=\frac{r{w}_0}{2}$

Hence,

option $\left(C\right)$ is correct answer.