Question

A solid sphere spinning about a horizontal axis with an angular velocity $\omega$ is placed on a horizontal surface. Subsequently it rolls without slipping with an angular velocity of.

• A. $2\omega /5$
• B. $7\omega /5$
• C. $2\omega /7$
• D. $\omega$

Answer 1

Answer: (C)

$2\omega /7$

${\omega }_{final}=\frac{v_f}{r}$ , $I=\frac{2m{r}^2}{5}$

$\frac{I{\omega }^2}{2}=\frac{I{\omega }_{final}^2}{2}+\frac{m{v}_f^2}{2}$

${\omega }_{final}=\frac{2\omega }{7}$