Question

A solid cylinder is given an angular speed $\omega$ and placed on a rough plate of negligible thickness. The horizontal surface below the plate is smooth.Then the angular speed of the cylinder when it starts pure rolling on the plate will be:

• A. $\frac{\omega }{2}$
• B. $\frac{\omega }{3}$
• C. $\frac{2\omega }{3}$
• D. None of these

Answer 1

The correct option is B $\frac{\omega }{3}$

No torque about hence angular momentum is conserved
$\therefore$ initial $L$ =final $L$
initial $L$=$\frac{M{R}^2}{2}.\omega$
Final $L$= $\frac{3}{2}M{R}^2.{\omega }^{\prime }$

On equating we get :

${\omega }^{\prime }=\frac{\omega }{3}$