Question

A cylinder $A$ rolls without slipping on a plank $B$. The velocities of center of the cylinder and that of the plank are $4m/s$ and $2m/s$ respectively in the same direction, with respect to the ground. The angular velocity (in $rad/s$) of the cylinder if its radius is $1m$ is:

Answer 1

Draw a diagram of given problem.

Calculating angular velocity of cylinder.

Given,
Velocity of center of cylinder, $v_{cm}=4m/s$
Velocity of plank, $v_A=2m/s$
$v_{cm}-R\omega =v_A$
$4-\omega =2$
$\Rightarrow \omega =2rad/\sec$