Question

A disc of radius $R$ rolls without slipping at speed $v$ along positive $x-$axis. The velocity of the point $P$ at the instant shown in $Fig.2.194$ is:

Answer 1

When the disc is in rolling motion, the particle at point P is in combined motion ( Rotional motion+translational motion)

so, velocity of particle at point P is

$\begin{array}{c}{v}_p=v+w{r}_{op}\\ =v+w\left(R-r\right)\end{array}$

Hence, the disc is in rolling motion without slipping , therefore the value of $v$ at point P is zero

so, the velocity of particle at point P is

$v_p=w\left(R-r\right)$