Question

A ring of radius $R$ rolls on a horizontal ground with linear speed $v$ and angular speed $\omega$ For $\theta =\pm {\cos }^{-1}\left(\frac{xv}{R\omega }\right)$ the velocity of point $P$ is in vertical direction.Find $x$. $(v<R\omega )$.

Answer 1

If $R\omega \cos \theta =v$ then velocity of point $P$ is vertically upwards.
$\therefore \theta =\pm {\cos }^{-1}\left(\frac{v}{R\omega }\right)$