Physics - Rotation Question with Solution | TestHub

This can assumed as a pure rotation about point of contact say O with angular velocity

$\mathrm{\omega }=\frac{\mathit{\text{v}}}{\text{R}}\text{,}\text{R is the radius of hoop.}$

speed of P will be :

$v_p=\left(\text{op}\right)\mathrm{\omega }=\left(\text{2 R sin}\frac{\mathrm{\theta }}{2}\right)\mathrm{\omega }$

or$v_p=\left(2\text{R}\mathrm{\omega }\right)\text{sin}\left(\frac{\mathrm{\theta }}{2}\right)$

or$v_p=2v\sin \left(\frac{\theta }{2}\right)$