Question

A wheel rolls purely on the ground. If the velocity of a point ${}^{\prime }{P}^{\prime }$ as shown on the periphery of a body has a velocity equal to the velocity of the centre of mass of the body. Find $\theta =?$.

Answer 1

for any point on the rim the velocity due to rotation = ${}^{\prime }r{\omega }^{\prime }$

and for pure rolling $r\omega =v$ [where v is the velocity of center of mass]

Hence the net velocity of any point on the rim is the vector addition of two vectors of magnitude 'v'

so,

$\sqrt{v^2+v^2+2.v.vcos\theta }$= v

or $cos\theta =\frac{-1}{2}$

or $\theta ={120}^o$