Question

A hoop of radius r and mass m rotating with an angular velocity 0 w is placed on a rough horizontal surface.

The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoopwhen it ceases to slip?

Answer 1

Radius of hoop = r, Initial angular velocity = ${\omega }_0$, Initial velocity( u) = 0, velocity of centre of hoop =?
By momentum conservation, initial momentum of hoop will be same as final momentum
i.e., L_i =L_{f
$$\begin{gathered} m{r}^2{\omega }_0=mvr+m{r}^{2}v/r \\ r{\omega }_0=v+v \\ v=\frac{r{\omega }_0}{2} \end{gathered}$$}