Question

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A hoop of radius r and mass 'm' rotating with
angular velocity as, 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 hoop when it ceases to
slip?
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Answer 1

Answer:

A hoop of radius r and mass m rotating an angular velocity as ωo is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero.

The velocity of the centre of the hoop when it ceases to slip will be:-

$m {r}^{2} w0 = mvr + m {r}^{2} \frac{v}{r} \\ or, \: m {r}^{2} w0 = 2mvr \\ or, \: v = \frac{rw0}{2}$

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