A hoop of radius r and mass m rotating with an angular velocity 0 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?

Engineering

Physics

Rolling

Angular Momentum and Conservation of Angular Momentum

Question

A hoop of radius r and mass m rotating with an angular velocity $ω$ ₀ 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?

$\frac{{rω}_{0}}{3}$

$\frac{r ω_{o}}{5}$

$\frac{{rω}_{0}}{2}$

$\frac{{rω}_{0}}{4}$

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${mr}^{2} ω_{0} = mvr + {mr}^{2} \frac{v}{r}$

${mω}_{0} = \frac{2 Mv}{r}$

$v = \frac{ω_{0} r}{2}$