First slide

Rolling motion

Question

A solid sphere is sliding with a velocity $V_{0}$ on a rough horizontal surface. Its velocity when it starts pure rolling is

Moderate

A

$\frac{5}{7} v_{0}$
B

$\frac{2}{7} v_{0}$
C

$\frac{v_{0}}{14}$
D

$\frac{5 v_{0}}{14}$

Solution

By conservation of angular momentum
${mv}_{0} r = Iω + mvr$
${mv}_{0} r = \frac{2}{5} {mr}^{2} ω + mvr$
$v_{0} = \frac{2}{5} rω + v = \frac{7}{5} v [v = rω]$
$v = \frac{5 v_{0}}{7}$

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