First slide

Rolling motion

Question

A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of $3 v^{2} / 4 g$ w.r.t. the initial position. The object is

Moderate

A

ring
B

solid sphere
C

hollow sphere
D

disc

Solution

$\frac{m v^{2}}{2} + \frac{I ω^{2}}{2} = m g \times \frac{3 v^{2}}{4 g} \Rightarrow I = \frac{m R^{2}}{2}$
For pure rolling condition, $v = R ω$

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