First slide

Rolling motion

Question

When a sphere rolls without slipping the ratio of its kinetic energy of translation to its total kinetic energy is

Moderate

A

1 : 7
B

1 : 2
C

1 : 1
D

5 : 7

Solution

f = $\frac{{KE}_{t}}{{KE}_{t} + {KE}_{r}} = \frac{\frac{1}{2} {mv}^{2}}{\frac{1}{2} {mv}^{2} + \frac{1}{2} {Iω}^{2}} = \frac{5}{7}$
[ $ω = \frac{v}{R}, I = \frac{2}{5} {mR}^{2}$ ]

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