First slide

Rolling motion

Question

A hoop rolls down on an inclined plane. The fraction of its kinetic energy that is associated with only the rotational motion is

Moderate

A

1 : 2
B

1 : 3
C

1 : 4
D

2 : 3

Solution

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

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