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Moment of Inertia of a Rod

Two wheels ar...

Question

Two wheels are connected by a belt. The radius of larger wheel is three times that of the smaller one. What is the ratio of the rotation inertia of larger wheel to the smaller wheel, when both wheels have same angular momentum?

A

3

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B

6

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C

9

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D

12

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Solution

The correct option is B 3
Given Angular momentum is constant
$L_{1} = L_{2}$
$I_{1} w_{1} = I_{2} w_{2}$
$\frac{I_{1}}{I_{2}} = \frac{w_{2}}{w_{1}} = \frac{(v_{2} / r_{2})}{(v_{1} / r_{1})} = \frac{r_{1}}{r_{2}} [∴ v_{1} = v_{2}]$
$I_{1} : I_{2} = 3 : 1$

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