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Q.

Wheels A and B in Figure are connected by a belt that does not slip. The radius of B is 3.00 times the radius of A. What would be the ratio of the rotational inertias $\frac{I_{A}}{I_{B}}$ if the two wheels had same angular momentum about their respective geometrical axis.

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a

$\frac{3}{4}$

b

$\frac{2}{3}$

c

$\frac{1}{2}$

d

$\frac{1}{3}$

answer is C.

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Detailed Solution

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We use L = I $ω$ and the speed of points on the rim of wheels A and B must be the same and equal to the speed of belt.So $ω_{A} = \frac{v}{R_{A}} a n d ω_{B} = \frac{v}{ω_{B}}$
Since $L_{A} = L_{B}$ = L , We can write $I_{A} ω_{A} = I_{B} ω_{B}$
$\frac{I_{A}}{I_{B}} = \frac{ω_{B}}{ω_{A}} = \frac{(v / R_{B})}{(v / R_{A})} = \frac{R_{A}}{R_{B}} = \frac{1}{3}$

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Wheels A and B in Figure are connected by a belt that does not slip. The radius of B is 3.00 times the radius of A. What would be the ratio of the rotational inertias IAIBif the two wheels had same angular momentum about their respective geometrical axis.