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 `I_A//I_B` if the two wheels had same angular momentum about their central axes.
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Options

A. `(3)/(4)`
B. `(2)/(3)`
C. `(1)/(3)`
D. `(1)/(2)`

Answer

C

Explanation

( c) We use `L = I omega and K = (1)/(2) I omega^2` and observe that the speed of points on the rim (corresponding to the speed of points on the belt) of wheels `A` and `B` must be the same (so `omega_A R_A = omega_B r_B`)
If `L_A = L_B` (call it `L`) then the ratio of rotational inertias is.
`(I_A)/(I_B) = (L//omega_A)/(L//omega_B) = (omega_A)/(omega_B) =(R_A)/(R_B) = (1)/(3)`.