Answer
$\frac{I_A}{I_B} = \frac{1}{3}$
Work Step by Step
Since the belt does not slip, the linear velocity $v$ on the rim of each wheel must be equal.
Let the angular speed of wheel A be $\omega_A$
$\omega_A = \frac{v}{R_A}$
We can find an expression for the angular speed of wheel B:
$\omega_B = \frac{v}{R_B}$
$\omega_B = \frac{v}{3R_A}$
$\omega_B = \frac{\omega_A}{3}$
We can find the ratio of $\frac{I_A}{I_B}$ if the two wheels have the same of angular momentum:
$L_A=L_B$
$I_A~\omega_A = I_B~\omega_B$
$\frac{I_A}{I_B} = \frac{\omega_B}{\omega_A}$
$\frac{I_A}{I_B} = \frac{\frac{\omega_A}{3}}{\omega_A}$
$\frac{I_A}{I_B} = \frac{1}{3}$
