Answer
The rotor is required to make $~~500~~$ revolutions.
Work Step by Step
We can find the angular speed of the rotor $\omega_r$ in terms of the angular speed of the probe:
$I_m~\omega_m = I_p~\omega_p$
$\omega_m = \frac{I_p}{I_m}~\omega_p$
$\omega_m = \frac{12~kg~m^2}{2.0\times 10^{-3}~kg~m^2}~\omega_p$
$\omega_m = 6000~\omega_p$
We can find the number of revolutions of the rotor:
$\theta_m = 6000~\theta_p$
$\theta_m = (6000)(30^{\circ})$
$\theta_m = 180,000^{\circ}$
$\theta_m = \frac{180,000^{\circ}}{360^{\circ}/rev}$
$\theta_m = 500~rev$
The rotor is required to make $~~500~~$ revolutions.
