The rotor of an electric motor has rotational inertia `I_(m)=2.0xx10^(-3)kg*m^(2)` about its central axis. The motor is used to change the orientation of the space probe in which it is mounted. The motor axis is mounted along the central axis of the probe, the probe has rotational inertia `I_(p)=10kg*m^(2)` about this axis. Calculate the number of revolutions of the rotor required to turn the probe through `30^(@)` about its central axis.

Explanation

To solve the problem, we need to determine how many revolutions of the rotor are required to turn the space probe through an angle of \(30^\circ\) (or \(\frac{\pi}{6}\) radians). We will use the principle of conservation of angular momentum since there is no net external torque acting on the system.

### Step-by-Step Solution:

1. **Understand the System**:
- The rotor of the motor has a rotational inertia \(I_m = 2.0 \times 10^{-3} \, \text{kg m}^2\).
- The space probe has a rotational inertia \(I_p = 10 \, \text{kg m}^2\).
- We need to turn the probe through an angle of \(30^\circ\) or \(\frac{\pi}{6}\) radians.
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