An ice skater has her arms outstretched and is spinning with a rate of 2 rotations per second. Her moment of inertia at this instant is `1.48kgm^(2)`. She then pulls her arms inside to increase her rate of spin and her moment of inertia becomes `0.56kgm^(2)`. Calculate her new rate of rotation.

Explanation

To solve the problem, we will use the principle of conservation of angular momentum. The angular momentum of a system remains constant if no external torque acts on it.

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- Initial moment of inertia, \( I_{\text{initial}} = 1.48 \, \text{kg m}^2 \)
- Initial rate of rotation, \( f_{\text{initial}} = 2 \, \text{rotations per second} \)

...