The rotational inertia of a collapsing spinning star drops to `1/4` its initial value. What is the ratio of the new rotational kinetic energy to the initial rotational kinetic energy?

Explanation

To solve the problem, we need to find the ratio of the new rotational kinetic energy to the initial rotational kinetic energy after the rotational inertia of a collapsing spinning star drops to \( \frac{1}{4} \) of its initial value.

### Step-by-Step Solution:

1. **Understand the Conservation of Angular Momentum**:
Since the star is collapsing and there are no external torques acting on it, we can use the conservation of angular momentum. The angular momentum \( L \) is given by:
\[
L = I \omega
...