An ice skater having moment of inertia `l` rotating with angular speed `omega` suddenly opens her arms, which reduces her angular velocity to `(omega)/(4)`. Calculate the change in moment of inertia of the dancer.

Explanation

To solve the problem, we will use the principle of conservation of angular momentum. Here's a step-by-step solution:

### Step 1: Understand the conservation of angular momentum
The principle of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of the system remains constant.

### Step 2: Define the initial conditions
Let:
- \( I_1 = I \) (initial moment of inertia)
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