A uniform rod AB of length 2l and mass `m` is rotating in a horizontal plane about a vertical axis through A, with angular velocity `omega`, when the mid-point of the rod strikes a fixed nail and is brought immediately to rest. Find the impulse exerted by the nail.

Explanation

To solve the problem, we need to find the impulse exerted by the nail when the midpoint of the rotating rod strikes it and comes to rest. Here's the step-by-step solution:

### Step 1: Understand the Initial Conditions
The rod AB has a length of \(2l\) and mass \(m\). It is rotating about a vertical axis through point A with an angular velocity \(\omega\).

**Hint:** Identify the key parameters of the system: length, mass, and angular velocity.

### Step 2: Determine the Moment of Inertia
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