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 of finding the impulse exerted by the nail on the rotating rod, we can follow these steps:

### Step 1: Understand the System
We have a uniform rod AB of length \(2l\) and mass \(m\) rotating about a vertical axis through point A with an angular velocity \(\omega\). When the midpoint of the rod strikes a fixed nail, it is brought to rest.

### Step 2: Identify the Change in Angular Momentum
The impulse exerted by the nail can be found using the relationship between angular impulse and change in angular momentum:
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