A wheel is rotating at an angular speed `omega` about its axis which is kept vertical. An identical wheel initially at rest is gently dropped into the same axle and the two wheels start rotating with a common angular speed. Find this common angular speed.

Explanation

To find the common angular speed of the two wheels after they are combined, we can use the principle of conservation of angular momentum. Here’s the step-by-step solution:

### Step 1: Understand the System
We have two identical wheels:
- The first wheel (Wheel 1) is rotating with an angular speed \( \omega \).
- The second wheel (Wheel 2) is initially at rest.

### Step 2: Define the Moment of Inertia
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