Two discs of moments of inertia `I_(1) and I_(2)` about their respective axes (normal to the disc and passing through the centre), and rotating with angular speed `omega_(1) and omega_(2)` are brought into contact face to face with their axes of rotation coincident . What is the angular speed of the two-disc system ?

Explanation

To solve the problem of finding the angular speed of the two-disc system when two discs are brought into contact, we can follow these steps:

### Step 1: Understand the System
We have two discs, Disc 1 and Disc 2, with moments of inertia \( I_1 \) and \( I_2 \) respectively. They are rotating with angular speeds \( \omega_1 \) and \( \omega_2 \).

### Step 2: Calculate Initial Angular Momentum
The angular momentum \( L \) of a rotating body is given by the formula:
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