A disc is rotating with angular speed `omega_(1)`. The combined moment of inertia of the disc and its axle is `I_(1)`. A second disc of moment of inertia `I_(2)` is dropped on to the first and ends up rotating with it. Find the angular velocity of the combination if the original angular velocity of the upper disc was (a) zero (b) `omega_(2)` in the same direction as `omega_(1)` and (c) `omega_(2)` in a direction opposite to `omega_(1)`.

Explanation

To solve the problem, we will use the principle of conservation of angular momentum. The total angular momentum before the second disc is dropped onto the first disc must equal the total angular momentum after they start rotating together.

### Step-by-Step Solution

1. **Initial Angular Momentum Calculation:**
- The initial angular momentum of the system (only the first disc is rotating) is given by:
\[
L_{\text{initial}} = I_1 \omega_1
...