A uniform disc of radius `r_(0)` lies on a smooth horizontal plane. A similar disc spinning with the angular velocity `omega_(0)` is carefully lowered onto the first disc. How soon do both discs spin with the same angular-velocity if the friction coefficient between them is equal to `mu`?

Explanation

To solve the problem of how soon both discs spin with the same angular velocity after one is lowered onto the other, we can follow these steps:

### Step 1: Understand the System
We have two uniform discs of radius \( r_0 \). The first disc is at rest on a smooth horizontal plane, while the second disc is spinning with an angular velocity \( \omega_0 \). When the second disc is lowered onto the first, they will eventually reach a common angular velocity due to the friction between them.

### Step 2: Apply Conservation of Angular Momentum
Before the second disc is placed on the first, the angular momentum of the system is solely from the second disc:
\[
...