A uniform disc of mass `m` and radius `R` is rotated about an axis passing through its center and perpendicular to its plane with an angular velocity `omega_()`. It is placed on a rough horizontal plane with the axis of the disc keeping vertical. Coefficient of friction between the disc and the surface is `mu`, find
(a). The time when disc stops rotating
(b). The angle rotated by the disc before stopping.

Explanation

To solve the problem step by step, we will break it down into two parts as required: (a) the time when the disc stops rotating and (b) the angle rotated by the disc before stopping.

### Part (a): Time When Disc Stops Rotating

1. **Identify the Forces and Torque**:
The frictional force \( F \) acting on the disc is given by:
\[
F = \mu mg
...