A wheel of mass 2 kg and radius 20 cm initially at rest is free to rotate about its axis. It receives an angular impulse of `4kgm^(2)s^(-1)` initially and similar impulse after every 5 s of initial one. Calculate the angular speed of the wheel 22 s after the initial impulse.

Explanation

To solve the problem, we need to calculate the angular speed of the wheel after 22 seconds, given that it receives an angular impulse of \(4 \, \text{kg m}^2/\text{s}\) initially and every 5 seconds thereafter.

### Step-by-Step Solution:

1. **Determine the Moment of Inertia (I)**:
The wheel is a solid disc, and its moment of inertia about its central axis is given by the formula:
\[
I = \frac{1}{2} m r^2
...