A cylinder of mass `5 kg` and radius `30 cm` and free to rotate about its axis receives an angular impulse of `3 kg m^(2) s^(-1)` initially, followed by a similar impulse after every `4` second. What is the angular speed of the cylinder `30 s` after the initial impulse ? The cylinder is at rest initially.

Explanation

To solve the problem step by step, we will follow the process of calculating the angular speed of the cylinder after 30 seconds, taking into account the angular impulses given at regular intervals.

### Step 1: Understand the given data
- Mass of the cylinder, \( m = 5 \, \text{kg} \)
- Radius of the cylinder, \( r = 30 \, \text{cm} = 0.3 \, \text{m} \)
- Initial angular impulse, \( J = 3 \, \text{kg m}^2/\text{s} \)
- Time interval for subsequent impulses, \( \Delta t = 4 \, \text{s} \)
- Total time after which we want to find the angular speed, \( t = 30 \, \text{s} \)
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