A man stands on a rotating platform, with his arms stretched horizontal holding a `5 kg` weight in each hand. The angular speed of the platform is `30` revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from `90 cm` to `20 cm`. moment of inertia of the man together with the platform may be taken to be constant and equal t `7.6 kg m^(2)`. (a) What is the his new angular speed ? (Neglect friction.)
(b) Is kinetic energy conserved in the process ? If not, from where does the change come about ?

Explanation

To solve the problem, we will break it down into two parts as specified in the question.

### Part (a): Finding the New Angular Speed

1. **Identify Initial Conditions**:
- The initial angular speed \( \omega_1 \) is given as \( 30 \) revolutions per minute (rpm).
- Convert this to radians per second:
\[
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