A turntable turns about a fixed vertical axis, making one revolution in `10 s`. The moment of inertia of the turntable about the axis is `1200 kgm^(2)`. A man of mass `80 kg`, initially standing at centre of the turnable, runs out along the radius. What is the angular velocity of the turtable when the man is `2 m` from the centre?

Explanation

To solve the problem step by step, we will use the principles of rotational dynamics, specifically the conservation of angular momentum.

### Step 1: Determine the initial angular velocity of the turntable
The turntable makes one revolution in 10 seconds. We can calculate the initial angular velocity (ω_initial) using the formula:
\[ \omega_{\text{initial}} = \frac{2\pi}{T} \]
where \( T \) is the time period for one revolution.
...