A uniform disc is rotating freely about a vertical axis passing through its centre and makes 100 rpm. A small piece of gum of mass 8 g falls vertically on the disc and sticks to it at a distance of 5 cm from its axis. If the number of rotations per minute reduces to 80 rpm find the moment of inertia of the disc.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Convert RPM to Angular Velocity
The initial angular velocity (ω_initial) is given as 100 rpm. We need to convert this to radians per second.

\[ \omega_{\text{initial}} = 100 \, \text{rpm} \times \frac{2\pi \, \text{rad}}{1 \, \text{rev}} \times \frac{1 \, \text{min}}{60 \, \text{s}} = \frac{100 \times 2\pi}{60} = \frac{10\pi}{3} \, \text{rad/s} \]
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