Question

A solid cylinder of mass M = 1 kg and radius R = 0.5 m is pivoted at its centre and has three particles of mass m = 0.1 kg mounted at its perimeter as shorn in the figure. The system is originally at rest. Find the angular speed of the cylinder when it has swung through 90° in anticlockwise direction.

Answer 1

The answer is-
Let moment of inertia 
mass of cylinder m = 1 kg
mass of the three point masses = 0.3 kg
I total =0.25/2 + 0.3 × 0.25 = 0.2
from the law of conservation of energy
1/2 I total ω² =  mgh
1/2 × 0.2 × ω² = 1.3 × 0.39
ω = 2.25 rad/second.