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Initial angular velocity of a circular disc of mass M is ω1. Then two small spheres of mass m are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

1. ((M + m)/M) ω1
2. ((M + m)/m) ω1
3. (M/(M + 4m)) ω1
4. (M/(M + 2m)) ω1

Correct answer: (M/(M + 4m)) ω1

Solution

The final angular velocity is derived from the conservation of angular momentum, where the initial angular momentum of the disc must equal the final angular momentum after the spheres are added. Since the spheres are added at diametrically opposite points, their contribution to the moment of inertia effectively increases the total moment of inertia of the system, leading to a decrease in angular velocity.

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