Question

Two persons stand at the edges of a rotating circular platform at diametrically opposite points. If they start moving towards each other at uniform velocity, then its

• A. angular velocity decreases
• B. moment of inertia increases
• C. moment of inertia remains increases
• D. angular velocity increases and moment of inertia decreases
• E. both angular velocity and moment of inertia remain constant

Answer 1

The Correct Option is D

The two persons are initially at diametrically opposite points on a rotating platform. As they move towards each other, their distance from the center of the platform decreases, which means the moment of inertia of the system decreases. The moment of inertia \(I\) of a rotating system is given by the formula: \[ I = m r^2 \] Where \(m\) is the mass of the person and \(r\) is the distance from the center. As \(r\) decreases, \(I\) decreases. According to the law of conservation of angular momentum, when the moment of inertia decreases, the angular velocity \( \omega \) must increase to keep the angular momentum constant. Therefore, the angular velocity increases and the moment of inertia decreases as the persons move towards each other.

The correct option is (D) : angular velocity increases and moment of inertia decreases

Answer 2

When two persons standing at diametrically opposite ends of a rotating circular platform move towards each other, they are moving closer to the axis of rotation. 

Since no external torque acts on the system, the angular momentum is conserved.

Moment of inertia depends on the mass distribution with respect to the axis of rotation. As they move towards the center:

• The moment of inertia decreases because mass is getting closer to the axis.
• To conserve angular momentum, angular velocity increases.

Answer: angular velocity increases and moment of inertia decreases