question_answer

A circular disc is rotating with angular velocity If a man standing at the edge of the disc walks towards its centre, then the angular velocity of the disc:

A) is not changed 

B) be halved

C)  decreases         

D) increases

Correct Answer: D

Solution :

If M is mass of disc, R is radius then moment  of inertia is \[I={{\frac{1}{2}}^{2}}MR\] From law of conservation of angular momentum \[J=I\omega =\text{cosnstant}\] where, \[\omega \]is angular velocity. Hence, if\[I\]decreases \[\omega \]increases and vice versa. \[J=\frac{1}{2}M{{R}^{2}}\omega =\operatorname{constant}\] When man standing at the edge of the disc walks towards its centre, R decreases, hence angular velocity increases.