A circular platform is mounted on a frictionless vertical axle. Its radius R $$=$$ $$2$$ m and its moment of inertia about the axle is $$200$$ kg $$m2$$. It is initially at rest. A $$50$$ kg man stands on the edge of the platform and begins to walk along the edge at the speed of $$1$$ $$ms-1$$ relative to the ground. Time taken by the man to complete one revolution relative to the platform is

Question

A circular platform is mounted on a frictionless vertical axle. Its radius R $$=$$ $$2$$ m and its moment of inertia about the axle is $$200$$ kg $$m2$$. It is initially at rest. A $$50$$ kg man stands on the edge of the platform and begins to walk along the edge at the speed of $$1$$ $$ms-1$$ relative to the ground. Time taken by the man to complete one revolution relative to the platform is

Infinity Learn · Accepted Answer

From conservation of angular momentum                  I ω $$=$$ mvr               $$200$$ × ω $$=$$ $$50$$×$$1$$×$$2$$                ω $$=$$ $$12rad/s$$                 veloccity of edge of platform $$=$$ rω $$=$$ $$1$$ $$m/s$$.So velocity of man relative to the platform $$=$$ (1+1) $$m/s$$ $$=2m/s$$                  T $$=$$ $$2$$$$π$$$$r/2$$ $$=$$π$$r=2$$π s

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