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A man is standing on a rough (cofficient of friction=0.5) horizontal disc rotating with angular velocity 5rad/sec. At what distance from centre should he stand so that he does not slip on the disc?

A man is standing on a rough (cofficient of friction=0.5) horizontal disc rotating with angular velocity 5rad/sec. At what distance from centre should he stand so that he does not slip on the disc?

Grade:12

2 Answers

Mallikarjun Maram
50 Points
9 years ago
Here, friction provides required centripetal force to keep the man rotating without slipping. For safe rotation without slipping centripetal force should be less than maximum possible friction. At the upper limit mrω2 = μmg with the symbols having usual meanings. Hence rmax = μg/ω2. Substituting the values, we get rmax = 0.2 m.
Mallikarjun Maram
50 Points
9 years ago
Here, friction provides required centripetal force to keep the man rotating without slipping. For safe rotation without slipping centripetal force should be less than maximum possible friction. At the upper limit mrω2 = μmg with the symbols having usual meanings. Hence rmax = μg/ω2. Substituting the values, we get rmax = 0.2 m.

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