In an amusement park there is a rotating horizontal disk. A child can sit on it at any radius (Shown in figure). As the disk begins to “speed up”, the child may slide off if the frictional force is insufficient. The mass of the child is 50 kg and the coefficient of friction is 0.4. The angular velocity is 2 rad/s. What is the maximum radius R where he can sit and still remain on the disk?
Text Solution
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Sol.
Under the critical circumstance that the child just starts to slide,
mR 
2 = µmg.
Hence R = 
= 
= 0.98 m
As the centrifugal force is proportional to the radius, this is the maximum radius for no-sliding.
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