A coin is placed on a horizontal disc rotating with constant angular speed 4 rad/s. The coefficient of static friction between the coin and the disc is 0.8. Take g = 10 m/s². If the maximum distance from the centre at which the coin can remain at rest relative to the disc is r = N/20 m, find N.
Physics · Circular Motion · friction and circular motion
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Question

A coin is placed on a horizontal disc rotating with constant angular speed 4 rad/s. The coefficient of static friction between the coin and the disc is 0.8. Take g = 10 m/s². If the maximum distance from the centre at which the coin can remain at rest relative to the disc is r = N/20 m, find N.

Physics · Circular Motion · friction and circular motion

G1 Physics · Accepted Answer

The required centripetal force is supplied by static friction. For no slipping, mω²r ≤ μₛmg. At the limiting condition, mω²r_max = μₛmg. Therefore r_max = μₛg/ω² = (0.8×10)/4² = 8/16 = 1/2 m. Given r_max = N/20 m, N/20 = 1/2, so N = 10.