A 1 kg coin is placed 0.5 m from the centre of a horizontal disc. At an instant the disc has angular speed 2 rad/s and angular acceleration 4 rad/s². If the required frictional force is N√2 newton, find N.
Physics · Circular Motion · friction and circular motion
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Question

A 1 kg coin is placed 0.5 m from the centre of a horizontal disc. At an instant the disc has angular speed 2 rad/s and angular acceleration 4 rad/s². If the required frictional force is N√2 newton, find N.

Physics · Circular Motion · friction and circular motion

G1 Physics · Accepted Answer

The radial acceleration is a_r = ω²r = 2²×0.5 = 2 m/s². The tangential acceleration is a_t = αr = 4×0.5 = 2 m/s². These components are perpendicular, so the total acceleration is a = √(a_r²+a_t²) = √(2²+2²) = 2√2 m/s². Therefore f = ma = 1×2√2 = 2√2 N. Hence N = 2.