A coin is at a fixed distance r from the centre of a horizontal disc. The disc is rotating and its angular speed is gradually increasing. Which statements are correct?
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Question

A coin is at a fixed distance r from the centre of a horizontal disc. The disc is rotating and its angular speed is gradually increasing. Which statements are correct?

G1 Physics · Accepted Answer

When the disc has angular speed ω and angular acceleration α, the coin needs radial acceleration a_r = ω²r and tangential acceleration a_t = αr. Therefore friction may need both radial and tangential components: f_r = mω²r and f_t = mαr. The total required friction is f = √(f_r² + f_t²). Static friction adjusts as needed and only satisfies f ≤ μₛmg before slipping; it is not necessarily equal to μₛmg.