A disc is standing on a flat rough surface. Its centre is suddenly given a velocity of 5m/s in the forward direction. In how much time will pure rolling start? Mass = 1kg, Radius = 10cm. Coefficient of friction = 0.4.

A disc is standing on a flat rough surface. Its centre is suddenly given a velocity of 5m/s in the forward direction. In how much time will pure rolling start? Mass = 1kg, Radius = 10cm. Coefficient of friction = 0.4. Correct Answer 0.25 s

Friction force will decrease its linear velocity & increase its angular velocity. f = Ma . Friction ‘f’ = μN = 0.4*1*10 = 4N. Thus, v = v0 – at & w = w0 + (a/R)t. For pure rolling v = wR, thus: v0 – at = R(w0 + (a/R)t). a = f/M ∴ 5 – 4/1 = 0.1(0 + (4/0.1)t) ∴ 10 = 40t OR t = 0.25 s.
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