A disc of circumference s is at rest at a point A on a horizontal surface when a constant horizontal force begins to act on its centre. Between A and B there is sufficient friction to prevent slipping, and the surface is smooth to the right of B. AB = s. The disc moves from A to B in time T. To the right of B,
Text Solution
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(b, c, d)
Let P = external force F = force of friction between A and B
a 1 = acceleration between A and B, a 2 = acceleration beyond B.
P – F = ma 1 and P = ma 2 . ∴ ∴ a 2 > a 1 .
Let α α = angular acceleration between A and B. for one rotation,
θ θ = 2 π π = 1/2 α α T 2
or T = (4 π π / α α ) 1/2 = time of travels from A to B.
Angular velocity at B = ω ω B = α α T.
For one rotation to the right of B,
θ θ = 2 π π = ω ω B t or
t = 
.
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