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Question
A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping.
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Solution
Mass of the hollow cylinder, m = 3 kg
Radius of the hollow cylinder, r = 40 cm = 0.4 m
Applied force, F = 30 N
The moment of inertia of the hollow cylinder about its geometric axis:
I = mr2
= 3 × (0.4)2 = 0.48 kg m2
Torque, t = F x r
= 30 × 0.4 = 12 Nm
For angular acceleration `alpha`, torque is also given by the relation:
`t = Ialpha`
`alpha = t/I = 12/0.48`
`= 25 " rad s"^(-2)`
Linear acceleration = `ralpha = 0.4 xx 25 = 10 ms^(-2)`
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