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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?

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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, τ=Fr=30×0.4=12 Nm
For angular acceleration α, torque is also given by the relation:
τ=Iαα=τI=120.48=25 rad s2
Linear acceleration =rα=0.4×25=10ms2


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