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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Prachi Gupta

Mass of the hollow cylinder, m = 3 kgRadius of the hollow cylinder, r = 40 cm = 0.4 mApplied force, F = 30 NThe moment of inertia of the hollow cylinder about its geometric axis:I = mr2= 3 × (0.4)2 = 0.48 kg m2Torque, τ = F × r = 30 × 0.4 = 12 NmFor angular acceleration α,...
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Mass of the hollow cylinder,m= 3 kgRadius of the hollow cylinder,r= 40 cm = 0.4 mApplied force,F= 30 NThe moment of inertia of the hollow cylinder about its geometric axis:I=mr2= 3 × (0.4)2= 0.48 kg m2Torque, τ =F×r = 30×0.4 = 12 NmFor angular acceleration α, torque is also given by the relation:τ = Iαα = τ /I = 12 / 0.48 = 25 rad s-2Linear acceleration = τα = 0.4 × 25 = 10 m s–2 read less
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