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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Answer 1

Answer:

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 = F × r = 30 × 0.4 = 12 Nm

For angular acceleration α, torque is also given by the relation:

τ = Iα

α = τ / I = 12 / 0.48 = 25 rad s-2

Linear acceleration = τα = 0.4 × 25 = 10 m s–2

Answer 2

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 = F × r = 30 × 0.4 = 12 Nm

For angular acceleration α, torque is also given by the relation:

τ = Iα

α = τ / I = 12 / 0.48 = 25 rad s-2

Linear acceleration = τα = 0.4 × 25 = 10 m s–2