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.
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
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
This is the required linear acceleration of the rope.
This is the required linear acceleration of the rope.
