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.

Answer 1

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 = mr 2

= 3 × (0.4)2 = 0.48 kg m2
Torque, π = F × r

= 30 × 0.4 = 12 Nm

For angular acceleration , torque is also given by the relation : π = Ia

α =$\frac{ π }{ I} = \frac{12 }{ 0.48}$

= 25 rad s -2

Linear acceleration = rα = 0.4 × 25 = 10 m s-2