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.

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