A rope of negligible mass is wound around a hollow cylinder of mass 3 kg and radius 40 cm and then the entire arrangement is placed on a smooth horizontal surface. What is the angular acceleration (in rad s - 2 ) of the cylinder if the rope is pulled with a force of 30 N?

Step-by-step solution

Given, M = 3 kg R = 40 cm = 0.40 m F = 30 N Moment of inertia of the hollow cylinder about its axis of symmetry I = MR 2 = 3 × (0.40) 2 = 0.48 kg-m 2 Torque acting on the cylinder by the applied force, τ = F × R = 30 × 0.40 = 12 N-m. Angular acceleration produced in cylinder, α = τ I = 12 0.48 = 25 rad/s 2 Linear acceleration, a = R α = 0.40 × 25 = 10.0 m/s 2