A rope is wrapped several times around a cylinder of radius 0.2 m and mass 30 kg. What is the angular acceleration of the cylinder if the tension in the rope is 40 N and it turns without friction?
Torque τ in angular motion is given by
Where α is the angular acceleration and I is the moment of inertia of the cylindrical body. For a cylindrical body, moment of inertia is , m being the mass and r the radius of the cylinder.
Similarly, torque is also given by
F is the force in the rope and here it is the tension in the rope.
Equating both equations
Now put values in the above equation