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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?

Solution

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

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