Wrapping around a pole

Classical Mechanics Level 4

One end of a string is attached to a vertical pole fixed to the ground. A small particle is attached to the other end. The particle is given a velocity \(v_i\) such that it starts rotating along a circle in a horizontal plane. The string initially makes an angle of \(\theta\) with the pole. The string now starts wrapping itself around the pole. The final velocity of the particle is \(v_f\). Find \(v_f/v_i\).


  1. The particle can be assumed to travel along a circle at any instant.

  2. The friction between the pole and the string is sufficient to prevent the string from slipping over the pole.


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