# Wrapping around a pole

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 $$v_f/v_i$$.

Assumptions

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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