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.