A light string with a particle of mass $m$ at one end, wraps itself around a fixed vertical cylinder of radius $a$. The entire motion is in the horizontal plane(neglect gravity). The angular speed of the string (and the particle) is $\omega_0$ when the distance of particle from point of contact between the string and the cylinder is $b$. If the angular speed is $\omega$ and the tension in the string is $T$ after the string has turned through the additional angle $\theta$.
what I have tried doing is to conserve the angular momentum. But I am facing difficulty in writing angular momentum when the string had turned by an angle $\theta$