A bicycle wheel is mounted on a fixed, frictionless axle, with a light string wound around its rim. The wheel has moment of inertia I$=$kmr$2,$ where m is its mass, r is its radius, and k is a dimensionless constant between zero and one. The wheel is rotating counterclockwise with angular speed $\backslash$omega $0,$ when at time t$=0$ someone starts pulling the string with a force of magnitude F$.$ Assume that the string does not slip on the wheel.

uppose that after a certain time tL $,$ the string has been pulled through a distance L $.$ What is the final rotational speed $\backslash$omega final of the wheel? Express your answer in terms of L $,$ F $,$ I $,$ and $\backslash$omega $0.$