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=kmr2, 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 ω0, 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.

a) Suppose that after a certain time t, the string has been pulled through a distance L. What is the final rotational speed omega_final of the wheel? Express answer in terms of L, F, I, and omega_0.