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 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_L, the string has been pulled through a distance L, What is the final rotational speed ω_final of the wheel?
(b) What is the instantaneous power P delivered to the wheel via the force F at time t=0?
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