Pulling a wheel with a string?
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 = k m r^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 velocity 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.
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. i found that the final kinetic energy of the wheel is k_f = .5i omega_0^2 + fl, but i can't find an equation that relates this to final rotational speed.
b. what is the instantaneous power p delivered to the wheel via the force f at time t = 0?