Calculating the Force on a Bicycle Wheel

[BrettF]

I have been trying this problem for a while and can't seem to figure it out:

A bicycle wheel has a radius R = 32.0 cm and a mass M = 1.82 kg which you may assume to be concentrated on the outside radius. A resistive force f = 137 N (due to the ground) is applied to the rim of the tire. A force F is applied to the sprocket at radius r such that the wheel has an angular acceleration of 4.50 rad/s^2. The tire does not slip.

a. If the sprocket radius is 4.53 cm, what is the force, F (in Newtons)?
b. If the sprocket radius is 2.88 cm, what is the force, F?
c. What is the combined mass (kg) of the bicycle and rider?

I know that the tangential acceleration a = rα where α is rotational acceleration.
I also know the Kinetic energy must be K = ½ Iω^2+ ½Mv^2 where the first term is the rotational kinetic energy and the second term is the translational kinetic energy.
Finally, I know that I which is the moment of inertia for a shell (the shape of the bicycle) is Mass*Radius^2.
I've been doing the algebra with it and can't seem to get any meaningful results. Am I on the right track with this thinking? Thanks in advance for the help.

 

[mfb]

I've been doing the algebra with it and can't seem to get any meaningful results.

Please show what you did (that's the point of the homework template - please do not delete it).

Working with energy is possible, but using forces and torque everywhere is probably easier.

 

[haruspex]

The linear KE cannot be interesting because you do not know the mass of the bicycle. Concentrate on torques and angular acceleration.