A bicycle wheel has a diameter of 63.8 cm and a mass of 1.79 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 117 N is applied tangent to the rim of the tire.
(a) What force must be applied by a chain passing over a 9.01-cm-diameter sprocket in order to give the wheel an acceleration of 4.53 rad/s2?
(b) What force is required if you shift to a 5.60-cm-diameter sprocket?
m= wheel mass
F=Resistive force tangent to tire
r=radius of sprocket
α=angular acceleration of the wheel
τf= Torque from the bike wheel
τext=external torque for sprocket
Moment of Interia of a hoop
The Attempt at a Solution
First calculate torque on the bike wheel
Due to laws of rotational dynamics and why the wheel is spinning relate the torque of the wheel to torque of sprocket to moment of interia of the wheel
Break down each term into quantities we already know
Rearrange and solve for F
Maybe I messed up somewhere but I've tried twice already submitting the answer online and this is wrong but that was my shot, thank you for helping.