Question

A bicycle wheel has a radius R = 32 cm and a mass M = 1:80 kg which you may assume to be
concentrated on the outside radius. Assume that you apply a force F to a sprocket so that the wheel
has an angular acceleration ® = 4:50 rad/s2. A resistive force f = 131 N is applied to the rim of the
tire when it is moving.
calculate the strength of the required
force F, when the radius r is:
(a) 4.53 cm.

I worked out the problems using the sum of the Torque=I@

I@=-rFsin90+Rfsin90
Then I solved for F but my answer is 40 Newtons away from the right answer which is 940 N.
There is a picture of the problem in google if you just paste the entire problem on the search space it brings out a pdf file that has the picture it is problem 10-8

Answer 1

mr^2*4.5=r*F-131*.16

1.80*..32^2*4.5=.0453*F-131*.32

I get 940