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A bicycle wheel has radius R = 32.0 cm and mass M = 1.82 kg which you may assume to be concentrated on the outside radius. A resistive force f = 100 N (due to friction with the ground) is applied to the rim of the tire.  A force F is applied to the sprocket at radius r by the bicycle chain such that the wheel has an angular acceleration of alpha(a) = 4.50 rad/s2. The tire does not slip with the ground, and the lower part of the chain (not shown) exerts no force. 

What is the combined mass of the bicycle and rider? 

Hint: The force F also acts on the front sprocket of the bicycle.
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Added Fri, 03 Jul '15
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You know the angular acceleration of the wheels so you also know the linear acceleration of the bike
= ang accel x 0.32 ( the radius of the wheel ) = 4.50 x 0.32 = 14.4 m/s2

The friction force is the forward driving force , operating on the mass of the bike and rider
F = ma
m = F/a = 100/14.4 = 6.944
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Added Fri, 03 Jul '15
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