Chapter 8, Problem 7Q

To determine

To Find: The case in which it is harder to pedal (smaller or larger rear sprockets, smaller or larger front sprockets).

Explanation of Solution

Introduction:

The torque at the rear sprocket is what actually accelerates the bicycle.

Assume the force at both front and rear sprockets to be equal. The force is related to torque at each sprocket by F R, and so R R F F R R. The torque at the rear sprocket is what actually accelerates the bicycle, and so R F R F R R. To achieve a given torque at the back sprocket, a larger front torque (due to pedalling) must be present when the rear sprocket is small. Thus, it is harder to pedal with a small rear sprocket. Likewise, to achieve a given torque at the back sprocket, a larger front torque (due to pedalling) must be present when the front sprocket is larger. Thus, it is harder to pedal with a larger front sprocket.

Conclusion:

It is harder to pedal with smaller rear sprocket and likewise it harder to pedal with a larger front sprocket.