Pulling the bicycle pedal backwards

Question

A bicycle is held upright (someone steadies it without pushing) on level ground, in a normal gear, with the chain on. One pedal is at its lowest point. A string is tied to that pedal and pulled gently backwards, horizontally, in the direction of the rear wheel.

Which way does the bicycle move, and which way does the pedal move relative to the bicycle?

Accepted Answer

The bicycle moves backwards, in the direction of the pull, and the pedal, relative to the bicycle, moves forwards, so the crank turns "backwards" as if pedalling in reverse. Why. Suppose instead the bicycle rolled forwards at speed v. The rear wheel turns, the chain turns the crank, and the pedal goes round. With normal gearing, the crank turns much more slowly than the wheel: one turn of the crank moves the bike several metres, while the pedal only travels round a circle of radius about 17 cm. So the pedal's speed relative to the bike is much less than v. At its lowest point the pedal is mov…

Pulling the bicycle pedal backwards

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