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Ride in bicycle

Ride in bicycle

A cyclist leaves his house riding his bicycle. The two wheels of the bicycle are identical and no skidding occurs during the ride. After a couple of hours he returns home.

Which of the two wheels has turned the most during the ride?

Solution

The front wheel travels a longer trajectory so it rotates more than the rear. The explanation is as follows: circulating in a straight line, both wheels spin equally but since the route started and ended at the same point, the cyclist has had to turn at some point. In curves, the layout of the front wheel is more external than that of the rear wheel so the wheel will have to turn more. It can be seen more easily by imagining the extreme case in which the rear wheel turns on itself while the front one describes a complete circle. The rear wheel will not have moved while the front wheel will have traveled a circle of radius equal to the distance between the axles of the two wheels.