A bicycle with tires 68 cm in diameter travels 9.2 km. How many revolutions do the wheels make?

The movement of an object along a circular route is described as the object's circular motion, and when an object moving along a circular route with constant speed is called a uniform circular motion.

Given data:

The diameter of the tire is\({\rm{d}} = 68\;{\rm{cm}}\).

The distance traveled is \({\rm{l}} = 9.2\;{\rm{km}}\).

The expression for the circumference of the tire is as follows:

\(c = \pi d\)

The number of revolutions made by the tire can be calculated as follows:

\(\begin{aligned}{l}n &= \frac{l}{c}\\n &= \frac{l}{{\pi d}}\\n &= \frac{{\left( {9.2\;{\rm{km}}} \right)\left( {\frac{{{{10}^3}\;{\rm{m}}}}{{1\;{\rm{km}}}}} \right)}}{{\pi \left({68\;{\rm{cm}}}\right)\left({\frac{{{\rm{1}}{{\rm{0}}^{{\rm{2}}}}\;{\rm{m}}}}{{{\rm{1}}\;{\rm{cm}}}}}\right)}}\\n&=4308.7\;{\rm{rev}}\approx{\rm{4309}}\;{\rm{rev}}\end{aligned}\)

Thus, the number of revolutions made by the tire is 4309 rev.