Question

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

Short answer

The number of revolutions made by the tire is 4309 rev.

Step-by-step solution

Meaning of circular motion and uniform circular motion

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 information

Given data:

The diameter of the tire is$\mathrm{d}=68\mathrm{c}\mathrm{m}$.

The distance traveled is $\mathrm{l}=9.2\mathrm{k}\mathrm{m}$.

Calculate the number of revolutions made by the tire

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:

$\begin{array}{rl}ln& =\frac{l}{c}\\ n& =\frac{l}{\pi d}\\ n& =\frac{\left(9.2\mathrm{k}\mathrm{m}\right)\left(\frac{{10}^3\mathrm{m}}{1\mathrm{k}\mathrm{m}}\right)}{\pi \left(68\mathrm{c}\mathrm{m}\right)\left(\frac{10^2\mathrm{m}}{1\mathrm{c}\mathrm{m}}\right)}\\ n& =4308.7\mathrm{r}\mathrm{e}\mathrm{v}\approx 4309\mathrm{r}\mathrm{e}\mathrm{v}\end{array}$

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