The image above is a close-up shot of three wheels, all connected to each other. When one wheel moves, so must all the others. Toothed wheels like these are called gears, and each is connected with a shaft (not pictured) that would move with it.
Why It Matters
Now consider the image below, in which the gears are of different sizes. They were made this way for a reason: the person who designed them needed their shafts to turn at different speeds. How do the wheels yield different speeds, and how does this relate to the circumference of circles?
If we call the leftmost wheel and the middle wheel , we can see that when makes a full revolution, must make more than one revolution. This is because the circumference of wheel is larger than the circumference of wheel . Since the two wheels must move together, wheel has to make more than one revolution to keep up with wheel . Therefore, wheel must spin faster.
By choosing the size of the gear wheels, the designer can produce any speed he or she desires. Car engines are just one application in which gears—and therefore circumferences—come into play. Take a look with this video showing how the gearbox in an MGB sports car works: http://www.youtube.com/watch?v=-lAXy3teCLw
Watch the video below to see a how a motorcycle entertainment troupe puts circumferences to use in its shows.