Question

Hi Can you please assist me with the questions below.

A coin is rolled around the edge of another stationery coin without slipping. Each coin has radius r.
1. Explain why the outer coin will rotate twice on its journey around the inner coin.
2. Generalise your argument to predict the number of times a coin of radius r/2 will rotate when
rolled around a coin of radius r.

Answer 1

Analysis and solution

The radius of the path is the sum of the coins' radii; hence, the circumference of the path is twice either coin's circumference. The center of the moving coin travels twice the coin's circumference without slipping; therefore, the moving coin makes two complete revolutions.