Quote:
Originally Posted by Maffett
I think the answer is two times.
Sorry for the poor quality sketch. The contact point between the coins "travels" a distance of 6pi. The smaller coin has a circumference of 2pi. Therefore the smaller coin "rolls" three times during the trip. But point B only circumnavigates point A twice. It would circumnavigate three times if the trip had been in a straight line. But one doesn't happen because the distance traveled was a circle.  |
Good diagram, but it shows 4 rotations. The point on the small coin marked "B" starts at 3 o'clock (relative to the center of the small coin), it passes through 3 o'clock at 1/4 of the way around the large circle, again at 1/2 way, again at 3/4 way, and finally when it completes the trip - that is 4 times.
Maybe think about it this way. Suppose the large coin had radius zero, it is just a point. Rotate the small coin around that point - it makes 1 rotation even though the circumference of the large coin is zero. So you have to add 1 rotation to the 3 rotations that the small coin has to do just to travel around the circumference of the large coin.