A circle with radius 1 rolls without slipping once around a circle with radius 3. How many revolutions does the smaller circle make?

Does it matter if the smaller circle rolls on the inside or outside of the larger circle?

radius of 1 and 3 = diameter of 2 and 6.
pi d = the circumference.
so, 1 pi d = x pi d
1 pi 6 = x pi 2
(pi 6) / (pi 2) = x
x = 3

But, it's going around in a circle, while it's going along the path, so it makes one more revolution, while completing the path. It would be 3, if it was following a straight line.
As it's following a circle, it's 4, if it is following the outside of the larger circle.
2 if it's following the inside of the circle.
3 if it's following the edge, on the side... but it will be more of a spiral this way.
Edited on June 27, 2004, 6:30 pm

Posted by Half-Mad on 2004-06-27 18:26:31