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14 minutes ago, Not a cat said:

Help me out here.  I've read up on this and it's still not clicking why the extra rotation occurs- the sites I see simply say because the center of A is rotating around the center of B but I'm still not getting it.

So if B rotated around A it would be 4/3?

Sincerely, a liberal arts major 

It's because for circle A to travel around the circumference of circle B, its CENTER must traverse 360 degrees, rather than a point on the circumference.  And its center is at 4/3r.

So you have to set the circumference of circle b equal the circumference of the imaginary circle traversed by the center, which has a radius 4/3r, and the multiplier n for the number of rotations.

Another way to see it is to replace the circle B with a point. Now, the circle B is just turning around a point that is located on its circumference (the common point between the two circles in the diagram, call it C). Now, the circle B is going around point C, but during the full rotation, the point C hasn't moved. 

So, a circle going around any path adds one extra rotation to the number of rotations corresponding to the distance of the path. You can also see it by replacing circle B with a square. When the circle A reaches a corner of the square, its point of contact doesn't move but it rotates by 90 degrees. It crosses 4 corners amounting to an extra full rotation (360 degrees).

  • 2 years later...

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