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 You say you want a revolution... (Posted on 2004-06-27)
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?

 Submitted by SilverKnight Rating: 2.7500 (4 votes) Solution: (Hide) 4 if the smaller circle rolls on the outside of the larger circle; 2 if it rolls on the inside. Imagine you are rolling a wheel by pushing it along the equator of the earth. Suppose the circumference of the wheel is one third of that of the earth. By the time you return to your starting point, the wheel finishes 3 revolutions relative to you. But do not forget you yourself also finishes 1 revolution in the same direction. As a result, the number of absolute revolutions is 3+1=4. But if the small circle is rolling inside the large circle, the answer is then 3-1=2, because in this case the wheel makes a counter-revolution as you walk once around.

 Subject Author Date Veefessional strikes again! Vee-Liem Veefessional 2004-07-30 02:51:23 damn'it vije 2004-07-07 13:53:39 pi pi vije 2004-07-07 13:51:49 Physical thought experiment Larry 2004-07-05 22:55:47 I think... Cesar Ali 2004-06-30 11:17:55 radii rixar 2004-06-27 22:37:02 Revolutions Half-Mad 2004-06-27 18:26:31 You say you want a revolution... Ron Anthony 2004-06-27 16:48:26 solution Charlie 2004-06-27 15:06:38 re(2): No Subject, mmmmmm Richard 2004-06-27 14:39:10 re: No Subject, mmmmmm Juggler 2004-06-27 13:58:03 No Subject Elisabeth 2004-06-27 13:13:31

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