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You say you want a revolution... (Posted on 2004-06-27) Difficulty: 3 of 5
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionVeefessional strikes again!Vee-Liem Veefessional2004-07-30 02:51:23
Solutiondamn'itvije2004-07-07 13:53:39
Solutionpi pivije2004-07-07 13:51:49
Hints/TipsPhysical thought experimentLarry2004-07-05 22:55:47
SolutionI think...Cesar Ali2004-06-30 11:17:55
Solutionradiirixar2004-06-27 22:37:02
SolutionRevolutionsHalf-Mad2004-06-27 18:26:31
You say you want a revolution...Ron Anthony2004-06-27 16:48:26
SolutionsolutionCharlie2004-06-27 15:06:38
re(2): No Subject, mmmmmmRichard2004-06-27 14:39:10
Solutionre: No Subject, mmmmmmJuggler2004-06-27 13:58:03
No SubjectElisabeth2004-06-27 13:13:31
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