Circle question

Jomo

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You have a circle of radius R/3 that is rotating around a circle of radius R. How many revolutions does the smaller circle make to go around the bigger circle exactly one time?
 

MarkFL

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Do you mean the smaller circle is rolling without slipping around the circumference of the larger circle? If so, 4 times. :)
 

Jomo

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Do you mean the smaller circle is rolling without slipping around the circumference of the larger circle? If so, 4 times. :)
Your assumptions are correct. Before I say if your answer is correct or not can we please wait for at least one other response.

This problem was on a past SAT exam and 4 was NOT a choice.
 

MarkFL

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Your assumptions are correct. Before I say if your answer is correct or not can we please wait for at least one other response.

This problem was on a past SAT exam and 4 was NOT a choice.
A slightly more general form of this question was given at a university math competition in which I competed as a student way back when. I thought of the Moon orbiting the Earth and was one of a very few who got it correct. It stuck out in my memory. :)
 

Harry_the_cat

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Yes I agree with MarkFL. 4 times.
 

Subhotosh Khan

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You have a circle of radius R/3 that is rotating around a circle of radius R. How many revolutions does the smaller circle make to go around the bigger circle exactly one time?
This is also a very common "dynamics" (kinematics) problem. The coin at the center said have a "pseudo-rotation".
 

Jomo

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Yes, 4 times is the answer. I suspect that the author of the question and all of the reviewers thought the answer was 3 (as 4 was not a choice on the SAT exam). Do you guys ever make mistakes??
 

MarkFL

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Oh yes, I make mistakes. Interestingly, I recently posted a variant of this question on a non-math related site I help admin, and no one got the correct answer, and didn't believe me until I demonstrated it with an animated image.
 

Jomo

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Harry_the_cat

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My first thought was 3, but then thought that was far too easy for a SAT question. I drew a diagram, where P was the point on the smaller circle where the circles originally touched. The next time P touched the big circle (one third of the way around the big circle), the small circle had rotated 4/3 times. Lovely question!!
 

Jomo

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My first thought was 3, but then thought that was far too easy for a SAT question. I drew a diagram, where P was the point on the smaller circle where the circles originally touched. The next time P touched the big circle (one third of the way around the big circle), the small circle had rotated 4/3 times. Lovely question!!
It would have been more lovely of a question if the SAT exam had 4 as one of their choices.
 

Harry_the_cat

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Yes that error should have been picked up before it went to print. I wonder how much time was wasted on that question trying to get a "matching" answer. It invalidates the whole test really.
 

Jomo

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Yes that error should have been picked up before it went to print. I wonder how much time was wasted on that question trying to get a "matching" answer. It invalidates the whole test really.
The SAT people just removed the question from the scoring once they were told that the question did not have a valid answer. I agree that the whole test was therefore invalid.
 
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