- Dec 30, 2014
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?
Your assumptions are correct. Before I say if your answer is correct or not can we please wait for at least one other response.Do you mean the smaller circle is rolling without slipping around the circumference of the larger circle? If so, 4 times.
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.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.
This is also a very common "dynamics" (kinematics) problem. The coin at the center said have a "pseudo-rotation".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?
Actually I did not see this article before. The site I got this problem from was not a very good reference. Thanks for finding this link!A reference would have been nice. I suppose you're referring to this: https://www.nytimes.com/1982/05/25/us/error-found-in-sat-question.html
It would have been more lovely of a question if the SAT exam had 4 as one of their choices.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!!
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.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.