Can you solve this SAT math question?

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Naysaspace
03/19/2024
05:18 PM
#1
Two coins. These coins are the exact same and have the same radius and circumference.

Roll the top coin around the bottom coin until it gets back to it's starting position. How many full rotations does the top coin make?
https://gamefaqs.gamespot.com/a/forum/8/8a275a1e.png

This is known as the coin roll paradox.
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R1masher
03/19/2024
05:20 PM
#2
360
R1R1R1R1R1R1
Naysaspace
03/19/2024
05:21 PM
#3
This is a handy explanation

https://graphicmaths.com/recreational/paradoxes/rotating-coin/
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bigblu89
03/19/2024
05:23 PM
#4
Yes. I can.
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LonelyStoner
03/19/2024
05:24 PM
#5
720 degrees. You have to account for the first coins area and circumference. It takes two rotations to match up perfectly.
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VideoboysaysCube
03/19/2024
05:30 PM
#6
Naysaspace posted...
This is a handy explanation

https://graphicmaths.com/recreational/paradoxes/rotating-coin/

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EndOfDiscOne
03/19/2024
05:32 PM
#7
I had to visualize it, and I realized my initial guess was wrong. I haven't looked up the answer, but I would have gotten it wrong on an SAT since I'd be working faster.
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RetuenOfDevsman
03/19/2024
05:32 PM
#8
It would have to be two. If it just did one, the top of Washington's head would always be away from the eagle, which would be sliding instead of rolling. Then since the circumferences are the same, it would have to roll once in addition.

Or to think of it another way, if you drew a line the length of the circumference and rolled it along ng it would rotate once, then there's another rotation when the path is curved into a circle.
NeonOPPAl
03/19/2024
05:34 PM
#9
I guess 2 because it rotates once from the circumference being the same, and another for the viewing angle (ie: when it's halfway around, it will be right side up for us)
https://imgur.com/aMaI3hj https://imgur.com/7PsdJNc
https://imgur.com/eK8vZVn https://imgur.com/u2HR4nG https://imgur.com/nQGM5cZ
MarcoRubio
03/19/2024
05:37 PM
#10
It's fucking two
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Naysaspace
03/19/2024
05:46 PM
#11
Why it's 2 and not one: The stationary coin is also technically rolling. Think like they are two gears, there is no "sliding". But the camera/view is "locked" to the "stationary" coin. It still moves, so the movement is "transferred" to the outside/rolling coin.

When i found this out it blew my mind. The problem i worked on was a bit tougher (two different sized circles, one circumference 1, other circumference 3, and the answer is 4, not 3). AFAIK, the formula for rotations is Large R/ small r + small r.
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Naysaspace
03/19/2024
05:49 PM
#12
RetuenOfDevsman posted...
It would have to be two. If it just did one, the top of Washington's head would always be away from the eagle,
1 full rotation actually has the top of the head facing the eagle, but it's at the bottom rather than back in the starting position
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DDP886
03/19/2024
06:01 PM
#13
Reminds me of the GRE
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Evening_Dragon
03/19/2024
06:05 PM
#14
Just visualized it and only 2 looked right. Thanks for that explanation link.
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kelemvor
03/19/2024
06:07 PM
#15
Isnt this a question that was wrong on an official SAT test?
Naysaspace
03/19/2024
06:18 PM
#16
kelemvor posted...
Isnt this a question that was wrong on an official SAT test?
it was, i believe that was a long time ago however.
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radical_rhino
03/19/2024
06:28 PM
#17
Thats not what a paradox is.
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Baphometa
03/19/2024
06:40 PM
#18
radical_rhino posted...
Thats not what a paradox is.
https://gamefaqs.gamespot.com/a/forum/2/2fee5932.jpg
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Robot2600
03/19/2024
06:48 PM
#19
weird!
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Seaman_Prime
03/19/2024
07:12 PM
#20
Holy shit im doing this with my fingers and its blowing my mind
Current Events » Can you solve this SAT math question?