I was super suspicious about the answer I came up with when I tried to solve this problem on my own. Then I watched the rest of the video, and it turned out I got it right.
Super neat. I didn’t even get what it was asking until he cut out the circles and demonstrated it on the table. My SAT in general was probably one of the lowest scores in human history lol.
Before I watched the video, I did (basically) the same thing, but with bottle caps instead of coins. I noticed the bottle cap went around it twice and assumed it would be double.
What really makes it click for me is: imagine the first coin were rolling around a point (like a very thin needle) rather than another coin. It would still need to rotate in order to roll, and it would complete exactly one rotation to roll around the point by a full revolution.
Very cool. The answer most people think is right technically makes sense if you only think from the perspective of circle B. But since the assumption is from your outside viewpoint, there’s some additionally thing going on.
Relating it to Earth’s rotations makes it clearer for me. A day either is or isn’t a full rotation depending on whether you’re coming from the perspective of the sun (or using the sun as a marker) versus from someone outside of the solar system.
The other way to imagine it is if circle A doesn’t “roll” around its circumference. Imagine that radius line as drawn is always pointed towards the center of B as it revolves around B. From the perspective of B, A doesn’t rotate in this scenario. But from our outside perspective, A does a kind of slow, single flip as it revolves around B.
This is how the moon orbits the Earth, always facing the same way. From our perspective on Earth, it doesn’t rotate. But from an outside perspective (e.g. the sun and how different sides of the moon are illuminated), it does.
If you want to argue that 3 revolutions is correct from the revolving point of view of circle B, then it is equally correct to say that circle A revolves zero times from its own perspective. Just like how you revolve zero times around the earth each day from your own perspective.
The least dumb answer is taken from the least dumb perspective. Which may or may not be the observer’s, depending on the observer.
I got the correct answer, 4, because I’ve seen a question like this before. After it rotates 1/3 of the way around the big circle, the same side is touching the big circle, but it is tilted by 1/3. After 3 rotations, you end up with the extra rotation.
Based on interpretation the answers could have been 1, 3, or 4. Only 3 was in the available answers, so it’s clearly the best answer. I’d be pissed if I lost 10 points because of this.
People who studied for SAT know that you don’t look for the most-correct answer, you look for the least-incorrect answer.
I’m still kinda confused it rotates 3 times from the perspective of the coin…so wouldn’t that mean it only rotates three times and this the question is still correct? They didn’t specify the perspective
Edit: Nevermind I think I understand it out now. It is rotating +1 times because it’s also translating around the larger circle
Very cool. Once the quarters moved I saw that it was the center of the outside quarter was traveling its radius plus the center coin radius, the extra revolution made sense.
My mind was blown when the perspective of the viewer changed the outcome. But then I applied the concept to a car and differentials and I think it made more sense to me.
In a straight line the wheels turn the same speed. When in a turn, the inside wheels turns less than the outside wheel and if you draw that out in a straight line then the difference in distance traveled is evident. But if you are an observer watching a car traveling around you in a roundabout, then your perspective is radial and the inside and outside tire seem to travel the same distance.
Please correct me if I am way off but this helped me understand why perspective affects the solution. It’s a linear vs radial perspective thing right?
I couldn’t explain it mathematically….ever, but after visualising it in my head, my answer would have been 4. I chose 9/2 because it was the closest answer.
Videos like this; ah yes, that makes sense. Then my brain malfunctions. Just like when I try to understand time dilation. I can almost understand it, but then I become donkey brained.
This video was very interesting to me. I got the answer wrong too.
I was super suspicious about the answer I came up with when I tried to solve this problem on my own. Then I watched the rest of the video, and it turned out I got it right.
The revolution thing threw me. I didn’t know that definition only applied in astronomy so I was thinking I was so smart for about half the video.
..what?
Super neat. I didn’t even get what it was asking until he cut out the circles and demonstrated it on the table. My SAT in general was probably one of the lowest scores in human history lol.
Before I watched the video, I did (basically) the same thing, but with bottle caps instead of coins. I noticed the bottle cap went around it twice and assumed it would be double.
Neat, that was a great explanation!
What’s maddening about it is I originally thought it was 4, but then I saw the answers and didn’t see 4 so I changed my answer to 3
what the fuck
I feel really dumb that this is pretty mind blowing to me.
What really makes it click for me is: imagine the first coin were rolling around a point (like a very thin needle) rather than another coin. It would still need to rotate in order to roll, and it would complete exactly one rotation to roll around the point by a full revolution.
Very cool. The answer most people think is right technically makes sense if you only think from the perspective of circle B. But since the assumption is from your outside viewpoint, there’s some additionally thing going on.
Relating it to Earth’s rotations makes it clearer for me. A day either is or isn’t a full rotation depending on whether you’re coming from the perspective of the sun (or using the sun as a marker) versus from someone outside of the solar system.
The other way to imagine it is if circle A doesn’t “roll” around its circumference. Imagine that radius line as drawn is always pointed towards the center of B as it revolves around B. From the perspective of B, A doesn’t rotate in this scenario. But from our outside perspective, A does a kind of slow, single flip as it revolves around B.
This is how the moon orbits the Earth, always facing the same way. From our perspective on Earth, it doesn’t rotate. But from an outside perspective (e.g. the sun and how different sides of the moon are illuminated), it does.
Flat earthers need to watch this from 11:38
Before he said that the actual answer was not listed on the test I thought I was stupid.
My thought was that it has 3 times the circumference, but that moving around in a circle is like another revolution.
This is incredibly unintuitive, but I’m glad I understand better now.
Lol I always thought sidereal was pronounced side-reel because it’s like the perspective “from the side”
If you want to argue that 3 revolutions is correct from the revolving point of view of circle B, then it is equally correct to say that circle A revolves zero times from its own perspective. Just like how you revolve zero times around the earth each day from your own perspective.
The least dumb answer is taken from the least dumb perspective. Which may or may not be the observer’s, depending on the observer.
Can someone explain how 4 rotations seems like 3 when you look from circles perspective? I didn’t seem to understand that part
I got the correct answer, 4, because I’ve seen a question like this before. After it rotates 1/3 of the way around the big circle, the same side is touching the big circle, but it is tilted by 1/3. After 3 rotations, you end up with the extra rotation.
Based on interpretation the answers could have been 1, 3, or 4. Only 3 was in the available answers, so it’s clearly the best answer. I’d be pissed if I lost 10 points because of this.
People who studied for SAT know that you don’t look for the most-correct answer, you look for the least-incorrect answer.
This was FASCINATING…. I love the internet.
I was just hung up on the wording; I thought “revolution” and “rotation” mean different things.
I’m still kinda confused it rotates 3 times from the perspective of the coin…so wouldn’t that mean it only rotates three times and this the question is still correct? They didn’t specify the perspective
Edit: Nevermind I think I understand it out now. It is rotating +1 times because it’s also translating around the larger circle
Very cool. Once the quarters moved I saw that it was the center of the outside quarter was traveling its radius plus the center coin radius, the extra revolution made sense.
My mind was blown when the perspective of the viewer changed the outcome. But then I applied the concept to a car and differentials and I think it made more sense to me.
In a straight line the wheels turn the same speed. When in a turn, the inside wheels turns less than the outside wheel and if you draw that out in a straight line then the difference in distance traveled is evident. But if you are an observer watching a car traveling around you in a roundabout, then your perspective is radial and the inside and outside tire seem to travel the same distance.
Please correct me if I am way off but this helped me understand why perspective affects the solution. It’s a linear vs radial perspective thing right?
Before the multiple choices were revealed, I paused and visualized it. Guess I got dumb lucky, because I guessed 4.
After the choices were revealed, I thought huh… must be 9/2, since it’s closest to my guess, but also figured 3 because that’s the 1/3 thought.
I patted myself on the back for blind luck when they explained it.
Not enough info, surely? Could be any number.
I couldn’t explain it mathematically….ever, but after visualising it in my head, my answer would have been 4. I chose 9/2 because it was the closest answer.
Am I getting Deja Vu? Because why have i seen a video about this already
Videos like this; ah yes, that makes sense. Then my brain malfunctions. Just like when I try to understand time dilation. I can almost understand it, but then I become donkey brained.
RIP, like most the word “revolution” immediately made me assumed it was from the perspective of the inner circle.
I wouldn’t say 3 is *wrong*, as much as it was an ambiguous question
Alright this is amazing
That was the most fun I’ve had watching a science related video in a while!