The Coin Problem
- Thread starter Acylum
- Start date
So in other words, how many circumferences of B will it take to equal the circumference of A? Assuming no slippage
No. That’s the gotcha of the problem and is not correct.
The issue is the question asked in the original post is not the same as the video. They are confusing circumference and radius assuming they are the same thing.
EDIT: I am also an idiot. That should not matter.
EDIT: I am also an idiot. That should not matter.
They are not the same but the ratio of the small one to the big one is the same whether you use radius or circumference.
That would be three. Which is how I did it in my head. I just imagined the larger circumference as a straight line and how many revolutions it would take for the smaller circle to travel that distance. Which is wrong and apparently what the SAT writer did also.
I came up with the same answer but got there a different way. I knew it would roll around the larger circumference three times -- that is FDR's neck would hit the larger circle three times -- but he would end up making one more revolution because the point his neck hits the large circle ends up adding up to another revolution.
I know that explanation doesn't make sense but it does to me.
For the first part you can stretch the large circle's circumference out to a straight line and roll along it. Then you need to add in how going around a circle rather than on a straight line adds or subtracts to the total rotation of the small coin.
If you take a coin and rotate it in place around a fixed point, it makes one revolution. So just to rotate around anything adds a revolution. Then add another three revolutions for the diameter of the larger coin.
