Why Are There 2 Rotations? (The Coin Paradox)

While This Seems Impossible, Mathematics Found a Way to Justify it Geometricly, but What's the Reasoning?

#maths #shorts #geometry #mathstricks #education

[the_math_behind]

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[greenpoha]

But it's making only one roatation

[hellobruh]

Well here's the mathematical explanation

No of revolutions = distance traveled/circumference of circle

Distance traveled here is 2π(r+r) (since it's rotating around the centre and the centre is r+r away from the edge of the rotating circle)


So no of revolutions = 2π(r+r)/2πr = 2

[allypezz]

Someone made the good point that if the inner circle had a radius equal to zero (a dot), the outer coin would make one full rotation. This is translation. Therefore the number of rotations of two circles is proportional to circumference, plus translation.

[skill_issuesmo]

my thought is that since it is spinning around a circle it makes a rotation but since the outer circle is also spinning it does 2 rotations

[chrisg]

To roll right round a point, or a circle of zero circumference, the circle has to make 1 rotation. Now imagine that point expanding to equal the circle's circumference. The circle this time has to make an extra rotation. So 2 rotations.

[janthony]

What am I missing. I see one rotation happening... Red dot is hitting the same spot on circle one.

[boetasturgeon]

divide the rotating coin in half and you will see its only traveled half the distance, if i say the earth rotated around the earth in one year, and you made the earth the same size as the sun are you going to stop halfway? if you say yes im beating you with a chair

[chrisg]

"It has to do with the fact that the outer coin is traveling along a curved path and not a straight line"

Right. So let's compare how many circles we can get on a straight line, just touching and not overlapping, and on a circle with a circumference equal to that line. I got 9 and very close to 11 respectively.