Rotating Coin Paradox



Consider two round coins of equal size. Imagine holding one still so that it does not move and then rolling the other coin around it, making sure that it does not slip. The rims are kept touching at all times. How many times will the moving coin have rotated after it has completed one revolution of the stationary coin?
Don't try it until you have thought about it.
You may be surprised.

CONTINUE



Most people believe that the answer will be once and are therefore surprised to discover that the truth is in fact twice...

coin

...Or is it? Think about it.

From Earth we always see the same same face of the moon, but looking at it form Mars we would see it spinning. So, does the moon rotate, or doesn't it?

CONTINUE



It could be argued that relative to a fixed point on the stationary coin, the moving coin only rotates once. How many times the coin rotates would seem to depend on the frame of referrence of the observer.

So, does the moon rotate about its own axis?
A Foucault pendulum can be used to detect the inertial effects caused by the rotation of astronomical bodies. If this pendulum were placed on the moon it would indicate that the moon does indeed rotate as it circles the earth.
However, this does not put an end to the argument. If the moon did not rotate, but instead the universe rotated about the moon, the pendulum would still act in exactly the same way. General realtivity shows that the gravity fields created by a rotating universe about a non-rotating moon would produce the same effects as the inertia fields which are generated if the moon rotates in a fixed universe.

It would therefore seem that in order to get to grips with this problem one needs to think in terms of relative motion.

CONFUSED?



Maybe it's time you thought about buying Albert Einstein's
"Relativity : The Special and the General Theory"


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This problem was first published in Scientific American in 1867 and sparked heated debate as imformed readers took opposing sides.

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