Coin Rotation Paradox

Max Born

Our mind is in trouble, because:

Set the ratio to 1:1, set revolve on and move the green point C to 06:00 - clock-position.
  • Then, watch the rolling outer circle: It is at the same horizontal position as starting at 12:00. Hence, it must have been turned around, it revolved completely around C.
  • Then, envision the distance passed by (or rolled over) as a straight line: It's
How come?

And the solution is...

We compare the circular motion with the circular rotation: The outer circle is moving from 12:00 to 06:00, a fixed distance.
  1. [revolve Off] Circular motion: The segment LR stays orthogonally to line AC (g).
  2. [revolve On] Circular rotation: The segment LR rotates around C.
If we just watch 1, the outer circle is forced to rotate around C. This fact is hidden to our mind, as we assume that the rollover drives all the rotation. Watching 1 we can see that the orientation of the outer circle against A does not change. But the outer circle is rotating with respect to its orientation at the starting position.

And the item learned is ...

  • Rotation is not a relative motion.
  • If you walk on a not straight line, you will turn yourself!