The Rotating Coin Paradox
The rotating Coin Paradox is a everyday Paradox, that derives from a wrong assumption, when looking at rotating objects along none straight paths.
Since a rolling Cylinder (in this case a coin) rotates on a straight path, it has to traverse exactly the length of its own circumference by rolling in order to rotate once along its own center.
When looking at rotating objects on none straight paths, this assumption of "counting" the length of the covered ground, tricks us into making wrong assumptions about the traversed distance between full rotations of the object.
This phenomenon plays a big part in all sorts of gearboxes, especially in planetary gearboxes.
Mathematically the point is:
The length of the path of the Center of the rolling coin, is equal to the Circumference of the Circle, derived from this Centerpoint rotating around the Center of the stationary Coin.
Since the radii of the two Coins are the same, the Circumference of this "big Circle", happens to be:
C1 = 2*Pi* (r+r) = 2*(2*Pi*r) = 2*C0
with C0 being the Circumference of a single Coin:
C0 = 2*Pi*r
This is my first YouTube Video ever, so i hope you enjoyed it and i could help straighten up the behavior of rolling bodies on none straight paths for you.
Other names for this Paradox are:
Rolling Coin paradox or Rolling Cylinder Paradox
Resources:
https://en.wikipedia.org/wiki/Coin_ro...