The first test the governor proposes is to insure all quarters are the same size

Question

The first test the governor proposes is to insure all quarters are the same size. He borrows two quarters
from Professor Larson, and puts them edge to edge as shown below, rolling the outer quarter around
the middle quarter without slipping. “If the quarters are the same size,” the governor explains at a
press conference, “then their edges will roll along each other and George will be right side up when I go
once around.” But right before his very eyes, when the quarter is halfway around its journey, George
is rightside up again!
What!” he exclaims. “The quarters are defective! By the time I’ve gone all the way around, the rolling
quarter will have made two rotations! Since the edges are touching, that must mean one quarter is
larger than the other! Either the quarters are defective, or Larson is counterfeiting coins – lock him
up just to be safe!”
explain how the quarters are not defective, and how the outer quarter is
making two rotations even though the edges of the two coins are touching. Do not use equations —
this is a conceptual exercise.

Explanation / Answer

ok, think of the earth rotating around the sun, it is both rotating around its axis and revolving around the sun at the sam time same as a quarter, it goes around the other quarter once, but it is rotating twice on its own axis...which is why Washington's head is rightside up halfway in the journey.. therefore the quarter revolves once around the other quarter but twice across its axis. Here use this link if you need more help.. http://www.donaldsauter.com/rolling-circles.htm

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