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If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid (shown above), combining both forward and circular motion. What is the length of the path formed by one complete revolution? Assume the wheel has a radius of 1.

The answer is 8r, where r equals the radius of the wheel.

The distance as the dot moves from the 3:00 to 9:00 postion counterclockwise is 4*2^1/2. As it moves from the 9:00 position to the 3:00 position the distance is 8- 4*2^1/2, assuming the r=1.

 

 

Michael Shackleford, A.S.A.