Take two quarters and lay them on a table. Press down on one quarter so it canno

Question

Take two quarters and lay them on a table. Press down on one quarter so it cannot move. Then, starting at the 12:00 position, roll the other quarter along the edge of the stationary quarter, as the drawing suggests. How many revolutions does the rolling quarter make when it travels once around the circumference of the stationary quarter? Surprisingly, the answer is not one revolution. (Hint: Review the paragraph in the text that discusses how the distance traveled by the axle of a wheel is related to the circular arc length along the outer edge of the wheel.)


rev

Explanation / Answer

The center of the rotating quater follows a circular path   having radius 2 r the distance of this center of this center of the quater is S = 2*2r                                                                                           = 4r The revolutions the rolling quarter make when it travels once around the circumference of the stationary quarter is                               = 4r / r                                  = 4                                  = 2 revolutions

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