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**76. mmh
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 just before Equation 8.12 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.) |
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Viewing the dotted circle, we
can see that its diameter is equal to 2 quarter’s diameter. So the circumference of that circle is |
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Where R is the radius of a
standard quarter. |
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A quarter rolling without
slipping, tells us that |
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Since |
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