6. 9 A disk of diameter d 1 rests on a table. A second disk of diameter d 2 is p

Question

6. 9

A disk of diameter d1 rests on a table. A second disk of diameter d2 is placed with its rim touching the rim of the first disk. See the figure below. You hold the inner disk down so it does not move, and you roll the outer disk around the circumference of the first one, making sure that there is no slipping of the disk. If

A disk of diameter d1 rests on a table. A second disk of diameter d2 is placed with its rim touching the rim of the first disk. See the figure below. You hold the inner disk down so it does not move, and you roll the outer disk around the circumference of the first one, making sure that there is no slipping of the disk. If d1 = 1.5d2, how many revolutions does it make in one round trip? Consider the linear distance the center of the outer disk moves through in one round trip. rev

Explanation / Answer

Circumference of circle of motion = 2x(3.14)x(d1+d2)/2 = 3.14x(d1+d2) = 3.14x(1.5d2+d2) = 7.85d2

Distance covered in 1 revolution = 2x(3.14)x(d2)/2 = 3.14d2

No. of revolutions = 7.85d2/3.14d2 = 2.5

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