Question

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 = 2d₂,

how many revolutions does it make in one round trip?

Answer 1

Since you did not include the picture and the problem statement is not explicit,
I have to assume that the inner disk is the one that has a diameter of d1 and
that the moving disk has a diameter of d2.

d1 = diameter of the inner or non-moving disk
C1 = circumference of the inner or non-moving disk
d2 = diameter of the moving disk
C2 = circumference of the moving disk
π = ratio of the circumference of a circle to its diameter (pi) = 3.14159...

d1 = 2d2

C1 = πd1
C1 = π(2d2)
C1 = 2πd2

C2 = πd2

C1 = 2(C2)

Since the circumference of the inner non-moving disk is two times that of the
moving disk, then the moving disk takes two revolutions to make one trip around
the circumference of the non-moving disk.

In case of any doubt, please comment.