Consider two gears placed as illustrated in the first picture below. The bottom gear is fixed (it can not rotate or move in any way). The top gear is not fixed and can spin around the bottom gear while maintaining contact (thus spinning around its own axis).
Try to answer the following questions:

a. How much will the free gear have spinned around its own axis if its initial position is that in fig. 1 and its final position is that in fig. 3?

b. Solve the same problem, but for gears with different radiuses.

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