Calling the example of only one coin rotating as the other revolves around it as "rotating" feels like a bit of a stretch. The coin isn't *just* rotating, it is also translating in space. If you eliminate the translation and fix the center point of both coins, you will get 4 and 1 rotation respectively. That is because in this example, both coins are a part of the same body, so when one rotates, the other must counter rotate else one of the coins is forced to move through space.

The coin is *not* rotating 5 and 2 times, respectively, it is *seeming* to rotate from a fixed point perspective while also counter rotating through space an entirety of its circumference by the time it arrives back at its origin.

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