Coin rolling around a coin

EasyBrainteasers~4m

A small coin of radius 1 rolls without slipping all the way around the outside of a fixed coin of radius 3, returning to its start. How many full rotations does the small coin make (relative to the ground)?

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The small coin's center traces a circle of radius $R+r$ , not $R$ .
Rotations $= \frac{\text{center path}}{\text{own circumference}} = \frac{R+r}{r}$ .

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Coin rolling around a coin

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