A coin rolling around a coin three times its size
A fixed coin has radius 3. A small coin of radius 1 rolls around its edge without slipping, all the way round, until it is back where it started.
How many complete rotations does the small coin make about its own centre? Most people answer 3. Explain why that is wrong and what the right count is, both for this case and for two equal coins.
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Separate the rolling from the travelling. The small coin's centre moves around a circle of radius 3 + 1 = 4, and that motion itself carries a full rotation.
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