You’re going to run into engineering limits long before you run into theoretical ones. A fan’s spin is limited by the strength of the material making up its blades, and the very strongest materials available (if they’re at a roughly human-sized scale) cap out at around 100,000 rpm. Which turns out to be a good thing, because [those centrifuges are one of the major bottlenecks for enriching weapons-grade uranium](https://en.wikipedia.org/wiki/Zippe-type_centrifuge).
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