Physics Problem: Angular Velocity for Artificial Gravity

A rotating space station is said to create “artificial gravity”-a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. If the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of 9.80m/s2 at the rim?
I'm working through chapter summaries for introductory physics (algebra-based). I'm using the Openstax online (free) textbook College Physics. You can access this book here openstax.org/details/books/co...
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• Online Physics 1 2024

[@brookestephen]

but moving mass around within the rotating habitat can bring on the flip - the Dzhanibekov effect - which destroys the strongest station.

[@GeoffryGifari]

Hmmm what I don't understand is that we equate the centripetal force formula to the normal force, but that means the artificial gravity only works when a person is in contact with the surface right? shouldn't there be another force tethering the person to the surface for the effect to last?
consider what would happen in these scenarios:
1. initially the spaceship is already rotating, but the spaceman is floating way above the inner surface
2. initially the spaceman is standing on the inner surface and rotating with the spaceship (feeling "gravity"), then he jumped really hard