Newtonian Mechanics – Does Artificial Gravity Based on Centrifugal Force Stop Working if You Jump Off the Ground?

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In an answer to another question of mine, concerning gravity, there was a link to a video about the creation of artificial gravity, based on rotation.

The question I have might be silly (or with an obvious answer), but it puzzles me non the less. As I understand it, in order for the centrifugal force (which is responsible for creating gravity, in this case) to work, the object it works upon should be attached to the wheels 'spoke' or 'rim'. If an astronaut walks on the inside of the 'rim' (like here in the video), the contact with the 'rim' is maintained via legs, thus the centrifugal force is in action.

Now, the question: if, while being inside a rotating space station, an astronaut would jump really high, wouldn't he in that case experience zero gravity until he again will touch some part (wall or floor) of the station? Am I missing something in my understanding?

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Now, the question: if, while being inside a rotating space station, astronaut would jump really high, wouldn't he then experience zero gravity until he again will touch some part (wall or floor) of the station? Am I missing something in my understanding?

Well, here's a related question. Suppose you find yourself in an elevator at the top floor of a skyscraper when the cable suddenly snaps. As the elevator plummets down, you realize you'll die on impact when it hits the bottom. But then you think, what if I jump just before that happens? When you jump, you're moving up, not down, so there won't be any impact at all!

The mistake here is the same as the one you're made above. When you jump in the elevator, you indeed start moving upward relative to the elevator, but you're still moving at a tremendous speed downward relative to the ground, which is what matters.

Similarly, when you are at the rim of a large rotating space station, you have a large velocity relative to somebody standing still at the center. When you jump, it's true that you're going up relative to the piece of ground you jumped from, but you still have that huge tangential velocity. You don't lose it just by losing contact with the ground, so nothing about the story changes.

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