Krdytkyu

In an answer to another question of mine, concerning gravity, there was a link to a video about 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, 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 centrifugal force is in action.

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?

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 reaches 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 rotational velocity. You don't lose it just by losing contact with the ground, so nothing about the story changes.

If you jump then you are in free fall, apart from air resistance, so you are weightless. This holds for any jump. For a brief moment you experience zero gravity!

This is an inertia problem. The phrasing of your question presupposes that the astronaut loses inertia when jumping, resulting in their upward trajectory being the only major acting force. At any point while rotating in a stationary position, the inertia of the astronaut is outwards from the rotational path at a 90 degree angle from the line connecting the astronaut and the axis of rotation. When the astronaut jumps, this inertia is maintained and two new forces are generated, namely the force the astronaut enacts on the space station (resulting in negligible acceleration on the part of the space station) and the force the space station enacts on the astronaut (resulting in non-negligible acceleration on the part of the astronaut towards the axis of rotation). The astronaut's relative velocity is related linearly to the vector sum of the inertial force acting on him as well as the force from his jump. This is why the "gravity" felt by the astronaut is determined by the angular velocity of the station floor; greater angular velocity means greater inertia as well as greater centripetal (and centrifugal) force, which means greater force (applied by jumping) is required to accomplish the same (relatively) vertical displacement.

The feeling of being pressed to the ground in an artificial gravity chamber is due to the rotating floor pushing the astronaut towards the rotational axis, when the astronaut (from a physics perspective) wants to keep going along the inertial path. This force resulting in this central acceleration is the centripetal force, while the opposing force enacted by the astronaut on the space station floor is the centrifugal force.

You can find this information in any basic university level physics book; pay special attention to chapters covering angular momentum and gravitational/circular forces. Fundamentals of Physics by David Halliday and Robert Resnick was the one I used in college.

Of course, the biggest problem with the supposition of becoming 'weightless' (returning to a null-G state) by making a 'big' jump is this: Assuming the OP was talking about not a created micro-gravity (.2G or less) but closer to one full gravity (Earth standard), is the size of the 'room' required to create that much tidal force. The smaller it is, the faster it would have to be spinning to create sufficient centripetal force to give the impression of that 'gravity', and subsequently the thinner the band of that 'gravity' as the further from the zone of that 'gravity' the less the force.

So unless it were some silly, tiny spinning room, the size of the 'station' required to create a 'natural gravitational' feel would far exceed the astronaut's ability to jump without outside propulsion. In that case, of course, the ability to then travel outside the functional 'gravity' into decreasingly accelerated zones (by removing his own laterally imparted velocity) he could then eventually reach the 0G center of the station or room.

However, with the additional concept of scale, the same could be said of the Earth itself. If you could 'jump' to a 'high enough' height, you could reach 0G (not really, but sufficient micro gravity as to be indistinguishable from 0G). This does give pause for thought, as not only would such a station need to be QUITE large, but that you'd better be wearing a low-pressure suit at the same time, as the atmosphere should be quite thin, since the Nitrogen/Oxygen atmosphere would ALSO be affected by the centripetal force of the station's rotation, thus not only be thin, but definitely not made up of the proper gasses for breathing (lighter gasses rising into the center of spin)... At least that's what I'd expect.

You're not making any mistake except for thinking "artificial gravity" could be
nearly constant over a region as big as the structure itself. It really always
applies only to a region "much smaller" than the structure itself.

So, yes, a big jump (up and backwards on the wheel) could send you through the
middle of the wheel, where you would just float. Or, more simply, running fast
enough (backwards on the wheel) will cause you to levitate.

This non-constant variation of your "artificial gravity" in spacetime was already
explained as a "tidal force" in my2cts's comment.