How does centripetal force produce artificial gravity

I think I lack a fundamental knowledge of physics to answer this myself. In many sci-fi stories, there is a rotating spaceship that gives the feeling of being pulled "downwards" against the sides of a cylinder. What I can't seem to grasp is how that works in zero gravity.

What is keeping you from floating freely while the cylinder rotates around you? Are there any experiments that can explain this?

That is an excellent thought experiment to consider for a spinning vehicle. You are correct that if you simply enter the open space inside the rotating cylinder, somehow not following the rotation yourself, you will not experience a force to pull you to the outside. You could just hang there and watch the "floor" rotate below you.

However you probably won't be able to just hang there, assuming that there is air in the space. If you're alive and breathing, then the air will also be moving by you (the boundary effect with the floor and walls will be moving the air around with them), which will start you moving in the same direction as the floor. As it imparts a force in that direction, you will start moving on a trajectory perpendicular to the radius. You will then be on a trajectory to intersect the floor, which is curving up in front of you. As you get closer, the air will be moving faster, further accelerating you to the floor in front of you. It will seem like falling towards, as well as catching up with, the floor.

In what is normally seen in depictions of such a vehicle, you would not float into the space and wait to be directed to the floor by the moving air, but rather you would control your descent on a ladder. (Seems sensible, as opposed to an uncontrolled fall, however slow.) Then you are rotating with the floor, with your angular velocity increasing as you descend, increasing the the apparent weight on your feet on the ladder as you descend.

• Are there any experiments we can do on earth to show this? Such as a spinning tube and a weight attached to a string? I'm mainly concerned about setting it up correctly if such an experiment existed. Sep 30 '15 at 3:43
• I suppose you could, but there's no need to. The physics is extremely simple, so you would do better to write a a computer simulation and move things in it. I've always thought that a good video game would be trying to play basketball in a large rotating space station. It would be impossible to get the ball to go into the hoop using Earth intuition. Sep 30 '15 at 3:52
• This ancient movie, archive.org/details/frames_of_reference#, at around 17:00 demonstrates the effect of centripetal/centrifugal force.. There are probably newer ones, but Drs Hume and Ivey were my physics professors... Sep 30 '15 at 4:58
• @TomSterkenburg The best experiment to demonstrate this is a classic one: Take a bucket with a handle, add some water, then swing the bucket in a circle, even if you swing the bucket over your head the water will stay in the "bottom" of the bucket. In this case the centripetal force even overcomes the gravity of Earth, it would work even better in zero g. Sep 30 '15 at 6:13
• I guess my answer wasn't clear. There is no apparent force if you are not in contact with something that's going around in the circle. (Floor, wall, ladder, air, whatever.) Sep 30 '15 at 16:11

To extend Mark Adler's thought experiment a bit:

If you were in contact with the rotating floor and started walking or running in the direction of rotation, you would feel your weight increase. How much depends on the tangential velocity of the habitat floor and its radius. If the velocity is low enough, the added velocity from your own relative motion could noticeably increase your apparent weight.

Conversely, if you were to walk or run in the direction opposite to that of the floor, you would cancel out some or perhaps all of the centripetal acceleration. You might even find yourself back in a weightless condition. At least until you drift into something that is moving with the floor, or the air takes effect as in Mark's answer.

Although Mark Adler's thought experiment is nice, I think a better and straighter answer is this one:

If you just happen to appear there near the cylinder, you would simply watch it spin around you while you are standing still in open space. Nothing happens. In void (or something close to it), since there's no air friction (as in Mark Adler's experiment), you would be able to stand there forever (ignore for a moment the gravitation forces around you).

You would only experience the artificial gravity if you started rotating together with the cylinder. To do that, you would need to grab onto the rotating "floor", you would experience some bumps and accelerations, and in the end you would be "one with the floor". That means that on the tangent direction you would be moving uniformly (equivalent to not moving), while you would only experience the centrifugal force towards outside. It would be perfectly equivalent to standing still on Earth.

To complete the answer, the centripetal force produces gravity because it "pushes" you towards the center of the cylinder just like Earth pushes you towards the sky (otherwise you fall down towards the center of the Earth / towards the outside of the cylinder). But to obtain that centripetal force you must be in contact with the rotating floor, and standing still relative to it.

If you adopt the rotating reference frame of the spaceship then there are two fictional forces that you will see. One is centrifugal force - this is your artificial gravity. The other force is the coriolis force. In the scenario you describe the coriolis force balances out the centrifugal force and allows you to float above the floor.

But its unusual for these two force to exactly balance. Within this reference frame you only have the coriolis force holding you up because you are flying past the floor at high speed.