If "gravity" is generated by spin, as in the Ringworld or an O'Neil colony like Babylon 5, is something in the air, such as an aircraft, affected? My brian is telling me that you're only held to the surface by the spin, but once you've separated from the surface you're no longer affected by the spin.
Or is it that the air itself is being held down by the spin, and, being in that envelope of air, so is the flying object? Would that then mean that if the habitat contained a vacuum, a floating object would not be affected by the "gravity?"
That's essentially correct. It also depends on how the flying object is moving. Let's look at a couple of situations:
1) You're hanging from a high ledge on a building in an O'Neill cylinder. You lose your grip and fall. What happens?
While you're hanging, you're following a circular path around the center. Let go, and it's like cutting the cord on a whirling tetherball -- suddenly you're travelling in a straight line, tangent to the previous circle. This takes you outward, your momentum carrying you toward the perimeter of the cylinder, which brings you closer to the "ground." Basically you're flying sideways, but the ground curves up to meet you. To an observer within the rotating frame of reference, it looks like you're falling down on a curved path. The fictitious force that seems to be pushing you sideways is the Coriolis force.
2) You're in an aircraft hovering at the axis of the O'Neill cylinder. At this point, you're in free fall. What happens if you jump out?
If you stay close to the axis, you'd continue to hover. However, let's assume you push off the side of the aircraft and drift away from it. From the axis, any direction is "down." In a vacuum, you'd just keep drifting slowly until you converged with the surface -- although it would be rotating pretty fast relative to you and the landing could be messy as a result. An observer on the "ground" would see you spiraling outward, the Coriolis force "pushing" you sideways ever faster.
With atmosphere, however, things are different. This is where the transfer of force that Timo was referring to comes into play, though not in the way he implies. The air itself is rotating because of its mutual friction -- the rotation of the ground pulls the air in contact with it, which pulls the air higher up, and so on and so on. It doesn't all rotate as a solid mass; an observer on the surface would feel a steady, gentle Coriolis wind. Still, all the air is rotating at some velocity. So let's assume you push off from the plane in atmosphere. As you drift away from the axis, air resistance slows you, so you don't follow the same path you would in vacuum. But as you move partway out from the axis, the air is now rotating, and that tends to push you sideways. Again, because it's a circular habitat, going sideways (tangentially) takes you outward. So that pushes you into an area where the air is spinning a bit faster and pushes you farther sideways/outward. And so you're accelerated toward the surface, more gently at first than by actual gravity, but it adds up. To the observer on the ground, your path is different than it would've been in vacuum, still curved but not as severely, and with your acceleration being outward as well as sideways. The observer would perceive your fall in terms of the interaction of an outward gravitational/centrifugal force and a sideways Coriolis force, whereas in vacuum it would be perceived entirely in terms of the Coriolis force.
At least, I'm pretty sure that's how it works. Note that if your aircraft is not at the axis, but is flying opposite the habitat's direction of spin at a velocity equal to the rotational speed, then it's essentially standing still and its interior would be more or less in free fall. Even if you're in a car driving on the surface, your weight would increase if you drive fast in the direction of spin and decrease if you drive opposite to it. So aircraft would be advised to take off in an antispinward direction, since that would make it easier to leave the ground.
