I often see, in representations of space stations and space vehicles,
a chamber that revolves or spins, producing artificial gravity. How is that possible? If the object is floating and the room starts spinning, it will simply spin around the object. Centrifugal force depends on gravity to work, doesn't it?
It's centripetal, not centrifugal, force you're curious about. The confusion
is common. Centripetal force is the force of the floor pushing up against an astronaut, the force physicists use in calculations and diagrams. Centrifugal force is a fictitious force with the same magnitude but opposite direction of centripetal force. It refers to how much astronauts feel themselves being pressed into the floor. But the astronauts aren't pushing
the floor; it's pushing them.
Centripetal force is caused by inertia, the tendency of a moving object to continue moving in the same direction. To change direction, it must be acted upon by an external force. Take a baseball. Once thrown, it travels more or less in the same direction until gravity and air friction pull it down. Now imagine tying that baseball to a long string and attaching the other end to a flagpole. If you throw the ball now it will travel in a circle, because the string is constantly exerting a force upon it. That force, pushing the ball up toward the center of rotation, is centripetal force.
Now take the example of a ballroom-size spinning space station. You're absolutely right that an object -- a chair, say -- floating in the middle of the space station will continue to float. It's not moving anywhere and not being acted upon by a force, so inertia dictates it will remain motionless.
Same if you place the chair a foot above the floor -- it sits there, the floor spinning beneath it. But imagine that you push the chair so that
it's moving at the same speed as the floor. The chair will move in a straight line for a while but eventually hit the floor. Since the chair must change direction, and move upwards instead of straight ahead, we conclude that an upwards force acts on the chair. The chair will eternally try to move in a straight line, but the floor's upwards force spins the chair in a giant circle.
The upward force of the floor against the chair is a centripetal force, and it produces the effect of artificial gravity depicted in science fiction films. By varying the size of the station and the speed at which it spins, you can control how much force is needed to guide the chair in its circular path, and therefore how much artificial gravity the chair "feels."
There's a scene in 2001: A Space Odyssey in which one of the ill-fated astronauts is jogging around a circular room. We don't know which way the room is spinning, but it's interesting to note that if he is jogging in the same direction, he's rotating more quickly than he would if he were standing still; in that case, the centripetal force acting against him is stronger, and he feels heavier. If he's jogging in the opposite direction, he's rotating more slowly,
so he feels lighter.