The rotating spaceship

The trouble with space, among other things, is that there's no gravity.* Weightlessness is known to cause a variety of health effects, the most obvious being muscle atrophy. So how can we create an artificial gravity? There aren't really any other forces which behave quite like gravity, which always has a strength proportional to your mass. But wait, there's the centrifugal force! If you're on a large rotating spaceship, the centrifugal force is what flings you away from the center of rotation.

*Technically, there is still gravity if you're in orbit, but you can't feel it because an orbit is basically a free-fall trajectory.

At this point, I am obligated to defend my use of "centrifugal force". Some overzealous science teachers have insisted that there is no such thing as the "centrifugal force"; there is only the "centrifugal effects" and "centripetal acceleration". Take it from me, that is baloney. The centrifugal force is what we call a "fictitious force", a force that depends on our reference frame. But "fictitious" is a bit of a misnomer. Fictitious forces have effects that are equally real as any other force. It's also worth noting that under Einstein's General Relativity, gravity is also essentially a fictitious force. Gravity is still real, is it not? We're all physicists here, not solipsists!

This is Space Station V, as seen in 2001: A Space Odyssey. It is a fictional example of a spaceship which harnesses the centrifugal force to create artificial gravity. No real examples exist, not yet. On the Space Station V, there are two independently rotating wheels. Unless any rocket fuel is expended, angular momentum (which is a measure of rotation) is a conserved quantity. Therefore, to preserve fuel, the spaceship would have an overall angular momentum of zero. Therefore, the space station is built so that the two wheels rotate in opposite directions, canceling each other's angular momentum.

[ETA: They also could use fuel to make the entire space station rotate in the same direction. I'm not sure which is the case for Space Station V.]

To consider the physics of the spaceship, let us consider just one of the wheels, and consider a rotating reference frame. It is important to remember that a rotating reference frame is not an inertial reference frame. That means that Newton's Laws do not apply! An object at rest does not necessarily remain at rest. Not every force is necessarily accompanied by an equal and opposite force. How can we even make sense of the physics of our rotating reference frame? It turns out that we can make sense of it rather easily. We simply need to assume that a new force, the centrifugal force, is acting on all objects. The centrifugal force pushes all objects outwards, away from the center of rotation.

This situation should make sense in both the rotating reference frame and the stationary reference frame.

• Rotating reference frame: The centrifugal force pushes astronauts outwards, but the floor of the spaceship keeps him from being flung away.
  
• Stationary reference frame: The astronaut is circling around inside the rotating spaceship. He would continue flying in a straight line away from the spaceship, except the floor is stopping him.

Let's consider another thought experiment. Let's say the astronaut is not inside the spaceship, but just outside of it, stationary. Let's look at what's happening in the two frames. Remember, both frames should make sense.

Image not to scale

• Stationary reference frame: The spaceship is rotating, but the astronaut is not rotating with it. No forces are acting on him, so he remains stationary just outside the spaceship.
• Rotating reference frame: The astronaut is circling the spaceship. The centrifugal force is pushing him outwards, and yet, he remains in the circular path. How?

The answer is that there are not one but two fictitious forces associated with a rotating reference frame. We have the centrifugal force, which pushes the astronaut outwards, and the Coriolis force, which pushes the astronaut inwards. You can all breathe a sigh of relief--we haven't broken physics after all.

The Coriolis force works on all objects which appear to be moving in the rotating reference frame. That's why we didn't have to include it when we were talking about the astronaut inside the spaceship--he was stationary with respect to the rotating spaceship. The force does not always pull you inwards, but it is always perpendicular to the object's motion. Let's say you are inside the spaceship, facing the direction of rotation. If you run forward, you will feel heavier. If you run backwards, you will feel lighter. And this is a little harder to imagine: if you jump up, the Coriolis force pushes you slightly forward, and when you fall back down the Coriolis force pushes you slightly backwards.

If that made any sense, you can congratulate yourself for successfully performing a thought experiment, in very much the same spirit as Albert Einstein. If it didn't make any sense, it's probably my fault, and you can ask me in the comments. :)