centripetal, centrifugal, oy!

Cecil's Columns/Staff Reports
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I have no particular background in physics, which is probably why I found Chronos’s explanation of the artificial “gravity” found on spinning space stations totally confusing.

As near as I can make out, Chronos told us that if you start out floating weightless in space and then the space station around you is set into motion, you’ll continue floating until one of the “walls” of the space station “comes up and smacks you.” You have your feet on the “floor,” that is, “the space station’s outer rim.” All well and good, and just as “2001: A Space Odyssey” taught us.

And then Chronos said, you’re experiencing “a constant acceleration toward the center of the space station,” i.e., the space station’s inner core, which relative to you is your ceiling. “If you weren’t constantly being accelerated toward the center of the space station,” — i.e, experiencing centripetal force, with “the floor pushing [inward] on your feet” to boot — “you’d take off on a tangent into the void.”

Excuse me? Since you’re INSIDE the space station, exactly how would that work? If you take off on a tangent into the void, then centrifugal force has the magical property of rendering the “walls” of the space station drastically permeable, meaning you’ve died in the vastness of space long since and don’t really care in which direction you’re moving.

If you’re constantly being accelerated toward the center of the space station, I would think you would “fall” toward the center of the space station, and end up hanging weightless as you started out, but at the exact center rather than near one of the “walls.” If you’re constantly being accelerated toward “a tangent into the void,” then the “floor” of the space station, which is really its outer rim, comes between you and a gruesome death and provides “artificial gravity.”

I also don’t understand Chronos’s explanation of the Coriolis force. Say for the sake of argument that your space station is rotating counterclockwise (“east” to “west”) on its invisible axis. You, standing on the “floor” which is really the outside wall of the space station, are standing on a tile marked “California.” If you decided to walk from “California” to “New York” at the proper rate of speed, your position relative to an observer from a spaceship outside your space station would not change.

However, Chronos said, suppose you’re standing at “New York” and facing “California,” the direction in which the space station is rotating. Chronos says that if you jump straight up, because of Coriolis force, you will “land ‘forward’ (i.e., in the direction the station is rotating) of where you started.” I.e., you’ll jump up in “New York” and land in “California.” This we know intuitively to be true, but what does Coriolis force have to do with it? The “land” is rotating beneath you while you, hanging in the air, are “stationary.” Doesn’t pretty much the same thing happen on Earth, but in nano-nanometers rather than meters?

Mary

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Mary

Picture the space station looking down from the axis. You’re looking at a bicycle wheel with a little guy standing at the end of the spoke facing the direction that you’re about to turn the wheel. Now turn the wheel so the guy moves 1 inch. He didn’t travel in a straight line, did he? He moved closer to the hub than a straight line would have taken him. The pressure of the wheel against his feet caused him to diverge from the straight line he otherwise would have traveled–he was accelerated towards the hub. The acceleration is just enough to keep his feet down, not enough to give him velocity towards the center.

For Coriolis “force”, let’s make the wheel wider. You’re still looking down so that it looks like a big, flat loop–maybe you’re looking into a big beer vat that is spinning counterclockwise on its axis. (Aside: why do my examples involve beer so often?) Anyway, we see two kids tossing a ball. Kid A is counterclockwise from Kid B. Kid A throws the ball. The vat turns under the kids while the ball is in the air, so kid B has to back way the heck up to catch it. Now Kid B throws the ball. Again, the space station turns while the ball is up, and Kid B can’t throw it far enough to reach Kid A unless he’s John Elway, because Kid A is being moved away by the rotation. If the kids move so that they are side-by-side (lined up in your line of sight) the effect is a little different. Kid A throws the ball, the station moves while the ball is up and now Kid B is not where the ball is headed–he has to run clockwise to catch it.

All this can be affected by the motion of the air inside the station or on the surface of the earth. Without air, the effect is stronger/easier to see.

So Coriolis force is not a force, it just an effect. The same way that centrifugal force is not a force. They’re both just momentum–the tendency of an object to keep going in a straight line.

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Mary, if you’re inside the spaceship and moving around with it, inertia would of course try to send you in a straight line out into space, no? But something keeps you from doing that - it keeps pushing on you towards the inside of the spaceship to keep you in. This something is the floor of the spaceship, providing a centripetal force on you. I hope that’s clear.

In your Coriolis example, what your’re missing is that when you jump, Chronos isn’t saying that you jump so that you’re basically stationary to an outside observer. He’s saying that you jump, what looks like to you on the spaceship as straight up. Imagine that you’re standing on the floor of a large rotating spaceship, and you know that its rotation is moving you left to right. Now you jump, what seems like straight up. When you come down, you will land at a point that’s farther to the right than you expected to because of Coriolis. I think in your example you’d say that the ship would be rotating underneath you to make you land too far left. To really experience Coriolis, imagine taking a ball and playing catch with someone who is closer to the axis of rotation. Even though you throw the ball straight “up” at him, from your point of view, the ball will curve in flight, again to the right.

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Mary, I have edited your post to include a link to the Staff Report in question. It’s helpful to folks who read the thread, to be able to read the Staff Report first – saves duplication of effort and keeps us all on the same page. No biggie, but you’ll know for next time you start a thread.

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Cripes. I stupidly posted Chronos’s column on artificial gravity twice - once in July 2002, and once yesterday. The latter version was referenced only in our weekly mailing, and wasn’t scheduled to appear on our main page till Tuesday. I’ve now (a) scheduled a different Staff Report to appear on Tuesday, (b) deleted version #2 of Chronos’s article, and © slightly improved the original version, which is linked to above. Hope this clarifies matter, although at the rate things are going, I doubt it.

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Thank you, C.K., for including the appropriate link. I will indeed remember next time. And thank you, Ed, for improving the original article and clarifying it.

Here’s where my being totally ignorant is going to be a royal pain in the rear end to you: I understand what you’re saying to me (Ed did an excellent job of improving the original article), but I still don’t get it.

Ed, in your totally clear explanation of centripetal force, you say that velocity and acceleration mean one thing when one is traveling in a straight line and something completely different when one is moving in a circle. (NoCoolUserName seems to me to have said much the same thing.)

You say that when one is standing inside the outer rim of a rotating space station, one is actually constantly accelerating because the outer rim of the space station is pushing your feet inward toward the station’s hub. When you are standing near the circumference of a moving merry-go-round, I suppose you have to reach out and grab a support so the support can pull you toward the merry-go-round’s hub??

Do you see what I’m saying? Because an object in motion wishes to keep moving in a straight line, if the outer rim of the space station did not exist, you would go flying off into space like poor Frank did in “2001: A Space Oddyssey.” But the outer rim of the space station DOES exist, and prevents you from flying away by virtue of its completely inanimate and non-force-generating existence. In other words, you experience artificial gravity because centrifugal force is pushing you down against inanimate matter, rather than because inanimate matter (steel, or whatever) has suddenly acquired the ability to exert force and push you up. No force pushes you up; the existence of the steel beneath you dissipates the force that is pushing you down.

Okay, maybe centripetal force is an artificial construct useful for making physics equations work out. But I also STILL don’t understand the reasoning behind the Coriolis effect. If you’re in the Northern Hemisphere and throw a softball in a straight line toward someone, it will “pull” southward. If you’re in the Southern Hemisphere and ditto, it will “pull” northward. Doesn’t this simply reflect the fact that the Earth is an oblate spheroid, i.e., gravity is stronger at the Equator than it is at the poles?

Mary

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MotherMary writes:

The point Chronos was trying to make is that whether you think of the force operating in a spinning space station as centripetal or centrifugal depends on your frame of reference. You, Mary, are obviously thinking about it from the standpoint of somebody inside the space station, who is (literally) in the rotating (non-inertial) frame. The force appears to you to be centrifugal. If you were floating outside the space station and watching it rotate, you would be in the inertial frame and would think of the force as centripetal - that is, the outer rim of the space station is exerting force on the feet of the occupants and pushing them in toward the center. This is a conceptual barrier for a lot of people and I can only offer the small comfort that if you think about it long enough you’ll eventually get it. An analogy from simple relativity may help: If you and I are in space floating toward one another, I’m entitled to think that I am standing still and you are moving toward me; at the same time you’re entitled to think that you are standing still and I’m moving toward you. There’s no contradiction; it’s all a matter of point of view. The centripetal/centrifugal thing is much the same.

Chronos didn’t go into the Coriolis effect and I’m not going to go into it now. Believe it or not there’s a common-sense explanation that doesn’t require equations or reference to obscure laws of physics. Chronos offered to write a Staff Report on the subject a long time ago and I think I’ll take him up on it.

8

This is incorrect.The steel is indeed applying a force on you! If it didn’t, you would fly away.

Put it this way. A basic premise (that goes back to Newton) is that when you apply a force to an object, it accelerates, that is, its velocity changes. Well, gravity is a force! It is a force being applied to you, right this very second, and it wants to accelerate you at a rate of 10 meters per second every second. That’s a lot! Why aren’t you plummeting toward the center of the Earth?

It’s because I lied earlier. Only a net force accelerates you. If you have one force pulling you down, and another pushing you up by exactly the same amount, then they cancel (like a tug-of-war with exactly equal sides).

Gravity is indeed a force pulling you down. But the ground underneath you is pushing you back up with exactly the same force. If it didn’t, you would fall toward the center of the Earth. Basically, it’s the tension in the ground, its unwillingness to be compacted, that is supplying this force.

So the space station is in fact applying a force to you; the steel applies exactly the right amount to counteract the force trying to launch you into space.

9

The Coriolis effect also operates on a flat rotating disc, and in fact is easier to demonstrate on it. If you wish, you can take a gander at the linked PDF below. It was hurriedly written for a lower-division college class for nonmajors I teach.

Executive summary: Newton says objects move straight unless acted upon by forces. If you shoot a rocket to the north on a nonrotating Earth, the rocket travels due north. Yet on a rotating Earth, the rocket appears to curve away from due north. The rocket didn’t actually turn… our definition of what constitutes “north” did, because we are rotating. We don’t directly sense our rotation and hence we invent the Coriolis force to explain what we see.

A Coriolis explanation