Why does spinning a space station create artificial gravity?
Minor correction here. The author states:
I’m sure the author meant to say “…away from the center of the space station.” Otherwise a well-written and informative article.
Q.E.D.
No, the article is right. Look at it like this: If something was going in a straight line and you wanted it to curve right, you’d apply a force toward the right. If it curved all the way around in a circle, the force (and thus the acceleration) would point toward the center.
Your confusion comes from the much-quoted centrifugal force, which is the inertial equal-but-opposite reaction to the centripetal force. In a reference frame that is not rotating with the space station, only the centripetal force is ‘real.’
No. The article was referring to the acceleration on YOU (read it more carefully). If the acceleration on YOU was towards the center that’s where’d you’d go. Clearly that’s not right. YOUR acceleration is AWAY from the center, due to the inertia of your body trying to continue moving in a straight line. The article later mentions the force of the floor of the space station trying to push you towards the center, which is correct.
If there wasn’t a force on you, you would move in a straight line tangent. This means that you would be moving away from the center. By applying a force towards the center you are stopped from moving away.
Yes, you are undergoing an acceleration toward the center of the station. That acceleration is caused by the floor. Without that acceleration, you are no longer traveling in a circle. That you feel like your being pulled away from the center is an effect of inertia. It is not a force (i.e. acceleration).
I don’t know why you people are having such a hard time with this concept. Let’s try this: While you’re standing there thinking you’re being accelerated towards the center of rotation, you are holding a ball in your hand. If you hold this ball out at arm’s length, both you and the ball are experiencing the same motions–that is the rotation of the station is attempting to throw you and the ball off into space from the “centrifugal” force of its rotation, however the floor is keeping you from being flung into the void (and your hand is dong the same for the ball). When you let go of the ball, your hand is no longer keeping it in place (obviously) so, it continues to move in the same direction as it was at the instant you let go of it, and moves in a straight line following a tangent to the radius of rotation until the floor of the space station intercepts it. From your point of view (ignoring the coriolis “force”), the ball seems to accelerate downwards at 9.8 m/s^2 (assuming the space station is being rotated at a sufficient velocity to impart 1 g of acceleration). As any high school physics student knows, an object moves in the direction of acceleration…which in this case, must be away from the center of rotation, sice that’s the direction the ball went.
:wally
Oh, and the force that’s keeping you from flying out into space is called the floor. Or more precisely it’s the electromagnetic repulsion of the electrons in the floor’s surface acting against the electrons on the surface of your shoes. That’s not an acceleration, it’s a constant force, expressible in units like dynes or newton-meters. Or pounds. Stand on a scale on this space station and it will show your weight, just like it does on earth.
It isn’t a force if viewed from a nonrotating perspective; it just feels like one if you’re inside, and rotating with, the hull. In any case, force is measured in dynes or newtons. (Or pounds, but that brings up a completely new area of confusion.)
Velocity is in a straight line. In circular motion, this is tangent to the circle. But since you are tracing a circle and not a line, there must be some force applied to you. F*m=a, and accelleration is a vector in the same direction as the force. Since the force applied is towards the center of the circle, so is your accelleration. QED. 
Damn, F**/**m=a :smack:
Then why does the ball “fall” away from the center of rotation? Hmmm? It is experiencing precisely the same forces of acceleration that you are. Here, this should clear things up:
It should, but you still seem to be confused. That I can’t explain.
“centrifugal” force/acceleration is an “apparent” phenomenon, an artifact of your frame of reference. The ball in your hand, that when you let it go travels towards the space station’s outer deck, is NOT being subjected to a force that “drives” it “away” from the center, it simply is inertially retaining the motion it had at the moment you let go – it just looks to you like IT is “falling” because you and the room are moving in a circle while the ball is inertially retaining the straight-line motion it had when you let go of it.
Q.E.D., the article is correct. The acceleration towards the center is what makes the trajectory curve. Put an object at the end of a string and swing it around. The string is under tension. It is pulling towards the center. The string provides an acceleration towards the center of rotation.
Um, no, no it doesn’t. Not always, I mean. An object moves in the direction of its velocity. When an object is moving in a straight line and slowing down, it is accelerating in the direction opposite its motion. Acceleration is the vector of how velocity is changing; velocity is the vector of how the object is moving (how position is changing).
Everyone else is right, and you are wrong. (That sounds a bit antagonistic, doesn’t it? ;)) In the accelerating frame of reference of someone rotating with the space station, there is an apparent downward force. But in an inertial frame of reference, the only force is the push of the floor, which is “upwards” (toward the center). Because the acceleration is perpendicular to the velocity, the acceleration changes the velocity’s direction rather than its magnitude. There is no force on the dropped ball in the inertial frame. There is only an apparent force because the observer is accelerating.
Really, how could it be otherwise? The only force acting on you is the push of the floor, which is obviously directed toward the center.
You seem to be assuming that the ball is stationary before it is dropped, so there must be an acceleration in the direction in which it begins moving. In the observer’s non-inertial frame of refererence, this is indeed correct; hence the apparent downward force for him/her. However, viewed from an inertial frame, the ball is moving in a circle, constantly being accelerated toward the center of the station by the upward force in your hand and having a velocity tangent to its circle of motion. When “dropped” (“released” would probably be more accurate) that upward force is no longer acting on it, so it moves in the direction of its velocity, which naturally causes it to bump back into the floor (as its circle of motion lies within the circular floor). The ball moving toward the floor is the result of the removal of an “upward” force, not a sudden “downward” force.
Upon reflection, it seems that you’re assuming that the observer’s reference frame is the “correct” one, and under that assumption I think everything you’ve said is correct, except for that remark about the direction of acceleration being the direction of motion. :wally Everyone else is assuming otherwise, however, and you should recognize that. I think that by default the inertial reference frame is assumed to be “correct”, if only by convention.
I hope that clears up any confusion.
Sigh. Can I blame the editor here? Wait, what am I saying, of course I can blame the editor; scapegoat is part of Ed Zotti’s job description. I thought, at least, that my original write-up of it was clearer.
The key is, there are two different frames of reference which a person might reasonably want to use. Q.E.D, you seem to be using the rotating frame of reference. In that frame, you’re not accelerating at all: The force of the floor on your shoes is pushing you towards the center, the centrifugal force is pulling you away from the center, and the two balance out, so you stay at rest. When you let go of the ball, the only force on it is the centrifugal force (and the Coriolis force, but let’s not get into that), so it does accelerate, away from the center.
In the non-rotating frame, however, things are different. In that frame, there’s still a floor force on your boots, but centrifugal force doesn’t exist in a non-rotating frame. So the floor is pushing you towards the center, and you’re accelerating towards the center. When you let go of the ball, in this frame, there are no forces at all on the ball, so it moves in a perfectly straight line. The ball is not accelerating at all.
To recap that: In the rotating frame, you are not accelerating, and the ball accelerates outwards. In the non-rotating frame, you are accelerating inward, and the ball is not accelerating. Either frame works, but you have to pick one or the other.
I’m nowhere near as up on this subject as some of the people who have posted, but I would just like to say, Q.E.D., welcome to the boards, and good job getting a link to the original column in your OP. Most people miss that their first few tries.
Q.E.D. said:
Incorrect. You are correct in your description up to this point. But any high school physics student should learn that acceleration is a change in velocity over time. That change includes magnitude and/or direction. However, acceleration does not equal direction of movement. Direction of movement is part of velocity.
Velocity is any change in movement over time. Acceleration is change in velocity over time. This includes magnitude (amount) and direction. Velocity = motion. Acceleration does not require motion. Standing on Earth, you are experiencing an acceleration toward the center while not moving toward the center.
A car starts from rest. Pushing on the accelerator adds a forward acceleration. The car increases velocity. You reach a cruising speed, and begin to maintain that speed. Now you apply the brakes. This applies a force to slow down the car - a deceleration. A deceleration is, technically, an acceleration in the negative direction. The car is still going forward as it slows down, traveling in the opposite direction of the acceleration.
Similarly, if the car is at cruising speed and not speeding up or slowing down, but the driver initiates a turn, that applies a force to the car in a sideways direction. But a force is just an acceleration multiplied by a scaling factor - the mass of the object being acted upon. Ergo, the car is undergoing an acceleration by turning, despite having a constant speed.
The force on the car tires making it turn is pointed toward the center of the turn radius. Same thing with the space station. The force on the astronaut is the floor pushing up, toward the center of the turn radius.
So why does the ball fall “downward”, away from the center? Because the force that was being applied to it is removed. The ball tries to continue in a straight motion, according to inertia. That straight motion is tangentially away from the point of release. Part of that tangential velocity is in the same direction the astronaut and space station floor goes in the curved path. Thus the ball seems to stay with the astronaut and not fall behind him. But the other part of that tangential velocity is away from the center of the station. That is the movement that the astronaut sees as the ball falling under a force. The ball “falls” because there is nothing preventing it from falling. In other words, the force is removed, so the ball falls.
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Units of force are Newtons or dynes or pounds. http://www.bipm.fr/enus/3_SI/si-derived.html http://whatis.techtarget.com/definition/0,,sid9_gci762155,00.html
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Newton-meters are a unit of momentum, like pound-feet.
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An acceleration is a force. Note the standard equation for force of a constant mass. F=m*a Mass is the scaling factor. Acceleration of zero gives zero force, and non-zero acceleration gives non-zero force. (Variable mass can also cause a force without varying acceleration, but varying acceleration causes a force, with or without change in mass.)
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Yes, standing on a scale will show your “weight”. That weight is a force. However, the cause of the force is the floor pushing up on your feet as you follow inertia and try to travel tangentially away from the last point in the curve.
Q.E.D., Chronos states in the paragraph before that he is talking about the inertial case. In the inertial case, centrifugal force does not exist. Inertia and centripetal (i.e. center seeking) force are the components causing the effect. The appearance of falling away from the center is, strangely enough, caused by a force toward the center. There is also a tangential velocity component. This tangential component is the source of the motion outward.
friggin’ html compressing spaces.
No, change in position over time.
Yes, but you have not explained the difference between speed and velocity. (60 miles per hour is a speed; 60 miles per hour north is a velocity.)
No, newton-meters and pound-feet (more often expressed “foot-pounds”) are units of energy. Newton-seconds and pound-seconds are units of momentum.
No! No! No! Acceleration and force are incommensurable. Mass is not a “scaling factor”.