Yes, that’s exactly how it works.
Intuitively, imagine a rock tied to a string, and imagine spinning it around in a circle. See how you have to have a force pulling the rock into the center of the circle to keep it from flying away? It’s the same principle with the rotating spaceship. The real force is the force of the floor keeping you from flying away, the reason it feels like you are pushing down is that whole equal and opposite force thing Newton came up with.
You are accelerating towards the center because there is a constant change in the direction of your velocity, and that change is towards the center of the circle. Its called radial acceleration. In uniform circular motion, there is no other acceleration, and no other force. That is why centrifugal force is sometimes called a fictitious force; It is only necessary if you take the non-inertial reference frame and try to do newtonian physics in it. If you realize that you are constantly being pulled to the center of the circle (and missing, because of your sideways velocity), it is superficially like being in orbit, only instead of gravity, you have the floor keeping you there. And the force of the floor (pushing up on you) is the force you feel as “gravity” in such a spaceship.
I think that’s my misunderstanding.
It’s the force of the floor pushing up on you that makes you feel like gravity.
When an elevator starts going up, momentarily you feel like gravity has inreased.
But the floor affects your whole body. The floor doesn’t push more on your feet and less on your head - it pushes your body as a whole, in the same way an elevator rising increases the apparent gravity on your whole body.
That’s where my confusion lies. If this is how it works, then why would your head feel any less apparent gravity than your feet? I realize that the head travels less - but the force of the floor pushing up on it is the same. That’s also why I understand why standing on a deck in the middle of the disc has less apparent gravity than standing on the outer edge - because that floor would push left because of less acceleration. But I still intuitively think that the force your body feels is the floor pushing up, not its exact distance from the center, and so it still seems to me that the apparent gravity would feel equal throughout your body.
I’m probably wrong, but hopefully I’ve at least explained myself enough so someone can explain why.
Er, that should be that the floor would push less, not left, of course.
What Stranger On A Train said about centrifugal vs. centripetal force is correct: centrifugal force “doesn’t exist” because you don’t need it to explain what happens if you’re observing from an inertial reference frame (i.e., if the observer is neither rotating nor accelerating).
Imagine watching a person spin a ball on a rope above their heads. If you look at the ball, you can see only two forces acting on it: gravity and the tension in the rope. Ropes can’t push things away, only pull things towards the other end of the rope when the rope is taut. Thus there cannot be a force acting away from the circle, only one acting towards it.
In uniform circular motion (moving around a circle at a constant speed), the only thing this rope, or centripetal force of any type, does is change the direction in which the ball is moving. There’s an applet here that gives an illustration of this. If you were to cut the rope, the ball would move tanget to the circle, the direction indicated by the two vectors in the first image here.
The principle is basically the same on turntables or space stations or those carnival rides, except the object providing the centripetal force changes. On the carnival rides, the only difference is that the walls are providing the force, rather than a rope. We feel something like gravity because of Newton’s Third Law: the floor is pushing on us, so we must push back on the floor.
On preview, also what DrCube said. I really take too long to write posts.
The idea is that this is circular motion, not anything like an elevator. In an elevator, the force is indeed constant from your head to your feet. In uniform circular motion, the acceleration, and hence the force (mass times acceleration), tails off as the radius does. If the radial acceleration is V^2/r, then the force is mV^2/r. Since the velocity depends on the radius as V=rw (that w is omega, the angular velocity), then the force is mrw^2. Then df/dr is mw^2, assuming mass and angular velocity are constant. Since the derivative is not zero, the forces are different from your head to your feet. (That derivative means that as you change the radius one unit, the force changes mw^2 times that unit, just so you know. It is the rate of change of f as r changes.)
P.S. I’m totally winging it here. I’m just going from memory that the radial acceleration is V^2/r and that velocity is rw. It sounds right, but if I’m wrong, please correct me.
It’s essentially what Mangetout said:
The floor doesn’t really push on your head, so much as the floor pushes on your feet, which push on your legs, which push on your torso, which pushes on your head. Each time the push gets slightly weaker.
A different way to think of it. Here on earth, gravity does change slightly over the human body. We can imagine slicing a body into horizontal strips, each of which feels the same gravity throughout the strip. The amount the floor pushes up on you is the sum of the gravitational forces on every strip. The floor only pushes on your feet, and each slice pushes on the slice above it.
Same principle in artificial gravity. The force from the floor is the sum of what is needed to keep every slice moving in the correct circle. The floor pushes on the bottom of your feet, and each slice pushes on the ones adjacent to it.
Tell me if that makes sense to you.
But there’s another equally good way to perceive this situation. Start by asking: what do you think is making the rope taut? It seems to me to be the outward force away from the centre of the circle, which seems to arise from the motion (albeit contrained) of the ball on the end of the rope. Also, your phrase ‘ropes can’t push things away, only pull things towards the other end of the rope’ doesn’t seem to me to make sense. In your given scenario, I don’t see any evidence of one end of the rope pulling anything towards the other end (or if it is doing that, it’s not doing it very successfully, since the ball does not get any nearer the ‘centre’ end of the rope). On the other hand, it makes perfect sense to me to see that the ball is pulling on the rope, and doing so in a direction away from the centre. Which is why the rope is stretched taut.
And consider my other example - put a small number of loose objects on a turntable. Switch it on. None of the objects move towards the centre. All of them move towards the edge. Attach little threads or miniature ropes from the central spindle to each of these objects. No evidence whatsoever of any force inwards, towards the centre. No evidence of the ropes pulling towards the centre. Just lots of threads/ropes pulled taut. By what? By the outward mtion of the objects that the threads/ropes are attached to. Disconnect the ropes at the spindle end and the ropes too will move away from the centre.
Sorry if I’m being thick, here. It seems to me that I’m just destined never to understand this particular point. The more people try to explain it, the less I understand it. But thanks to you all for at least trying to come to my rescue.
Thats because you are thinking in the non-inertial reference frame which uses the ball on the end of the rope as the origin. Indeed, if you describe it that way we have to conjur up the fictitious centrifugal force that balances out the ropes force pulling in. However, if you think in terms of an inertial reference frame (an outside observer, perhaps), you see that the ball, if left to itself, should continue in a straight line forever. Since that doesn’t happen, there has to be a force keeping it from that straight line; that force is the centripetal force of the rope (or the deck of the spinning spaceship, to tie the OP into this). Forces cause masses to accelerate, thats Newton’s second law. There is no acceleration towards the outside of the circle, there is only the acceleration towards the center; The reason that the rock or the person doesn’t get any closer to the center is because of their velocity tangent to the circle is making up for the difference. Like sattelites in orbit, the ball keeps falling in and missing.
Sorry, I didn’t address this.
The reason that the objects move towards the edge of the turntable is inertia. Things want to move in straight lines forever unless forces act on them. They may not move in perfectly straight lines because of the friction on the turntable, but you can see that any straight line drawn through a circle is pointing away from the center at any point except the center. So the objects want to move away, by Newton’s first law. To keep them from moving away you have to have a force that pulls them back, that is the rope, or floor, or in general, the centripetal force.
I think your confusion here lies in your understanding of forces and motion in general. Forces are only needed to keep a body from moving at a constant speed in a straight line. Just because the objects are moving away from the center of the circle doesn’t mean a force is causing it. In fact, you can see (hopefully) now that the only force needed is the force keeping them from moving away. If that makes any sense.
I got nothing, except that this thread reminds me of my experience in a fairground attraction a year ago. We basically entered a giant centrifuge. We were asked to lean against the walls, which were covered with padded stretchers mounted on vertical rails. The whole thing started turning, faster and faster, untill we were pinned to the wall. I couldn’t even lift my head, and barely raise my hand, I just felt so incredible heavy. The machine turned even faster, and the stretchers, that were attached at a small angle, went up, with us on it. After a minute or so (it seemd much longer!) the whole thing came to a halt again.
It was a bit nauseating, and totally disorienting, but kinda cool. I guess I had about 3 G on my body. It just felt weird to have the weight not just on my feet, but on my whole body.
Ahh, the Gravitron. When we were kids we’d ride the thing over and over til we got bloody noses. Never had so much fun staggering around with a throbbing head until, years later, the Jack Daniels.
A couple things have happened here, that I’m going to try to sort out. The first one is a bit subtle, but you’ve moved from considering the ball as your system to considering the rope as your system. As you say, both viewpoints are valid, but we can’t necessarily conclude that what is true of one system pertains to the other. You say:
And this is true, when we consider the rope as our system. Newton’s Third Law states that every action has an equal and opposite reaction. When we consider the rope, there is a force pulling away from the center of the circle. When we consider the ball, there is an equal force exerted on it, pointing towards the center of the circle.
Another important point is that we are dealing with two separate quantities: velocity and acceleration. These are very much independent of each other. If you know the velocity of an object at any point in time, you can say nothing about the acceleration.
Perhaps an example that moves slightly slower might help. Consider again the ball on the rope, but this time place the ball on the ground, and attach the free end of the rope to the ground. Place the ball as far away from the center as you can. If you were to try to push the ball farther away from the center, you would not be able to, because the rope is also exerting a force on the ball, the “pull”. This pull is still there, even though the ball does not move any closer to the center. This pull only counteracts your attempts to move the ball farther away from the center. It is also true that the ball is exerting an outwards force on the rope, but this fact isn’t useful unless we’re considering the rope as our system. Here we’re only considering the ball as our system.
Now, instead of pushing outwards on the ball, push it perpendicular to the rope. The ball will not move perfectly perpendicular, but move along the circle. As you push it perpendicular to the rope, you are attempting to move the ball farther away from the center that it currently is. The rope won’t let you do that, so it pulls the ball towards it to counteract you pushing the ball farther away, exactly as in the last example. To keep the ball from moving farther away, the rope must exert a force on the ball towards the center of the circle. Again, we must remember that the ball is our system, and to avoid conflating facts that are only useful to other systems.
The ball being spun on the rope works in exactly the same way, only inertia plays the role of the person pushing the ball. As the ball spins, it is continually trying to move in a straight line, due to Newton’s First Law. However, moving in a straight line would move the ball farther from the center, so this must be counteracted by the rope pulling the ball towards its center. As in the first example, this pull is real regardless of whether the ball actually moves closer to the center.
We can also discuss this with an analogy to a ball on a string. Return to the second example, where the rope is attached to the ground, but this time assume that the rope is elastic. While rope does not allow for any movement away from the center after a certain point, elastic only resists movement away from the center, but does not completely prevent it.
Again, push the ball perpendicular to the elastic string. As the ball moves farther from the center, the elastic resists this movement, but not enough to prevent it entirely. The result is that the ball moves along a curved path, but the path is not quite a circle. When you push perpendicular and allow the string to stretch many times, you get the outward spiral shape seen from a turntable. When the elastic finally breaks (representing the object reaching the edge of the turntable) the object continues to move in the direction it previously was.
Again, the turntable works essentially the same way, with some combination of friction and inertia playing the roles of the pusher and the string. I should caution, however, that there is one important difference. Elastic becomes progressively harder to stretch as you stretch it more and more. This is not true of the friction on a turntable.
Once again, it’s important to realize that a force in one direction does not necessarily mean that an object will move in that direction, as DrCube noted, and it is important not to mix systems.
I’m going to disagree with Stranger on a Train, here. It’s possible for particles to exist in one reference frame but not in another. For instance, an observer freely falling into a black hole will observe no Hawking radiation, but one a safe distance away (and being held at that safe distance) will. Of course, it would take a quantum theory of gravity to answer definitively, but I think it’s safe to say that, for a person in a rotating reference frame experiencing a centrifugal force, there are virtual gravitons mediating that force, but for a person in an inertial reference frame, there are no such virtual gravitons.
I’m also going to disagree with Stranger on a Train. In general relativity centrifugal force is a real force. Sourceless but real.
SenorBeef if you’re still having trouble with this just imagine that you’re tall enough so that your head is at the center of rotation.
Actually, MikeS is right. As a consequence of the equivalence principle of General Relativity, there’s no real substantive difference between the acceleration due to the centripetal force and that due to gravity. Some physicists would say that the simulated gravity on the spinning space station is only ‘simulated’ insofar as the magnetism created by an electromagnet is ‘simulated’.
The equivalence principal states that at every point in space it’s impossible to perform any experiment that distinguishes between an accelerating frame of reference and a gravitational field.
OK then, if this is the case, then how come you can easily use a gyroscope (or a coffee pot) to determine whether or not the space station you’re in is spinning? Any Coriolis effect is readly detectable, belying the degree of any rotation. Isn’t this a violation of the equivalence principle?
Not really. The equivalence principle only holds at the local level - ie in a small neighborhood around each point in space. The Coriolis force is measurable at the macro-level; at the local level, the Coriolis component is zero.
Confirming (or possibly, disproving) the equivalence of rotational and gravitational inertia is an area of active research.
I’d guess so. Nobody can say for sure, since the question itself is a bit ambiguous, as we have no theory of quantum gravity. But by the equivalence principle, there’s no reason to think any consistent model of quantum gravity would not also explain the acceleration due to rotating reference frame. In fact, the relativistic frame-dragging effect of the Tipler Cylinder referenced above can be explained in terms of gravitons and the gravitomagnetic effect.
The bolded assumption is wrong, and that’s what’s making all the difference in your understanding. If the floor were to suddenly vanish, your body would not fly off in a direction away from the center of rotation, it would fly off in the direction tangential to the “circle” your feet were tracing out
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:smack: let’s try that again…
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Asterisks depicts the radius. Arrows show the direction of release.
So, bottom line it: Would Clarke’s rotating spaceships work? Discovery was not his only example. Remember, there was a spacestation that was rotating as well. I always thought that the scene in the phonebooth didn’t work. There was the image of the earth (?) rotating outside a window. The arc the earth moves isn’t nearly large enough.
First of all, are you asking about Clarke’s spacecraft, or Kubrik’s? They worked together, but their visions were not identical. And second, what’s your standard of “work”? It might be accceptable for your astronauts to be a bit discombobulated, if they don’t suffer atrophy of their bones and muscle mass, for instance, and we really don’t know how long it’d take for a human to get used to the Coriolis forces.