0123: "Centrifugal Force"

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Postby davean » Wed Jul 12, 2006 3:24 am UTC

xkcd wrote:
paige42: No, acceleration and force "exist", they both can exist in any dirrection. These other things are interpritations of effects and hence not valid, as are all opinions.

Snarkiness is only allowed when accompanied by clarity.



Sn, snarkiness? Me? What?


Actually there is clarity there xkcd, just in my usual "Find the solution that fits and thats the correct solution" way. I talk in prolog I guess, "Find the facts such that statement X makes sense." :-)

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Postby skeptical scientist » Tue Nov 28, 2006 10:10 am UTC

I'm new to the forum, so I thought I'd say 'hi'. I hope you don't mind thread necromancy...

xkcd wrote:
I'd like to present this thread as Exhibit A of why physics sucks and we should all stick to theoretical mathematics.

Made any progress on that axiom of choice lately, Kira? I'm having some trouble with your Banach-Tarski paradox

I really don't know why this is called a paradox, as it's really not. I'm sure it wouldn't bother you at all if I cut up a ball into infinitely many parts (its constituent points) and performed only translations on them (namely translated each point x by x) to create a ball with twice the demensions. It probably wouldn't bother you if I created two balls either - after all two balls have the same cardinality of one ball. All of the individual transformations are volume preserving, so why should the volume change when I cut the thing up, apply the transformations, and patch them back together? Simple - because when I cut the thing up, I cut it up into uncountable many pieces, and we don't expect such processes to preserve volume, nor should we.

So why should it be an issue if I take a single ball and cut it up into finitely many pieces and then reassemble them, when those pieces don't even have volume? (I don't mean they have 0 volume - I mean it is not possible to define 'volume' for the pieces.) Why should transformations which preserve volume on measurable objects preserve volume on objects for which no volume can be defined? Yes it's surprising that this is possible, but it's not paradoxical.

Some people try to use this theorem as evidence against accepting the axiom of choice, but the axiom itself is really pretty benign if you look at what it says, and it's been proved to be consistent with the other axioms, so I think it should be accepted without controversy, and its implications should be regarded as interesting and sometimes surprising, but unquestionably correct.
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Postby aldimond » Tue Nov 28, 2006 5:26 pm UTC

skeptical scientist wrote:I really don't know why this is called a paradox, as it's really not. I'm sure it wouldn't bother you at all if I cut up a ball into infinitely many parts (its constituent points) and performed only translations on them (namely translated each point x by x) to create a ball with twice the demensions.


It would certainly bother me. When you start playing with Infinity you might just put an eye out!
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Postby no-genius » Tue Nov 28, 2006 5:31 pm UTC

aldimond wrote:
skeptical scientist wrote:I really don't know why this is called a paradox, as it's really not. I'm sure it wouldn't bother you at all if I cut up a ball into infinitely many parts (its constituent points) and performed only translations on them (namely translated each point x by x) to create a ball with twice the demensions.


It would certainly bother me. When you start playing with Infinity you might just put an eye out!


Yeah, but you'd still have an infinite number of healthy eyes left
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Postby athelas » Thu Nov 30, 2006 2:31 am UTC

no-genius wrote:
aldimond wrote:
skeptical scientist wrote:I really don't know why this is called a paradox, as it's really not. I'm sure it wouldn't bother you at all if I cut up a ball into infinitely many parts (its constituent points) and performed only translations on them (namely translated each point x by x) to create a ball with twice the demensions.


It would certainly bother me. When you start playing with Infinity you might just put an eye out!


Yeah, but you'd still have an infinite number of healthy eyes left


And even if you didn't, you can break the eye into infinitely many parts and make two nice shiny new ones.

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Postby aldimond » Thu Nov 30, 2006 3:21 am UTC

You could maybe do that if you waited for an infinitely long time for someone to actually figure out how to do it, rather than just knowing that it's possible.

Of course, once you waited that long you'd still have an infinite amount of time to go, slicing up that eyeball, I want you to know, don't know about you, but I am un...
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Postby skeptical scientist » Thu Nov 30, 2006 5:25 am UTC

aldimond wrote:You could maybe do that if you waited for an infinitely long time for someone to actually figure out how to do it, rather than just knowing that it's possible.

The proof laid out the basic idea of how to do it (although it used the axiom of choice, so you need to make infinitely many arbitrary decisions to carry it out) but it could never be performed on a real eyeball, as the object in question needs to be infinitely divisible, and eyeballs, being composed of atoms, are not.
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Postby Jerf » Thu Nov 30, 2006 7:38 pm UTC

A "paradox" is, by definition, an apparent contradiction.

Since we don't call it a "contradiction", there is at least one point of view where it isn't. If you've attained the necessary understanding, a paradox will no longer be a contradiction to you.

So it's still a paradox, just like the "Twin Paradox" of relativity, which also isn't a "paradox" to those that understand the relevant math.

The Axiom of Choice is probably a lot easy for somebody with a modern education to understand because we've had decades to grapple not just with its implications, but how to teach those implications. At the time, it sure looked like a contradiction of "an unspecified property to be determined later". :)

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Postby eigenborg » Wed Dec 06, 2006 5:35 pm UTC

Hey uhm... I suppose Im a little confused about your centrifugal force. I am not going to say that there is no force there, indeed there is a force. But i think it would make everyone life easier if we refer to centrifugal force as a classification rather than a force. In bond's situation, the wall is pushing him towards the center, what he is feeling is the "normal" force from the wall, isn't it?

I'm a student, so if I'm wrong (plausible) please enlighten me!

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Postby Teaspoon » Thu Dec 07, 2006 11:29 pm UTC

Will he be crushed against the wheel by his own centrifugal force pushing him outwards or by the centripetal force the wheel is pushing him inwards with?

The answer, as I see it, is yes.

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Postby william » Thu Dec 07, 2006 11:37 pm UTC

Teaspoon wrote:Will he be crushed against the wheel by his own centrifugal force pushing him outwards or by the centripetal force the wheel is pushing him inwards with?

The answer, as I see it, is yes.

I agree. "Yes" is clearly the answer.
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Postby demeteloaf » Sat Dec 09, 2006 6:28 am UTC

eigenborg wrote:Hey uhm... I suppose Im a little confused about your centrifugal force. I am not going to say that there is no force there, indeed there is a force. But i think it would make everyone life easier if we refer to centrifugal force as a classification rather than a force. In bond's situation, the wall is pushing him towards the center, what he is feeling is the "normal" force from the wall, isn't it?


Basically, there are two distinct ways of looking at the problem, both equally valid. To say that "there's no such thing as centrifugal force" is an oversimplification that ignores one perfectly valid way of looking at the problem.

Method 1: the method you describe where you take yourself outside the rotation frame, and say that there isn't a force pushing the object outwards, it's just that the inertia of an object will make it want to move in a straight line, and the apparent "force" is not really a force but just the fact of inertia.

Method 2: Use a rotating coordinate system. If you use a coordinate system that rotates at a constant angular velocity, omega, and solve for the acceleration of an object in that frame, you will come up with the equation:

a_rot = a_inertial + 2v_rot x omega + omega x (r x omega)

The accelereation in a rotating frame of reference is equal to the acceleration in an inertial frame of reference plus two additional terms. One that is a coreolis effect (2v x omega) and one that corresponds to a centrifugal acceleration effect (omega x (r x omega)). So, since these are valid acceleration terms in your rotating frame of reference, there is absolutely nothing wrong with treating them as valid force terms.

Basically, while there is nothing wrong with treating everything as an inertial frame of reference and never dealing with non-inertial frames of reference, it is wrong to say something like "centrifugal force does not exist" which is what you actually do see a good deal if you go to a lot of intro physics classes.

In fact, one of the principles of Einstein's theory of General Relativity is that if you are in a closed box, it is impossible to tell whether you're on the surface of a planet, feeling the force of gravity pulling you downwards, or the box is accelerating upwards at the exact acceleration due to gravity. (i.e. It is impossible to tell the difference between a real force, gravity, and a "non-existant" force, your body's inertia's resistance to acceleration.)

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Postby andreffranca » Wed Jan 03, 2007 12:43 pm UTC

A few days before I saw a very interesting tricky problem (concerning the principle of equivalence of G.R. and hydrodynamics):

Imagine you're in a car accelerating frontwards, and there is an helium baloom attached by a rope to the floor. In which direction does it move when the car accelerates, frontward of backward?

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Postby Erasmus » Thu Jan 11, 2007 7:54 am UTC

andreffranca wrote:Imagine you're in a car accelerating frontwards, and there is an helium baloom attached by a rope to the floor. In which direction does it move when the car accelerates, frontward of backward?


In what reference frame are you asking?

In the road's reference frame, the balloon is probably moving forwards with the car (unless the car was moving backwards and accelerating by coming to a halt and then moving forwards).

In the car's reference frame: is the acceleration changing over time? If not, the balloon doesn't move at all.

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Postby Hawknc » Thu Jan 11, 2007 9:42 am UTC

You're half right. From the reference frame of the ground, the balloon would be seen to be accelerating forwards. From inside the car, though, the balloon would seem to move backwards to a point where the lift force (from the helium being lighter than the air), the gravity and the tension in the rope due to acceleration all cancelled out. Given a balloon size and car acceleration, you could even work out what angle it would settle at.

Just to clarify on Erasmus' last point - if it's constant acceleration, from inside the car the balloon would appear to have a transient section, then it would settle at a certain angle from the normal. If it's constant velocity, then no, it would not move at all and just stay perpendicular to the floor.

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Postby andreffranca » Mon Jan 15, 2007 4:23 pm UTC

Hawknc wrote:You're half right. From the reference frame of the ground, the balloon would be seen to be accelerating forwards. From inside the car, though, the balloon would seem to move backwards to a point where the lift force (from the helium being lighter than the air), the gravity and the tension in the rope due to acceleration all cancelled out. Given a balloon size and car acceleration, you could even work out what angle it would settle at.

Just to clarify on Erasmus' last point - if it's constant acceleration, from inside the car the balloon would appear to have a transient section, then it would settle at a certain angle from the normal. If it's constant velocity, then no, it would not move at all and just stay perpendicular to the floor.


Not really :P From the reference frame inside the car, the balloon will be see moving frontwards with the car. Why? Because the air is actually being "pushed" backwards by its inertia too, and since the baloon is less dense than the air, it will suffer impulsion frontwards.
Actually, Einstein thought that there is no way to tell the difference - at the frame of the body - if we're accelerating or being pushed by a stong gravitational field on the opposite side, so you can make the same anology, put a strong gravitational field behind the car, and you'll see the balloon move frontwards, as it's supposed to be.

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Postby parallax » Wed Jan 31, 2007 5:33 pm UTC

The centrifugal force that Bond will feel when the centrifuge is activated is indeed a real force and is commonly referred to as "gravity".

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Postby Grincement » Wed Jan 31, 2007 5:39 pm UTC

parallax wrote:The centrifugal force that Bond will feel when the centrifuge is activated is indeed a real force and is commonly referred to as "gravity".


Actually that would be weight not gravity...
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Postby The Sleeping Tyrant » Wed Jan 31, 2007 5:42 pm UTC

parallax wrote:The centrifugal force that Bond will feel when the centrifuge is activated is indeed a real force and is commonly referred to as "gravity".


Centripetal force acts perpendicular to the motion of any point on the centrifuge. Since some points on the centrifuge will be parallel to gravity at some point in time, the force due to gravity cannot be the centripetal force.

Since centrifugal force is apparently (first I've heard on the subject is the few posts regarding this before this) working in the opposite direction to centripetal force, it's not due to gravity either.

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Postby Mathmagic » Wed Jan 31, 2007 8:28 pm UTC

The Sleeping Tyrant wrote:
parallax wrote:The centrifugal force that Bond will feel when the centrifuge is activated is indeed a real force and is commonly referred to as "gravity".


Centripetal force acts perpendicular to the motion of any point on the centrifuge. Since some points on the centrifuge will be parallel to gravity at some point in time, the force due to gravity cannot be the centripetal force.

Since centrifugal force is apparently (first I've heard on the subject is the few posts regarding this before this) working in the opposite direction to centripetal force, it's not due to gravity either.

I like to explain the centrifugal "force" as more of an "effect" than a force, as there is no ACCELERATION in the direction of said centrifugal "force", and in order for there to be a FORCE, there must be an acceleration in the same direction.

This centrifugal effect is caused by the inertia you/the object posses, and it's tendency to continue in the direction that it WANTS to go (tangent to the rotation).

I know that this has been said before, but I may as well re-iterate it all for the last couple posters.
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Postby riley » Wed Jan 31, 2007 9:11 pm UTC

andreffranca wrote:From the reference frame inside the car, the balloon will be see moving frontwards with the car. Why? Because the air is actually being "pushed" backwards by its inertia too, and since the baloon is less dense than the air, it will suffer impulsion frontwards.
Actually, Einstein thought that there is no way to tell the difference - at the frame of the body - if we're accelerating or being pushed by a stong gravitational field on the opposite side, so you can make the same anology, put a strong gravitational field behind the car, and you'll see the balloon move frontwards, as it's supposed to be.


Interesting. Have you ever actually tried this? You're saying it moves forward in the frame of reference in which the car is stationary because of air pressure, but I never notice a change in air pressure when I accelerate, so any pressure change must be... unnoticeable. Is the unnoticeable difference in air pressure enough to move the balloon noticeably? I guess balloons are very light.

Also... let's say we accelerate at 1g. Then the balloon should go to the front of the car with the same force (relative to the car's frame of reference) that it goes up, away from the Earth, yeah?

Ok. I need a helium balloon and a big parking lot. I'm not sure my car can quite pull off 1g :( Maybe 0.5 g will suffice.

It will be interesting to see how much faster the balloon moves when it starts at the back of the car vs. when it starts towards the front. I guess the windshield is outer space!

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Postby The Sleeping Tyrant » Wed Jan 31, 2007 10:53 pm UTC

mathmagic wrote:I like to explain the centrifugal "force" as more of an "effect" than a force, as there is no ACCELERATION in the direction of said centrifugal "force", and in order for there to be a FORCE, there must be an acceleration in the same direction.

This centrifugal effect is caused by the inertia you/the object posses, and it's tendency to continue in the direction that it WANTS to go (tangent to the rotation).

I know that this has been said before, but I may as well re-iterate it all for the last couple posters.


I saw that on the last page, but I also found xkcd's arguments for it being a force quite compelling.

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Postby parallax » Thu Feb 01, 2007 1:38 am UTC

Squeak wrote:
parallax wrote:The centrifugal force that Bond will feel when the centrifuge is activated is indeed a real force and is commonly referred to as "gravity".


Actually that would be weight not gravity...


Actually, I mean gravity. According to General Relativity, the "forces" you feel while being rotated (in a centrifuge), or accelerated (in a car) are equivalent to the "force" you feel while near a massive object.

It should be noted that this centrifugal gravitational force only exists in Bond's reference frame. All goldfinger sees is the cenrtipetal normal force of the centrifuge accelerating Bond inwards. However, Bond feels the normal force of the centrifuge, and also an outward force pinning him against the centrifuge. In his own reference frame, Bond is not moving, so there must be two forces acting equally on him in opposite directions according to Newton's laws. One of them is the normal force of the centrifuge, pushing him inwards. The other is equivalent to what we call gravity.

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Postby narfanator » Thu Feb 01, 2007 2:14 am UTC

No. Won't work like that; you're forgetting the transfer of motion.

If you accelerate a car, say, by putting on the gas, the wheels push against the ground and that push is transfered to the frame of the car by the axle. The car is now being pushed, and thus the foward-facing surfaces of the car push against the the stationary air inside the car, causing an increase in pressure on those surfaces and a corresponding loss of pressure against the rear-facing surfaces as they move away, thus a pressure differential thus the balloon moves.

With gravity, nothing's pushing against something. If somehow spontaneosly create a gravitation source near the car, that gravitation force works on the car, the air and and the balloon nearly equally*, and they will all accelerate at the same same speed. *-> It's not actually equal, but the force is proportional to the object's mass and thus the accelerations are nearly equal.

The part where they're not equal is what causes gravity tides and tidal locking; if your gravity source is close enough, or you are large enough, then the far side expereinces significantly less gravity than the near side, and correspondingly less acceleration. This difference is, for instance, what keeps Io hot.

What Bond experiences is similar to gravity only given our own perceptions - He is experiencing a nearly constant force from a surface. The geometry of a centrifuge is what allows this constant force; if you wanted to do this linearly, you'd have to be constantly accelerating the surface (hence you hear things like "accelerating at 2 gees", which means that the object is accelerating literally at twice the gravitational acceleration something experiences on the surface of the earth.). The force that Bond experiences is, however, in no way similar to gravity as it does not act upon every instance of mass in his volume; it acts only upon his "downward" surfaces in contact with the centrifuge.

So, no, it's not gravity, and has nothing to do with General Relativity, in which a gravity source is typically graphically represented as a warped region in an otherwise 2-d plane.

It is equivelent to gravity *only* with respect to our perceptions as conscious entities, not as objects, and becuase you're using gravity to mean what the floor does, not what the Earth's mass does.

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Postby parallax » Thu Feb 01, 2007 2:47 am UTC

If you create a gravitational source near the car, that force will act on the air to create a pressure gradient which will cause the balloon to move away from the gravitational force in the same way as if your car were accelerating. It's the same reason Helium balloons move "up" in Earth's gravitational field.

The force Bond experiences does act on every instance of mass in his volume. If he were to "lift" an object toward the center of the centrifuge, and release it, it would "fall" towards the wall of the centrifuge, although it is not in contact with the centrifuge.

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Postby narfanator » Thu Feb 01, 2007 5:38 am UTC

Okay, I just spent waay to long trying to disprove the first of your statements, with math and everything, only to realize what you actually meant.

But, no, you're missing my point. It's not gravity /at all/ that's creating the pressure differential. It's the damn floor. If you had a cloud of gas in vaccuum (assume we don't need to consider the lateral dispersion), the gravity would accelerate the closer gas faster than the farther, creating - yes - a pressure differential, but one that points towards the gravitational source. In Mr Bond's case, the pretend "gravity" source is farther away from the axis of rotation, and the balloon will rise, due to pressure, towards that axis. For the car, the pretend gravity is behind it (opposite the direction of acceleratio), and, again, the balloon will move away from the pretend source, not towards it.

And on the volume thing - Okay, the force from the centrifuge upon Mr. Bond comes from the constant inwards acceleration of both - but Mr. Bond (if standing), expereinces that force conveyed through the materials of his body as a compressive force. Mr. Bond will be crushed.

So long as the source is not within the body, you cannot crush something with gravity. The closest you can come is to destroy it using tidal forces - exactly as the air seperates, due to gravity, as it falls. This is a tensile force.

That's what I mean by "affecting every instance of mass the volume". I should have said independantly - gravity affects each atom in your body indepedantly of the other atoms. A centrifuge only mimics the affect of gravity by having a force pass from each atom to each atom, as the bottom ones are pushed "upwards", and thus push the atoms above them "upwards" as well.

I also don't mean to sound angry, upset, or condescending, and I am sorry if I do. This is a silly thing to get worked up about.

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Postby riley » Thu Feb 01, 2007 6:55 am UTC

It's easy to see that the forces on Bond are not like gravity. Imagine that the villain places a ball within the radius of the centrifuge, but not touching it. There is no force emanating from the wheel that will make that ball accelerate towards some point on the wheel - the ball will fall towards the center of the Earth. This is the biggest problem I have with movies that show rotating space stations as if they have normal gravity. When you jump directly opposite to a gravitational field, you end up falling back to precisely the same position. In a rotating space station with the tiny diameter of, for example, the station in 2001: ASO, if you jump directly towards the center of the ship (or climb a ladder to the center), the effects could be very different. Imagine playing catch with someone 45 degrees away from you - the ball would fly along a very strange path from your perspective, because your "gravity" only works on surfaces stuck to the wheel. Just standing on the wheel would be uncomfortable because it would feel like your feet were constantly being pulled out from under you. These effects are all from the differences the post above this one mentions - the centrifugal force only affects the atoms in contact with the wheel, while gravity acts on every atom independently.

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Postby SpitValve » Thu Feb 01, 2007 7:29 am UTC

riley wrote:It's easy to see that the forces on Bond are not like gravity. Imagine that the villain places a ball within the radius of the centrifuge, but not touching it. There is no force emanating from the wheel that will make that ball accelerate towards some point on the wheel - the ball will fall towards the center of the Earth. This is the biggest problem I have with movies that show rotating space stations as if they have normal gravity. When you jump directly opposite to a gravitational field, you end up falling back to precisely the same position. In a rotating space station with the tiny diameter of, for example, the station in 2001: ASO, if you jump directly towards the center of the ship (or climb a ladder to the center), the effects could be very different. Imagine playing catch with someone 45 degrees away from you - the ball would fly along a very strange path from your perspective, because your "gravity" only works on surfaces stuck to the wheel. Just standing on the wheel would be uncomfortable because it would feel like your feet were constantly being pulled out from under you. These effects are all from the differences the post above this one mentions - the centrifugal force only affects the atoms in contact with the wheel, while gravity acts on every atom independently.


Dunno about that. Let's say you're in a space station with radius 10m, rotating at 10m/s (at the circumference), so you get Earthlike 10m/s/s "gravity". The radial speed is then 1 radian per second.

You then drop a ball from a height of 1m. As the ball is 9m from the centre, it is moving at 9m/s, and will continue to do so until it hits the floor, some 0.45 radians around and 0.48s later. (In 10m/s/s gravity it would take 0.45s to hit the ground).

After 0.48s, your feet have moved around 0.48 radians.

So the ball will land about 30cm behind you, a tiny fraction of a second later than it would on Earth. So it is different from gravity, but not wildly different.

If the station was 100m in radius, the ball would fall move like 20cm behind you, and would be much closer to 0.45s in falling - and as you get larger, it gets more gravity-like.


The point is that from a rotating frame, you do get "apparent" forces that appear to move things outwards, even if they're not touching the edge. Just like the James Bond villain said...

Also you would not feel your feet being constantly pulled out from underneath you. The only "real" force is the inwards centripedal force, accelerating you inwards. You won't feel yourself slipping backwards anymore than standing on the Earth's surface rotating at 200m/s.

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Postby phlip » Thu Feb 01, 2007 7:44 am UTC

riley wrote:Imagine that the villain places a ball within the radius of the centrifuge, but not touching it.

Better example:
Imagine that the villain places a ball within the radius of the centrifuge, but not touching it, and then throws it such that it is (initially at least) stationary relative to the wheel. That is, he throws it in the direction the wheel is spinning, at the same speed.

Discount the Earth's gravity, 'cause that'll just make it complicated, and that's not what we're looking at anyways.

So, from Bond's perspective, the ball is initially motionless (by "from Bond's perspective" I mean relative to him - from Bond's perspective, Bond and the centrifuge are both motionless, and the room is turning). From the villain's perspective, it'll move in a straight line towards the edge of the centrifuge, and then out into the universe.
From Bond's perspective, this path will be a curve through space. It starts motionless, but then starts moving directly towards the edge. This (apparent, from Bond's perspective) acceleration is caused by centrifugal force. The ball will continue accelerating towards the edge, but it will also curve in the opposite direction to the spin of the centrifuge - this (again, apparent) curve is caused by the Coriolis force.

It's important to note that nothing magical has happened here, and the fact that the centrifuge is spinning doesn't actually affect the ball's path. From any inertial reference frame, the ball will appear to be moving in a straight line. But when you trace the motion of the ball relative to the rotating wheel, and look at the formulae you get, there is a centrifugal term and a Coriolis term in the equation of motion. This is what the comic refers to with the "rotating reference frame".

riley wrote: Just standing on the wheel would be uncomfortable because it would feel like your feet were constantly being pulled out from under you.

Actually it wouldn't, because you'd also be moving sideways at the same speed as the floor... the only force you'd feel would be the centripetal force needed to make you go around in a circle (or, from your point of view, the centrifugal force that looks like gravity).

Certainly, throwing a ball at someone 45° away on the wheel would be strange, but only because we're used to a situation where gravity is in effectively the same direction and magnitude everywhere. Not just because it'd be flying under the effects of centrifugal force rather than gravity.

[edit]
As for the "centrifugal force is the indistinguishable from gravity" comment which is also being misunderstood... if it was possible (and it might be, I dunno) to set up a system such that the gravitational field was the same shape as the centrifugal forces in a rotating object - neutral in the centre, elsewhere pointing directly away from the centre and proportional to your distance... then the system would behave exactly the same way as if there were no gravity and it was simply rotating.

A point mass under the effects of centrifugal force will experience the same effects as a point mass under the effects of gravity.

It is only when you measure the force in several places and figure out the shape of the system that centrifugal forces are distinguishable from gravity.

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Postby Andrew » Thu Feb 01, 2007 11:05 am UTC

mathmagic wrote:in order for there to be a FORCE, there must be an acceleration in the same direction.

So gravity doesn't exist when I'm not in midair? That's some tripped-out Zen right there.



If centrifugal force does/doesn't exist, does Unruh radiation exist? Only

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Postby Mathmagic » Thu Feb 01, 2007 2:56 pm UTC

Andrew wrote:
mathmagic wrote:in order for there to be a FORCE, there must be an acceleration in the same direction.

So gravity doesn't exist when I'm not in midair? That's some tripped-out Zen right there.



If centrifugal force does/doesn't exist, does Unruh radiation exist? Only

Ummmm, gravity is a constant acceleration, therefore, there is ALWAYS a gravitational force...
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Postby Andrew » Thu Feb 01, 2007 4:32 pm UTC

mathmagic wrote:Ummmm, gravity is a constant acceleration, therefore, there is ALWAYS a gravitational force...

It's not, though, is it? If I'm sat here not moving for a while then I'm not accelerating, at least, not apart from the slight acceleration keeping me on the Earth's rotating and orbiting surface. So either you can have force without acceleration (though not a net force) or else gravity stops working when I hit the floor.

But then I suppose, general relativity tells us (in my limited understanding of it) that gravity and acceleration are one and the same thing. So really, I am accelerating, upwards at 9.8m/s/s, and that's why I feel all this gravity; it's just my body trying to stay still while the ground and atmosphere charges upward ever faster. So perhaps in a truly inertial frame, gravity doesn't exist either -- and come to think of it, that's what happens in orbit. In orbit you can say your reference frame is defined such that the gravity term drops out, or you can say that you're in a rotating frame around the Earth, and that the centrifugal force balances the gravity out. Either way, gravity and centrifugal force end up on apparently pretty similar footing. As far as I can see the simplest thing to do is to call all such things "forces" to avoid having to redefine everything later on when we learn more about how things work.

I'm in over my head here, so if anyone knows why any of that was nonsense, do please say so.

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Postby narfanator » Thu Feb 01, 2007 5:06 pm UTC

Instincts tell me you're wrong about general relativity.

There doesn't have be acceleration for there to be a force.You first sum the forces on a object, and then find it's acceleration. If forces cancel out, that doesn't mean they're not there.
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Postby Fieari » Thu Feb 01, 2007 5:15 pm UTC

I'm pretty sure you are still being accelerated downwards. It's just that the chair you're sitting in is accelerating you upwards. Gravity force, normal force.
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Postby riley » Thu Feb 01, 2007 6:13 pm UTC

SpitValve wrote:Dunno about that. Let's say you're in a space station with radius 10m, rotating at 10m/s (at the circumference), so you get Earthlike 10m/s/s "gravity". The radial speed is then 1 radian per second.

You then drop a ball from a height of 1m. As the ball is 9m from the centre, it is moving at 9m/s, and will continue to do so until it hits the floor, some 0.45 radians around and 0.48s later. (In 10m/s/s gravity it would take 0.45s to hit the ground).

After 0.48s, your feet have moved around 0.48 radians.

So the ball will land about 30cm behind you, a tiny fraction of a second later than it would on Earth. So it is different from gravity, but not wildly different.


Ok, so in the case in which Bond drops the ball from a height of 1m (waist height), the ball falls behind him by 30 cm. This is a 16 degree deviation from "straight down," which I think is pretty significant. But you're right, you could definitely get used to it, and maybe even ignore it in movies.

Let's consider another example in the same space station: You want to play catch with yourself. On Earth, starting at a height of 1.0m, you would throw the ball up with an initial velocity of about 6.3 m/s in order to throw it to a total height of 3.0m (which is a pretty normal throw-to-yourself height). So, you do the same thing in the space station.

On Earth:
The ball reaches its maximum height of 3.0 meters after about 0.6 seconds. It falls to the ground at your feet after 1.4 seconds.

On the Centrifuge:
The ball reaches its maximum height of 2.6 meters after about 0.4 seconds. It falls to the ground after 1.1 seconds, 79.0 centimeters in FRONT of you.

The differences get more and more significant as the heights and velocities increase with proportion to the radius of the space station. I think 10 meters is a pretty good estimate for the radius of the 2001: ASO station.

An even more dramatic example! From a height of 1 meter, you (the astronaut on the space station) throw the ball at 9 m/s against the direction of the spin of the station. On Earth, you expect the ball to fall down in a parabolic path. On the space station, the ball... orbits forever, never hitting the ground. Then you turn around and throw the ball at 9 m/s in the same direction as the spin. This time, the ball plummets to the ground. On Earth, you don't expect either of these behaviors... and you certainly don't expect the direction you throw the darn thing to matter.


I think we basically agree - it will appear to the space station inhabitants that there is generally something sucking stuff down to the ground. I'm just saying it's going to seem pretty different from gravity on Earth, and I've yet to see that acknowledged in a movie.

Edits: grammar, punctuation, sig digs

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Postby riley » Thu Feb 01, 2007 6:30 pm UTC

phlip wrote:
riley wrote:Just standing on the wheel would be uncomfortable because it would feel like your feet were constantly being pulled out from under you.


Actually it wouldn't, because you'd also be moving sideways at the same speed as the floor... the only force you'd feel would be the centripetal force needed to make you go around in a circle (or, from your point of view, the centrifugal force that looks like gravity).


I don't have an analytical argument ready to dispute this, but I'm not convinced. You say "you'd also be moving sideways at the same speed as the floor," but again I reiterate that only your shoes are going the same speed as the floor. In a centrifuge with a radius of 10m, your head will be going noticeably slower than your feet. I can't show that the forces wouldn't propogate up to your head in an even way that wouldn't make you feel off-balance, but you can't just say "you're moving the same speed."

phlip wrote:Certainly, throwing a ball at someone 45° away on the wheel would be strange, but only because we're used to a situation where gravity is in effectively the same direction and magnitude everywhere. Not just because it'd be flying under the effects of centrifugal force rather than gravity.


Someone who can jump sufficiently fast in the correct direction can gain complete independence from the centrifuge and never return to the side (again discounting Earth's gravity). This is one of the effects that I was referring to when I was imagining throwing a ball to someone 45 degrees away from you. This is not because the "gravity" changes direction as you move around in the centrifuge. Even in the rotating reference frame, some objects will seem to only have a constant acceleration towards the center of the centrifuge. This could be considered a NEGATIVE centrifugal term, or, if you were to consider the floor of the centrifuge as a flat plane instead of a circle, you could say that there was zero force on the ball and that it had a constant velocity parallel to the floor. Neither one looks anything like gravity.

If you want to describe it as a gravitational field that just changes direction depending where you are, you also need to say that it changes direction depending on where you are and on what your velocity is.

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Postby parallax » Thu Feb 01, 2007 7:04 pm UTC

Yes, the gravitational field is different depending on where you are and what velocity you have. However, just because the gravitational field is different from Earth doesn't make it any less gravity. I'm sure if you tried to play catch on Jupiter or the surface of the Sun, you would have similar problems.

Yes, your head will be going slightly slower than your feet. In a 10m centrifuge, assuming you are exactly 2m tall, your feet will be travelling at 10m/s while your head will be going 8m/s. Both your head and your feet will make one revolution in 2pi seconds. You won't feel as if your feet are being dragged under you.

Andrew's description of gravity in general relativity is basically correct. An inertial frame is one in which you are in free-fall. When standing on the surface of the Earth, you are actually being accelerated upward through a curved space-time. Hence, you feel gravity just as if you were in an accelerating car.

Acceleration is not necessary for forces to exist. Two equal and opposite forces will cause a net zero acceleration.

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Postby narfanator » Thu Feb 01, 2007 7:20 pm UTC

There's no gravitational feild in a centrifuge!

I might be misunderstanding you, but if you're trying to say that significantly increased gravity, coupled with a correspodingly massive normal force, would cause similar problems to catch in a centrifuge?

Yeah, no. Things fall faster, but the geometries of their fall would be the same. The example of throwing the ball at the rate of spin opposite the direction of spin is a great one.

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Postby riley » Thu Feb 01, 2007 8:04 pm UTC

parallax wrote:Yes, the gravitational field is different depending on where you are and what velocity you have. However, just because the gravitational field is different from Earth doesn't make it any less gravity. I'm sure if you tried to play catch on Jupiter or the surface of the Sun, you would have similar problems.


I disagree. The forces observed in a gravitational field caused by gravity are different from the forces observed in a "gravitational field" caused by a spinning reference frame. Specifically, there are no coreolis or centrifugal effects in a normal (inertial) reference frame.

Yes, your head will be going slightly slower than your feet. In a 10m centrifuge, assuming you are exactly 2m tall, your feet will be travelling at 10m/s while your head will be going 8m/s. Both your head and your feet will make one revolution in 2pi seconds. You won't feel as if your feet are being dragged under you.


Yes, I understand that the number of revolutions per second will be the same. That does NOT mean that the acceleration of your head and your feet will be the same, and it also does not mean that the forces on your head and your feet will be the same. Just like the ball dropped from one meter falls at an angle of 16 degrees, I suspect that there will be some angled forces on your body that will make you feel off balance, and no one's really explained why that wouldn't happen.

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Postby parallax » Thu Feb 01, 2007 8:27 pm UTC

There are also no gravitational forces in an inertial frame. An inertial frame is defined as a frame that is in "free-fall", and experiences no acceleration due to gravity.

It is true that the forces on your head and feet are different. The centrifugal force is proportional to your distance from the axis of rotation. Thus, your head will experience less gravity than your feet. This difference is lessened as you increase the radius of the space station. However, the coriolis force (which causes lateral motion, such as the ball falling behind you), is proportional to the rate of change of your distance from the axis of rotation. Assuming you are standing still, and not jumping or crouching or such, you will not feel any transverse motion of "your feet being pulled out from under you".

I never said that the gravitational field inside a centrifuge would be identical to that of the Earth. I merely stated that there would be a gravitational field. It has a different form than the field generated by a massive body, much as the gravitational field of the Earth is different from the gravitational field of a larger planet and is much different from the gravitational field of an irregularly shaped asteroid. Keep in mind that, ignoring air resistance, it is still possible to through a baseball on the Earth such that it never touches the ground. It just requires more force because the Earth is so large.


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