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direction of centrifugal force

Regarding this edit, asserting that:

ω x (ω x r) is always perpendicular to ω

I don't think this is true.

If F_centrifugal = mω x (ω x r)

then by the rules of the :

=F_centrifugal=m(${\displaystyle \mathbf {\omega } (\mathbf {\omega } \cdot \mathbf {r} )-\mathbf {r} (\mathbf {\omega } \cdot \mathbf {\omega } )}$ =m(${\displaystyle \mathbf {\omega } (\mathbf {\omega } \cdot \mathbf {r} )-\mathbf {r} \omega ^{2}}$).

Yes, the second term is always radially outward, since it has magnitude ${\displaystyle m*\omega ^{2}}$ in the r direction, but the first time doesn't have to be 0 so long as ${\displaystyle \omega }$ and r are not perpendicular.

For example, consider an objective in helical motion such that it is completing counterclockwise circles in xy plane as viewed from +z direction so that its r has a component n the z direction so that ${\displaystyle \omega }$ has a component in the xy plane. That would make ${\displaystyle \omega \cdot \mathbf {r} \neq 0}$ and thus ω x (ω x r) has a component in the ${\displaystyle \mathbf {\omega } }$ direction and is not only radially outward.--Louiedog (talk) 11:43, 5 June 2017 (UTC)

I have just realised that the formula for centrifugal force you quote from the article was missing a minus sign. But with that correction, yes indeed, F_centrifugal = – m {(ω · r) ω – (ω · ω) r} , and therefore

ω · F_centrifugal = – m {(ω · r) (ω · ω) – (ω · ω) (ω · r)} = 0 .

That is, F_centrifugal is perpendicular to ω. It is, in fact, a well-known property of the vector cross product, a × b, that it is always perpendicular to both of its multiplicands, a and b, and, in particular, –ω × (ω × r) is always perpendicular to ω. It is, in fact, just ω times the projection of the vector r onto the plane perpendicular to ω.

Note also that the centrifugal force is an artefact of the motion of the coordinate system in which the motion of objects is being described, and this does not necessarily bear any relation whatsoever to the motion of any of those objects themselves. I presume the helical motion you have in mind is one in which the body's position r(t) at time t is given by something like r(t) = ρ cos(ω t) i + ρ sin(ω t) j + v_z t k. But the ω in this expression is the angular velocity of the body in question about the z axis, and not (necessarily) that of the coordinate system in which the motion of the body is being described. If the coordinate system determined by the three unit vectors i, j and k is inertial, for instance, then the angular velocity of that coordinate sytem is zero, and there will be no centrifugal force on the body in that coordinate system. For the body to be following such a helical path, there must, of course, be a proper force,

m ..r(t) = − m ω ( ρ cos(ω t) i + ρ sin(ω t) j ) ,

acting on it. This force is directed towards, and perpendicular to, the z axis of the inertial coordinate system. In a coordinate system whose origin and z axis coincide with those of the inertial system, but is rotating with angular velocity ω = ω k, the x and y coordinates of the body will be constant, and it will be moving with uniform velocity parallel to the z axis. In this coordinate system there will be a centrifugal force m ω ( ρ cos(ω t) i + ρ sin(ω t) j ) acting on the body which exactly balances the proper force. This centrifugal force is clearly, as it must always be, perpendicular to ω.

David Wilson (talk · cont) 14:21, 5 June 2017 (UTC)

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Inertial Motion

I changed the lead sentence because it's inertial motion and not observation that gives rise to centrifugal force. If an object is drawn to the edge of a rotating system by centrifugal force, this can be observed from any vantage point. Newton's rotating bucket is a prime example. You don't have to be rotating inside the bucket in order to observe the water being pushed against the bucket's walls. 2A00:23CC:4D80:1101:8D3C:FAAF:EB21:11FE (talk) 21:45, 14 December 2023 (UTC) On another point, the last sentence in the top paragraph talks about something called reactive centrifugal force, as though it's something different. It's just the same centrifugal force pushing or pulling against a centripetal force. It would be there anyway, even if the centripetal force wasn't there, and so it's not a reaction. The centripetal force curves the path of the object and it doesn't even have to be equal in magnitude to the centrifugal force unless it is causing circular motion.2A00:23CC:4D80:1101:8D3C:FAAF:EB21:11FE (talk) 21:52, 14 December 2023 (UTC)

I'm in favor of simplifying, but that oversimplification crosses into being incorrect. It's not observation that gives rise to centrifugal force, but describing the motion using a rotating/non-inertial coordinate system. From an inertial coordinate system, there is never a reason to invoke this centrifugal force to explain the motion - Newton's second law and a centripetal force are sufficient to explain the Newton's rotating bucket thought experiment. In Newton's thought experiment, it is actually the need to invoke an ad hoc centrifugal force that tells you the coordinate system is rotating. The text follows what is found in reliable sources such as journal articles and university textbooks. If you can indicate where the text does not appear to follow reliable sources, that would be helpful in refining the article. --FyzixFighter (talk) 23:35, 14 December 2023 (UTC)

Well I'm afraid I'll have to disagree with you. The first paragraph mentions mechanical devices that operate on the basis of centrifugal force. How would these work if centrifugal force is only something that depends on the choice of coordinate frame? Surely centrifugal force has to be caused by inertial motion and not by choice of coordinate frame. 2A00:23CC:4D80:1101:58A2:F0FE:6C9A:FB30 (talk) 10:36, 15 December 2023 (UTC)

I agree with FyzixFighter. I have amended the lead to remove the suggestion that there are mechanical devices that operate on the basis of centrifugal force. Centrifugal force is a fictitious force, and it is lacking in rigour to use this force to attempt to explain the operation of certain rotating machines. Nevertheless there are people who incorporate the words “centrifugal force” into their explanation of operation of these machines.

Centrifugal force is like the luminiferous aether and caloric - scientists now know they don’t exist even though in by-gone days everyone thought they did. Dolphin (t) 12:32, 15 December 2023 (UTC)

In a centrifuge, the material that is rotating with the machine, flies out to the edge because of its tendency to continue in its straight line inertial path. It pushes against the edge of the machine and Archimedes' principle is invoked, segregating the heavier particles from the lighter particles. That's an example of centrifugal force. I don't see this as being an effect that depends on the choice of coordinate frame for analysis. Same principle with a centrifugal clutch or a centrifugal governor. However you might analyse these, there is a force pressing outwards that has a mechanical effect. Are you one hundred percent sure about what you have said above? Think about it. I simply can't agree with you. 2A00:23CC:4D80:1101:B0C8:EC5D:84BA:4D00 (talk) 13:01, 15 December 2023 (UTC)

Thanks for your prompt reply. If you spend some time carefully reading a physics textbook that covers introductory mechanics, and you focus on displacement, velocity and acceleration; and Newton’s laws of motion, we will end up agreeing with each other. When we try to explain some physical phenomenon using our intuition we often fail, showing that intuition is a poor teacher. Dolphin (t) 13:36, 15 December 2023 (UTC)

I don't think that maths needs to come into it at all. And I don't think our intuition is failing us when we observe the phenomenon of centrifugal force having a real physical effect. The non-physics public have usually been aware of centrifugal force since they were children, when they saw somebody swing a bucket of water over their heads and the water not falling out. It seems to me that you have got too distracted by the mathematical analysis, to the extent that you have made yourself believe that centrifugal force as a practical reality is merely a figment of a particular method of mathematical analysis. Before you wrote what you wrote above, I was going to sarcastically suggest that you remove all those references to centrifugal clutches and centrifugal governors etc., just in case the readers might get ideas that conflict with the fictitious narrative which the article seems to be promoting. Anyway, I've said all I can say and so I'll leave you to think about it. 2A00:23CC:4D80:1101:59EA:8F9E:A7A5:D64F (talk) 16:14, 15 December 2023 (UTC)

We don't need to argue maths or intuition - we could, but we've been down that path before and it rarely helps improve the article. We just need to follow reliable sources. Reliable sources indicate that when we are rigorous in our definition of what is a force (eg, something that appears on the left hand side of Newton's second law), the centrifugal force does not appear in inertial frames. When motion is described in rotating frames/coordinate systems, then it is included in the sum of forces if we want to "bootstrap" of Newton's laws to non-inertial frames. If you have reliable sources that say otherwise, or provide additional insight or commentary not currently found in the article, please share them and help us make this article better. --FyzixFighter (talk) 18:09, 15 December 2023 (UTC)

OK, I see what you are saying now. You are saying that centrifugal force doesn't conform to the definition of force as per Newton's laws of motion. And of course, that should be stated in the article. But I've been thinking more about the matter, and I think you are giving undue weight to a scientific definition of force, over the head of the common understanding of the very real phenomenon known as centrifugal force. Look at it this way. A car swerves round a corner at high speed and a passenger gets flung out the back door. We would all agree that this was because of the passenger's tendency to continue in their straight line inertial path. And this tendency caused the passenger to push against the car door, causing the car door to open and the passenger to be thrown out into the road. Now we'll all agree that this tendency was very real. But are we not allowed to call this tendency centrifugal force? What exactly is it that you are claiming is only an illusion in a rotating frame of reference? We can't write off the tendency to be pushed against the door, simply on the grounds that it is only an illusion under a certain kind of mathematical analysis. The effect is very real, and it's now clear to me that this discussion is purely over semantics. It's all about whether or not we are allowed to refer to, what is commonly known as centrifugal force, by its common name. I think we're all agreed that centrifugal force, under the common understanding, arises as a result of inertial motion, and not because of any choice of coordinate frame. But I do see your argument that centrifugal force within the common understanding does not conform with the strictly scientific definition of force as per Newton's laws of motion. I think the common understanding of centrifugal force should come first in the article, followed by the clarification that it is a local term not strictly in line with the definition of force as is used in Newtonian mechanics. I say this, because as the article stands now, it is counter intuitive, giving the impression that what most people see as a real effect with a familiar name, can be made to become an illusion by mathematicians operating in a rotating frame of reference. Those devices listed in the introduction really do operate by centrifugal force under the common understanding. You cannot write that fact off by insisting that it doesn't conform to a strict scientific definition of force. The issue is semantics, not physics. 2A00:23CC:4D80:1101:797D:908D:F9D2:B75A (talk) 20:15, 15 December 2023 (UTC)

And one final comment. The issue of contention lies totally with the fact that a centrifugal force is not a Newtonian force. But its physical effect in a rotating space station for the purpose of simulating weight, is identical to that of the force of gravity. Therefore it's more accurate to state that centrifugal force is a force in a different category of forces than Newtonian forces. It's a bit like that a lion and a tiger are both cats, but a lion isn't a tiger. A Newtonian force and a centrifugal force are both forces, but a centrifugal force is not a Newtonian force. I can't get this idea of writing centrifugal force off completely, as an illusion in a rotating frame, just because it isn't a Newtonian force. In fact, more accurately a centrifugal force is an inertial force, independent of whatever mathematical way we analyse it. 2A00:23CC:4D80:1101:10E3:814:D19C:C3B (talk) 23:03, 15 December 2023 (UTC)

Hence the article we have on this other category of forces, Fictitious force, which you will find is linked in the opening sentence of the article by one of its other names, 'Inertial force'. No changes appear to be needed to the article. MrOllie (talk) 23:15, 15 December 2023 (UTC)

You have written “A car swerves round a corner at high speed and a passenger gets flung out the back door. ... ...” This is a useful example and it is worth examining in further detail.

The car and its occupants are all travelling in a straight line at constant speed so the net force acting on each one is zero. The car then swerves and the passenger is ejected from the car and continues in a straight line at constant speed, at least for a short time. As the passenger is leaving the car a centrifugal force is acting on this unfortunate person. Once clear of the vehicle, the centrifugal force acting on the passenger falls to zero again. You are suggesting that the commencement of the centrifugal force, its magnitude, direction and duration are not determined by the trajectory of the passenger, but by the trajectory of the car. That is not consistent with Newton’s second law. Dolphin (t) 01:37, 16 December 2023 (UTC)

Mr. Ollie. The first sentence in this article confuses the issue. We're agreed that centrifugal force is not a Newtonian force. Therefore we need to remove the bit where it says "in Newtonian mechanics". The next bit where it says that centrifugal force is an inertial force is fine. But then it immediately delves into the issue that I first raised. Just because it is an inertial force doesn't mean that it is an illusion only observed in a rotating frame of reference. It's no illusion that centrifugal force can be used to simulate the weight of gravity in a rotating space station. I thought we had it all sorted when you correctly drew my attention to the fact that centrifugal force is not a Newtonian force. But it seems that you still think it is an illusion, dependent on choice of coordinate frame. This is clearly not the case. 2A00:23CC:4D80:1101:F0EB:BBD8:6848:CEA1 (talk) 23:39, 15 December 2023 (UTC)

The only one who has used the word 'illusion' is you. MrOllie (talk) 00:00, 16 December 2023 (UTC)

Mr. Ollie. It says in the first sentence, "appears to act on all objects when viewed in a rotating frame of reference". I interpret that as stating that it is only an illusion. But we know that it is not an illusion. It may not be a Newtonian force, but it is still a force, and it can have the same physical effect as a Newtonian force, as per the example I gave of weight being caused by rotation in a space station. I suggest that the introduction runs through the following key points,

     ″When an object is forced to rotate in a rotating system, a centrifugal force draws it away from the centre of rotation, due to the tendency of the object to continue along its uniform straight line inertial path. Centrifugal force is therefore an inertial force and not a Newtonian force, as the latter kind is not involved in uniform straight line motion. Centrifugal force is often analysed in a frame of reference that rotates with the rotating system″

In fact, that's about all there is to it. It's not a very extensive topic. 2A00:23CC:4D80:1101:8D8F:9CE:B079:7FFD (talk) 00:28, 16 December 2023 (UTC)

The "Appears to act" version is correct. Your suggestion is incorrect because it leaves out crucial information. If an observer is outside of the rotating system, they will not observe any such force - that is what distinguishes a fictitious force. It only 'appears' when the observer (that is, the frame of reference) is undergoing acceleration (in this case as rotation). MrOllie (talk) 00:42, 16 December 2023 (UTC)

(after ec) As MrOllie points out, that definition is incorrect and not supported by reliable sources. An object does not need to be forced to rotate in a rotating system for the centrifugal force to act on it. In the inertial frame there is no force that is pushing the passenger into the wall of the car or pushing astronauts against the floor in a spinning space station. Our intuition that there is one is due to our observations being in the non-inertial frame.

The centrifugal force that you mention is as real as the apparent force one feels pulling down when going up in an elevator. In the inertial frame the effects in the car, space station, and elevator are due to inertia and require no new force. In my opinion this is evident when we consider an object that is stationary in the inertial frame - when viewed in a rotating frame, the object appears to be moving in a circle and therefore undergoing centripetal acceleration. In the rotating frame, the centripetal acceleration is attributed to a combination of fictitious/inertial forces - the centrifugal force pointed outward and a Coriolis force pointed inward. The centrifugal force in this situation is the same as what arises for the passenger and astronauts, and appears because the frame has a rotational acceleration relative to the inertial frame. This is what reliable sources say. Again if you have reliable sources that say otherwise or clarify the concept, then please share. --FyzixFighter (talk) 00:59, 16 December 2023 (UTC)

Dolphin51, You misrepresented what I said above. I said that when the car swerves, centrifugal force throws the passenger against the door of the car, due to the tendency of the passenger to undergo his uniform straight line inertial path. We were already agreed that this centrifugal force is not a Newtonian force, but it is a force nevertheless. 2A00:23CC:4D80:1101:BDDC:2E1F:8186:E19E (talk) 09:30, 16 December 2023 (UTC)

Mr. Ollie, There is a paragraph in this link about how a centrifugal clutch works. We don't have to be rotating with the clutch in order it observe it working. https://www.lancereal.com/centrifugal-clutch-explained/ And here's another about the centrifugal pump, https://www.northridgepumps.com/article-346_what-is-a-centrifugal-pump You claimed above that we only observe the centrifugal force if we are in a rotating frame. This is obviously not the case. 2A00:23CC:4D80:1101:BDDC:2E1F:8186:E19E (talk) 09:33, 16 December 2023 (UTC)

Fyzixfighter, If an object in a rotating system doesn't rotate with the system, say due to lack of friction for example, then the object will not move outwards. There will be no centrifugal force. You seem to be totally absorbed in the mathematical analysis from the perspective of a rotating frame of reference, to the neglect of the actual concept of centrifugal force itself. Your example of viewing a stationary object from a rotating frame of reference is a totally unnatural example which turns the whole topic upside down. It was like asking how do children on a roundabout see a stationary child on the ground below the roundabout. The stationary child experiences no centrifugal force, while the ones on the roundabout see the stationary child moving in a circle. Meanwhile you are trying to use maths to account for why the child on the ground experiences no centrifugal force, as in, because it is cancelled by another fictitious force. That is totally inverted logic, well over the top. As regards reliable sources, that would be fine if reliable sources all spoke with a single narrative. But they don't. Reliable sources are a morass of confusion telling many different narratives. Some talk about rotating frames and fictitious forces, some talk about Newton's third law, and some think there has to be circular motion. It won't be possible to taper the article to the correct balance of reliable sources until there is first some evidence of comprehension of the topic on the part of the editors. So, are we first going to try and reason it out using natural reasoning, or are we going to use the canard about reliable sources every time a point is made that undermines the current narrative in the article? What about this source here, https://www.irjet.net/archives/V4/i1/IRJET-V4I1185.pdf ? It says in the abstract that the centrifugal governor works by centrifugal force. It doesn't say that it only works if you are rotating with the apparatus. And by the way, your analogy about the elevator was wrong. When an elevator accelerates upwards, the people feel an upward force coming from the elevator floor. No inertial forces are involved, and the floor exerts an active force on the people. But in the rotating space station, centrifugal force pushes the people against the floor. It's the other way around. 2A00:23CC:4D80:1101:BDDC:2E1F:8186:E19E (talk) 09:36, 16 December 2023 (UTC)

We've been down this path multiple times before. The archives are full of lengthy discussions with multiple editors, one in particular (FDT/David Tombe), that led to only marginal improvements in the article and certain editors (eg, FDT/David Tombe) being banned from physics-related articles and discussions. I'm not seeing anything new in this discussion, and in fact it seems to be largely rehashing those previous discussions. As we've fallen into trying to teach each other "correct" physics/semantics, I really don't see any further value in talk page discussion - this isn't a forum or discussion board. Perhaps an RFC or other dispute resolution avenue would be beneficial if you feel that there is a specific improvement needed in the article. --FyzixFighter (talk) 16:19, 16 December 2023 (UTC)

Well, if you've been down this path multiple times before, then maybe it's time to take note of the fact that the lead paragraph contains a ridiculous contradiction. On the one hand it lists mechanical devices that operate on the principle of centrifugal force, while on the other hand it claims that centrifugal force is only an illusion seen by those in a rotating frame of reference. I have explained to you, that you have got yourself absorbed in the mathematical analysis of centrifugal force in a rotating frame, at the expense of the concept itself. Just because it is not a Newtonian force doesn't mean that it is not a force. It still pushes and pulls. I have supplied references above that contradict the view that centrifugal force is only an illusion observed from a rotating frame of reference, and so there's not much more that I can do to help. Whatever, the article as it stands, is a total morass of confusion. By the way, I see reference to another article called "reactive centrifugal force". There is no such thing. It's just inertial centrifugal force pushing or pulling against an obstacle. Was that article, by any chance, started up in order to package away out of sight all scenarios that exposed centrifugal force as a frame-independent force? 2A00:23CC:4D80:1101:DD04:6DDA:A6E1:F358 (talk) 16:55, 16 December 2023 (UTC)

Was that article, by any chance, started up in order to package away out of sight all scenarios that exposed centrifugal force as a frame-independent force? You will find that launching conspiracy theories will not help your arguments. It seems that we are done here. MrOllie (talk) 16:59, 16 December 2023 (UTC)

Well if I am wrong, then why aren't those examples simply included in this article? Why did they have to be sided off to a separate article? 2A00:23CC:4D80:1101:DD04:6DDA:A6E1:F358 (talk) 17:05, 16 December 2023 (UTC)

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