What exactly is centrifugal force

[sophiecentaur]

I have to strongly disagree. It is not reactive centrifugal force that will cause the section to move farther away from the centre. It is the fictitious centrifugal force that would cause that (ie. it is inertia - the absence of centripetal force). The reactive centrifugal force disappears immediately as soon as the bolts are cut. This is exactly why the term "reactive centrifugal force" should not be used. It gets confused with the fictitious centrifugal force.

AM

But the other astronaut (sitting in the frame of the wheel) will see the departing astronaut accelerating, initially (during the first 90 degrees of motion, at least) and due to the geometry of the situation. Would he not conclude that there is a force still operating? This perceived force will also be making the departed astronaut perform a spiral outward path - so it would (might) not just be a centrifugal force that he would need in order to explain the guy's path.

 

[stevendaryl]

Give an example of how something follows from the fact that you call them "forces".

Of course, it doesn't matter what you call them, but the point is that Newton's laws relate motion of one object to vector quantities produced by other objects:

$m \frac{\stackrel{\rightarrow}{dU}}{dt} = \stackrel{\rightarrow}{F}$

The left-hand side is a fact about the motion of the object, and the right-hand side is about the external situation affecting that motion. In terms of coordinates:

$(\frac{\stackrel{\rightarrow}{dU}}{dt})^i = \frac{dU^i}{dt} +$ sum over $j, k$ of $\Gamma^i_{jk} U^j U^k$

where $\Gamma^i_{jk}$ are the so-called "connection coefficients", which are due to using nonconstant basis vectors. So the full equations of motion, in terms of components, are:

$m(\frac{dU^i}{dt} +$ sum over $j, k$ of $\Gamma^i_{jk} U^j U^k) = F^i$

What the idea of "fictitious forces" amounts to is moving the extra terms from the left side (where they describe motion) to the right side (where they are treated as forces):

$m \frac{dU^i}{dt} = F^i + F_{inertial}^i$

where
$F_{inertial}^i = - m$ sum over $j, k$ of $\Gamma^i_{jk} U^j U^k$

What difference does it make whether you group it on the left side, or the right side? Well, for one thing, when it comes to figuring out the reaction forces (Newton's third law), only the $F^i$ term is relevant. There are no reaction forces to $F_{inertial}^i$. For another, since real forces are vectors, the components transform in a standard way under a coordinate change: If you change coordinates from $x^i$ to $y^b$, then

$F^b =$ sum over $i$ of $\dfrac{\partial y^b}{\partial x^i} F^i$

"Inertial forces" DON'T transform that way.

So sure, you can group whatever terms together you want, and call them whatever you want to call them, but when it comes to reasoning about the physics, you have to separate out the "real" forces from the "inertial" forces. You're basically doing extra steps that have to be undone later.

 

[stevendaryl]

Haha
I suppose I have to take your point because my suggestion is not falsifiable. But I think that the inverse, - i.e. that Science definitely can establish 'real truth'- probably is falsifiable.

I tend not to talk about truth, one way or the other. I prefer to discuss the ideas without worrying too much about whether they are truth, or something in our heads, or what.

 

[dextercioby]

"Inertial forces" as you (stevendaryl in post #78) mention are a step forward from Newton's postulates (which always have the <with respect to an inertial reference frame> text in them) to Einstein's General Relativity, parallel in a way to the step in which you replace Newton's postulates to Einstein's ones in Special Relativity.

 

[sophiecentaur]

I tend not to talk about truth, one way or the other. I prefer to discuss the ideas without worrying too much about whether they are truth, or something in our heads, or what.

Then I guess you are not far from being a Real Scientist.

 

[Dale]

The claim that nothing matters other than quantitative predictions is itself a philosophical claim. It's funny that the people who bring up "that's just philosophy" as an argument are the ones who actually end up making the strongest philosophical claims.

I don't think it is a philosophical claim, I think it is a semantic claim. I.e. "physics" is defined as X, Y is not X, therefore Y is not "physics".

 

[stevendaryl]

I don't think it is a philosophical claim, I think it is a semantic claim. I.e. "physics" is defined as X, Y is not X, therefore Y is not "physics".

Okay, but who gets to define what the word means? It seems to me that the meaning is provided by watching what physicists actually do, rather than how they would answer question "What is physics?"

 

[Dale]

A reactive force is a response to acceleration of an object wrt inertial frame.

No, the reactive force is an equal and opposite reaction to the other force in a 3rd law pair. This is Newton's 3rd law, which seems to confuse people in rotating frames for some reason. It has nothing to do with acceleration of a specific object since the acceleration of the interacting objects can be different and the acceleration depends on the net force rather than the individual forces.

In an inertial frame, once the floor is cut, the astronaut and the floor cease to accelerate, so there is no reactive centrifugal force.

Sorry, I guess I didn't my proposed scenario clearly. I specified that the bolts were "suddenly" cut for a very important reason. As the astronaut is standing on the floor the floor is under stress with centripetal forces from the bolts and a centrifugal reaction force from the astronaut. The centripetal force is greater than the centrifugal reaction force so there is a net acceleration towards the center.

When the bolts are suddenly cut the stress is relieved from the outside of the section of floor, but the inner part of the floor (where the astronaut is standing) is still under stress. This sets up a shear wave where the floor material transitions from stress to stress-free. During the time between when the bolts are suddenly cut and when that shear wave reaches the feet of the astronaut the centrifugal reaction force still exists, the feet and floor are still in contact, and the floor is accelerating in a direction away from the center. It may help to think of the floor as being made of a stretchy rubber material.

The centrifugal force is every bit as "centrifugal" as the centripetal force is "centripetal". The centrifugal force points away from the center, the centripetal points towards the center. If either is unbalanced then it will result in acceleration in the corresponding direction. If there are other forces involved then the actual acceleration depends on the net force, per Newton's 2nd law.

In a rotating frame

I intended to discuss the reactive centrifugal force only from the perspective of the inertial frame in order to avoid any possible mix-up with the fictitious (inertial) centrifugal force in the rotating frame.

 

[Dale]

The reactive centrifugal force disappears immediately as soon as the bolts are cut.

Hi Andrew Mason, obviously my description was poor since rcgldr had exactly the same response. Please see my response to him in the post above.

 

[Dale]

Okay, but who gets to define what the word means?

Physicists, in particular, the subset of physicists who write physics textbooks. (Maybe we can include Webster and other dictionary writers too)

It seems to me that the meaning is provided by watching what physicists actually do, rather than how they would answer question "What is physics?"

That would be true if physicists did nothing besides physics. However, since physicists do other things besides physics, the definition must come from the answer to the question you posed. That way you can distinguishing between when they are doing physics and when they are doing things that are not physics.

 

[stevendaryl]

That would be true if physicists did nothing besides physics.

Granted. Here's an analogy: sports. Athletes are people who play sports. Of course, an athlete does things besides play sports, but I don't think that an athlete is any better at defining what a "sport" is than anyone else. They can describe what they do when they play sports. I don't think that physicists have any more insight into what "physics" is than an athlete does about what "sports" are.

Anyway, when Einstein, or Newton, or Schrodinger, or just about any other physicist was engaged in doing physics, it certainly wasn't coming up with formulas that make predictions. They were engaged in the struggle to understand the world. That activity is a big part, I would say the center, of what I consider to be physics.

 

[A.T.]

Of course, it doesn't matter what you call them...

So it doesn't matter if you call certain terms "forces" or not. After all it doesn't change the quantitative result of the calculations. That is my point.

 

[stevendaryl]

So it doesn't matter if you call certain terms "forces" or not. After all it doesn't change the quantitative result of the calculations. That is my point.

My point was that it doesn't make any difference what you call things, but that for reasoning, it gets in the way to lump things together that are different sorts of objects.

 

[A.T.]

This is exactly why the term "reactive centrifugal force" should not be used. It gets confused with the fictitious centrifugal force.

I don't see how you can confuse the two. One is an interaction force that exists in every frame, the other is an inertial force that exist only in rotating frames. The diferences are listed in the table here:
http://en.wikipedia.org/wiki/Reactive_centrifugal_force#Relation_to_inertial_centrifugal_force

Calling it "centripetal" as you suggest, despite the fact that it points away from the center, that would be confusing.

 

[sophiecentaur]

Anyway, when Einstein, or Newton, or Schrodinger, or just about any other physicist was engaged in doing physics, it certainly wasn't coming up with formulas that make predictions. They were engaged in the struggle to understand the world. That activity is a big part, I would say the center, of what I consider to be physics.

That assumes everyone has your view of things. I very much doubt that they were as naive as to think they were actually near a conclusion. You cannot have any knowledge of their motives but you must know that anyone who breaks ground in any of this (since the concept of God given laws has ceased to be taken for granted, at least) can only hope to improve on existing scientific models. Models are not 'truth'; they are statements that can be shown to predict the outcomes of certain experiments.
Your three example Scientists were as fallible and human as the next man in many respects and may well have believed at times that the truth is there but they would have been only too aware that it was their models that were the test of their achievements

 

[Dale]

I don't think that an athlete is any better at defining what a "sport" is than anyone else

I don't know the athletic literature very well, but whoever would write a mainstream textbook on sport would be the one who gives the authoritative definition of the word "sport". (or Webster et al.)

what I consider to be physics.

The problem is that if you define "physics" and I define "physics" and we don't agree to use some common definition that we both consider authoritative then we cannot easily communicate since we are using the same symbol with different meanings. That is why we rely on authoratitive sources for definitions of terms, not just each individual's whim. An individual who refuses to use standard definitions and insists on using their own causes all sorts of communication problems.

In any case, we are straying from my main point, which was that a "that's just philosophy" statement is a semantic statement, not a philosophical statement. I wasn't attesting to the accuracy of A.T.'s statement, and I won't debate the merits of different definitions. Semantic arguments are boring because they are always arguments from authority and someone can always refuse to recognize your chosen authority and substitute their own preferred authority (usually themselves).

 

[A.T.]

for reasoning, it gets in the way

Whatever that means...

 

[stevendaryl]

Whatever that means...

I gave plenty of examples of what I meant. If you didn't understand what I meant after that, you could ask follow-up questions.

 

[stevendaryl]

The problem is that if you define "physics" and I define "physics" and we don't agree to use some common definition that we both consider authoritative then we cannot easily communicate since we are using the same symbol with different meanings.

I don't think that's true. The fact that you and I might disagree about specific cases whether something is or is not "physics" or a "sport" or "music" does not get in the way of communication if there is substantial overlap.

 

[stevendaryl]

That assumes everyone has your view of things.

No, it doesn't. If people have different points of view, that's fine--there's room for lots of different kinds of physics. The sort of physics that is done by cosmologists, or loop quantum gravity people, or those working in the foundations of quantum mechanics is very different from the kind of physics that is done in solid state physics or biophysics. There is room for all.

 

[stevendaryl]

I very much doubt that they were as naive as to think they were actually near a conclusion. You cannot have any knowledge of their motives but you must know that anyone who breaks ground in any of this (since the concept of God given laws has ceased to be taken for granted, at least) can only hope to improve on existing scientific models. Models are not 'truth'; they are statements that can be shown to predict the outcomes of certain experiments.

I'm not sure what the relevance of this is to what I've said. Claiming that the goal of physics is understanding doesn't imply how close our current understanding is to the truth.

 

[A.T.]

I gave plenty of examples of what I meant. If you didn't understand what I meant after that, you could ask follow-up questions.

I understand that it is not relevant for the predictions.

Anyway, when Einstein, or Newton, or Schrodinger, or just about any other physicist was engaged in doing physics, it certainly wasn't coming up with formulas that make predictions.

Yes it was.

They were engaged in the struggle to understand the world.

Define "understand the world".

 

[Dale]

I don't think that's true. The fact that you and I might disagree about specific cases whether something is or is not "physics" or a "sport" or "music" does not get in the way of communication if there is substantial overlap.

The current discussion between you and AT seems to contradict this claim of yours. There is surely substantial overlap, and yet the remaining differences in the definitions are getting in the way of communication.

 

[Studiot]

How does any of this help or encourage the OP?

 

[Dale]

I think that there is no such thing as centrifugal force .

Am I right ? is this force fictitious ?

A centrifugal force is a fictitious force. That doesn't mean that there is no such thing as a centrifugal force.

 

[Andrew Mason]

But the other astronaut (sitting in the frame of the wheel) will see the departing astronaut accelerating, initially (during the first 90 degrees of motion, at least) and due to the geometry of the situation.

He would think the departing astronaut was accelerating only if he forgot that he was in a non-inertial (rotating) reference frame. To an inertial observer, the departing astronaut is simply continuing the motion he had when the bolts were cut.

Would he not conclude that there is a force still operating? This perceived force will also be making the departed astronaut perform a spiral outward path - so it would (might) not just be a centrifugal force that he would need in order to explain the guy's path.

I think the departing astronaut would prescribe a cycloidal outward spiral in the non-inertial reference frame of the astronaut on the rotating space station.

AM

 

[stevendaryl]

The current discussion between you and AT seems to contradict this claim of yours. There is surely substantial overlap, and yet the remaining differences in the definitions are getting in the way of communication.

I don't think that's a correct diagnosis.

 

[stevendaryl]

I understand that it is not relevant for the predictions.

Indirectly, it is. Getting straight the difference between connection coefficients and forces is an important step in understanding physics in curved spacetime. So if you want to go on to advanced topics, then understanding this is important.

Define "understand the world".

Come on. You know what the word "understand" means.

The idea that physics is exclusively about making quantitative predictions is just wrong.

We can go through many examples. Before Einstein developed Special Relativity, the equations of Special Relativity were already developed. That's why they're called the "Lorentz transformations" rather than the "Einstein transformations". Einstein's new theory didn't change the equations, it provided a new way of understanding those equations--a new way of deriving them. In the long run, this was a tremendous advance, making most of the physics since then possible. But the motivation wasn't new predictions, it was to understand things that people already knew about, but didn't understand.

Similarly for quantum mechanics. The Balmer series already gave a good quantitative prediction for the energy levels of hydrogen. It was just a guess. The steps that Bohr took, which opened up further developments by Schrodinger and Heisenberg, was an attempt to derive those energy levels from some kind of first principles. Of course, quantum mechanics ended up having enormous consequences and great predictive value. But the initial steps were an attempt to understand already existing information.

When Feynman developed his path integral formulation of quantum mechanics, at first it was simply a reworking of the Schrodinger--it was just a different way of understanding how to derive quantum amplitudes. It turns out that the ideas developed by Feynman in working on his path integral formulation had applicability beyond quantum mechanics, and could be applied in quantum electrodynamics and elsewhere.

The idea that there is nothing to physics other than quantitative predictions is a philosophical position, and in my opinion, it's very BAD philosophy. The attempt to understand data and formalisms has always been the most direct route to coming up with new theories that do make quantitative predictions. So even if, at the end, all you care about is quantitative predictions, trying to understand the mathematics, the data, and the models is a much more effective way to get to that point.

 

[Dale]

The idea that there is nothing to physics other than quantitative predictions is a philosophical position, and in my opinion, it's very BAD philosophy.

No, it is a definition of the term "physics", and in your opinion it is a very BAD definition.

 

[stevendaryl]

Some other examples: General Relativity. The motivation was to make a theory of gravity that was compatible with relativity. There was also a philosophical goal, which was to generalize the principle of relativity so that all coordinate systems were treated equivalently, not just inertial coordinate systems. The goal wasn't to make new predictions about bending of starlight, or whatever. The goal was reconciling two theories: Special Relativity and gravity. It certainly turned out that the project produced new predictions, and if hadn't produced new predictions, it would been considered a failure, or at best an interesting exercise. However, the goal of making predictions really didn't drive the development of the theory at all. Einstein was trying to understand the nature of gravity in a way that made sense in light of relativity.

I just think that the idea that there is nothing to physics other than quantitative predictions is just a severely claustrophic notion of what science is about. It is true that at the end of the day, your ideas have to have empirical consequences, but a lot of the development of a new theory is about clarifying concepts.

 

[D H]

TIME OUT! Thread temporarily closed.

For the last few pages you all have been bickering over the "reactive centrifugal force", which is (1) quite distinct from the "(fictitious) centrifugal force", (2) a concept of limited applicability, (3) something physicists don't quite like.

I'm splitting this off-topic discussion of the reactive centrifugal force into a separate thread. This will take some time ...

 

[D H]

The off-topic discussion on the reactive centrifugal force has been moved to [thread=668756]this new thread[/thread]. Please limit the discussion in this thread to the fictitious centrifugal force.

Thread reopened.

 

[D H]

Surely, the last step isn't doing anything for you.

This is just an opinion, not a fact. Quite a few people find the concept of inertial forces (or fictitious forces) quite useful.

They are different from other forces you're likely to encounter, because they don't depend on the substance an object is made of, and they don't have an equal and opposite reactive force.

That's why they're called inertial forces. They don't have third law counterpart. So?

The real confusion that is at the heart of discussions of "inertial forces" is the assumption that, if $\stackrel{\rightarrow}{U}$ is a vector (say, a velocity vector) with components $U^i$, then $\frac{\stackrel{\rightarrow}{dU}}{dt}$ must be a vector with components $\frac{dU^i}{dt}$. That's just bad mathematics.

You have a non-standard concept of what constitutes a vector. There's not one thing in the mathematical definition of a vector that says how they transform. Inertial forces aren't covariant or contravariant tensors, but tensors are something different from vectors. Don't confuse the two concepts.

 

[stevendaryl]

This is just an opinion, not a fact. Quite a few people find the concept of inertial forces (or fictitious forces) quite useful.

Well, give an example of how it might be useful.

You have a non-standard concept of what constitutes a vector.

I don't think that's true. What do you think a vector is?

There's not one thing in the mathematical definition of a vector that says how they transform. Inertial forces aren't covariant or contravariant tensors, but tensors are something different from vectors. Don't confuse the two concepts.

I think you're confused about what vectors and tensors are, yourself. The usual notion of a tensor includes vectors as a special case.

The issue, as I said, is what does it mean to take the derivative of a vector quantity. If $\vec{V(t)}$ is a vector quantity, such as velocity, then what is the meaning of $\frac{\vec{dV}}{dt}$?

However we define this derivative, we want it to obey the usual rules of calculus, such as the chain rule and the product rule. So if we decompose a vector $\vec{V}$ as a linear combination of basis vectors $\vec{e_\mu}$, we have:

$\vec{V} = \sum_\mu V^\mu \vec{e_\mu}$
$\dfrac{\vec{dV}}{dt} = \sum_\mu (\dfrac{dV^\mu}{dt} \vec{e_\mu} + V^\mu \dfrac{\vec{de_\mu}}{dt})$

So if we expect derivatives to work in their normal way, we can't blithely assume that
$(\dfrac{\vec{dV}}{dt})^\mu =\dfrac{dV^\mu}{dt}$ unless we assume that
$\dfrac{\vec{de_\mu}}{dt} = 0$

But if we assume that the basis vectors for Cartesian coordinates, $\vec{e_x}, \vec{e_y}$ are all constant, obeying $\dfrac{\vec{de_x}}{dt} = \dfrac{\vec{de_y}}{dt} =0$, then when we switch to polar coordinates $\vec{e_r}, \vec{e_\theta}$, those basis vectors CANNOT be constant, because, for instance:

$\vec{e_r} = cos(\theta) \vec{e_x} + sin(\theta) \vec{e_y}$

$\dfrac{\vec{de_r}}{dt} = -sin(\theta) \dfrac{d\theta}{dt} \vec{e_x} + cos(\theta) \dfrac{d \theta}{dt} \vec{e_y}$

So when using polar coordinates, there are additional terms in computing the time derivative of a vector $\vec{V}$ arising from $\dfrac{\vec{de_r}}{dt}$ and $\dfrac{\vec{de_\theta}}{dt}$. These additional terms are not forces, they are just derivatives of basis vectors.

 

[Dale]

Well, give an example of how it might be useful.

E.g. to design a turbine blade that will not break during operation.

Non-inertial coordinate systems are also often useful in solving problems where the equations become numerically unstable in inertial coordinates. E.g. in calculating orbits in multi-body gravitational fields.