I Don't Ever Mention "Centrifugal Force" to Physicists

[A.T.]

Why do we call an inertial frame one that does not have inertial forces but a non-inertial frame is one that does?

Why is "velocity" relative, but "velocity relative to X" absolute?

 

[Demystifier]

Some of you have seen this already when a similar discussion flared up and I apologize for the repetition. I resisted at first, but it is worth reviving because it encapsulates the controversy well.

View attachment 317957

The wheel acts by centripetal force on Bond. But then, by the 3rd Newton law, Bond acts on wheel by the opposite force. Isn't this opposite force the centrifugal force?

 

[Demystifier]

Why is "velocity" relative, but "velocity relative to X" absolute?

The latter is absolute precisely because it's relative.

 

[jbriggs444]

The wheel acts by centripetal force on Bond. But then, by the 3rd Newton law, Bond acts on wheel by the opposite force. Isn't this opposite force the centrifugal force?

That opposite force is sometimes called the "reactive centrifugal force". It is not, of course, the same as the inertial "centrifugal force" that is most often meant by the phrase.

One can argue that what is important to Mr. Bond is the stresses and associated deformation that he experiences as a result of the applied centripetal force. The essential problem is that this force is unevenly applied. Unlike inertial forces which are normally distributed evenly throughout a body (though see Niven's "Neutron Star"), the centripetal force on Mr. Bond is applied only to his back side.

Edit: In "Neutron Star", our hero, Beowulf Shaeffer pilots a craft build from a General Products hull to investigate a neutron star to which several missions have previously failed. Upon close approach to the star, he experiences a strange force that is able to penetrate the impenetrable hull. The "strange force" turns out to be tidal gravity. Beowulf then extorts compensation from the paranoid Puppeteers who produce the hull because he now deduces one of their secrets -- they evolved on a planet without a moon.

An amusing afterthought by the author:

"Niven writes: "I keep meeting people who have done mathematical treatments of the problem raised in the short story 'Neutron Star' ... Alas and dammit, Shaeffer can't survive. It turns out that his ship leaves the star spinning, and keeps the spin."

Thus we come full circle to a spinning man.

 

[sophiecentaur]

That opposite force is sometimes called the "reactive centrifugal force". It is not, of course, the same as the inertial "centrifugal force" that is most often meant by the phrase.

But if it quacks like a duck . . . . . Those two forces have the same values and would have the same visible effect (wherever you're looking from).
But isn't it all to do with what is implied by the word "outwards"? It is straining to go outwards but, once released it actually goes tangentially (to the outside observer). To Mr Bond, what he releases seems to go away and 'backwards'.
As a kid in school, how could you describe it?

 

[jbriggs444]

But if it quacks like a duck . . . . . Those two forces have the same values and would have the same visible effect (wherever you're looking from).

They do in some cases. Not all. The inertial centrifugal force continues to exist (in the rotating frame) even after the string breaks or the centrifuge explodes or the car hits a patch of black ice. The reactive centrifugal force ceases to exist when the string breaks, etc.

The centrifugal force also exists (in the rotating frame) even though it may be cancelled by a more-than-equal and opposite Coriolis force. In that circumstance, the reactive centrifugal force does not exist. [e.g. an object at rest in the inertial frame as viewed from the rotating frame. It has outward centrifugal force, inward Coriolis force and inward centripetal acceleration. But zero net external interaction forces.

Pick a frame. Then pick the associated inertial force laws. Objects will move as the forces demand.

Kids in school... are taught that there is one right answer to any question. The truth is otherwise.

 

[sophiecentaur]

The inertial centrifugal force continues to exist (in the rotating frame) even after the string breaks

That's because of the apparently curved / zig-zag path seen by Mr. Bond? Sounds very non-Newtonian, though.

 

[jbriggs444]

That's because of the apparently curved / zig-zag path seen by Mr. Bond? Sounds very non-Newtonian, though.

Archimedian spiral, approximately. It is Newtonian -- provided that you ignore the third law. Inertial forces such as centrifugal and Coriolis are not interaction forces. They have no third law partners.

As the cartoon suggests, perform a coordinate system transformation and force-like effects pop out.

 

[sophiecentaur]

Archimedian spiral, approximately. It is Newtonian -- provided that you ignore the third law. Inertial forces such as centrifugal and Coriolis are not interaction forces. They have no third law partners.

As the cartoon suggests, perform a coordinate system transformation and force-like effects pop out.

Well put. And something else to confuse young minds with - just after they learn to distinguish between third law pairs and forces in equilibrium.

 

[vanhees71]

The 3rd law is an approximation anyway ;-)). It's fully substituted by the momentum-conservation law (synmmetry under spatial translations) in special relativity and the necessity of dynamical fields for local interaction laws (there's no interacting-point-particle dynamics in SR anyway).

 

[Omega0]

I've just come across the following line while studying (Young & Freedman) and found it amusing.

It sounds like a dirty family secret we discuss once and then should never mention again

I very well remember that a prof told me the same. "This is not a force!"
Well, to be honest: If it feels phyisically like a force and I could measure it as a force it is force - for me.

 

[Ibix]

If it feels phyisically like a force and I could measure it as a force

You can't - that's kind of the point. You can measure things that (in a rotating frame) you might call a reaction to a centrifugal force, but you cannot measure the centrifugal force itself.

 

[A.T.]

it feels phyisically like a force

It doesn't. When analyzing from a rotating frame, the inertial centrifugal force applies to everything that is not on the frame rotation axis. Even to things that are perfectly inertial and definitely don't "feel" any force. It's just there to make the accelerations in the rotating frame consistent with Newtons 2nd Law, not to explain any deformation or stresses.

 

[Dale]

If it feels phyisically like a force and I could measure it as a force it is force - for me.

As others have said, you cannot feel or measure an inertial force like the centrifugal force. All that you can do is to infer it through the motion of the object wrt some frame given all of the directly measurable real forces.

For example, in a rotating reference frame you do not measure the centrifugal force on a co-rotating object. You measure the real centripetal force, and then because the object is not accelerating you infer that there must exist a centrifugal “inertial” force which balances the real centripetal force.

 

[Omega0]

You can't - that's kind of the point. You can measure things that (in a rotating frame) you might call a reaction to a centrifugal force, but you cannot measure the centrifugal force itself.

I am speaking about local measurements in spacetime. Is it just wording?

Say, you have a cylinder with a quite huge radius, rotating. You are inside and grown up inside and you can't see the other side, no curvature, nothing. You jump and you fall back. You call it, whyever, centrifugal force. In other topologies you may have called it gravitation, which I can measure, but in this world I call it "centrifugal force".

What is so wrong about this picture?

 

[Ibix]

You jump and you fall back. You call it, whyever, centrifugal force.

But that is a mistake. A careful analysis will show that you are moving inertially while not in contact with the cylinder - you move in a straight line.

In other topologies you may have called it gravitation, which I can measure,

Well, gravity is another thing you can't measure. You can measure the force from the floor on your feet (that's what a weighing scale does), but when you are in free fall there is no detectable force. That's a key insight (the equivalence principle) on the road to general relativity.

(Actually in a true gravitational field you will see tidal effects that are measurable, which you won't in free fall inside a spinning cylinder.)

 

[Dale]

Is it just wording?

It is not just wording. It is a matter of experiment. There is no physical experiment you can make to actually measure an inertial force. You can only infer it from the acceleration combined with measurements of all of the real forces.

You jump and you fall back.

I.e. you infer the force from your motion.

You cannot measure it in any other way. It does not produce a reading on an accelerometer or a strain gauge or anything else you can think of. While you are only under the influence of that force all local experiments will be the same as in free fall far from gravity.

 

[Ibix]

I.e. you infer the force from your motion.

Just to expand on that, you can infer from the changing relative motion between you and the floor that there's a force on at least one of you and the floor. And accelerometers attached to the floor will read non-zero while those attached to you read zero. Conclusion: there's a force on the floor and it's accelerating, you are inertial.

The centrifugal force (and other inertial forces) are essentially the terms you have to take from one side of $F=ma$ to the other so that you can say that the floor is not accelerating. That's certainly a useful perspective, but you choosing to juggle terms in the maths doesn't make your sensors behave differently - so centrifugal force is not a thing you can measure.

 

[Omega0]

Oh, okay, shame on me. I really thought that something which is actually called a force could be called a force. I know the laws from mechanics, we have
$$ \vec{F}_z = -m \vec{\omega} \times (\vec{\omega} \times \vec{r})$$
and that this has for example the name "centrifugal force". I mean, it is obvious that you can cancel the "thing" as an observer outside via a simple transformation. A "real force" is one you will get never get rid off, for example in a free falling system in a gravitational field. If you can't find a transformation from your IS to get rid of the "forces" like unusual displacements, they are forces, correct?

 

[Omega0]

You cannot measure it in any other way. It does not produce a reading on an accelerometer or a strain gauge or anything else you can think of. While you are only under the influence of that force all local experiments will be the same as in free fall far from gravity.

Ahhhh I got it, sorry. Absolutely right. Thanks. Maybe I watched too many movies where I thought afterwards that rotation is a nice alternative to gravitation but it is not. So clear. My fault.

 

[vanhees71]

As others have said, you cannot feel or measure an inertial force like the centrifugal force. All that you can do is to infer it through the motion of the object wrt some frame given all of the directly measurable real forces.

For example, in a rotating reference frame you do not measure the centrifugal force on a co-rotating object. You measure the real centripetal force, and then because the object is not accelerating you infer that there must exist a centrifugal “inertial” force which balances the real centripetal force.

As I tried to say before in this thread, in the mathematical derivation of the inertial forces in rotating reference frames (rotating against the class of inertial frames to be clear), the inertial forces belong to the left-hand side of Newton's equation $m \vec{a}=\vec{F}$, i.e., from expressing the components of $\vec{a}$ with respect to the rotating basis in terms of the corresponding position-vector components and its time derivatives:
$$\vec{a}' = \mathrm{D}_t^2 \vec{x}' = \ddot{\vec{x}}' + 2 \vec{\omega}' \times \dot{\vec{x}} + \vec{\omega}' \times (\vec{\omega}' \times \vec{x}') + \dot{\vec{\omega}}' \times \dot{\vec{x}}'.$$
Here $\vec{x}'$ etc. are the components of vectors wrt. the rotating basis, and dots denots usual time derivatives, while $\mathrm{D}_t$ is the "covariant time derivative",
$$\mathrm{D}_t \vec{V}'=\dot{\vec{V}}' + \vec{\omega}' \times \vec{V}',$$
and $\vec{\omega}'$ are the components with respect to the rotating basis of the momentary angular velocity of the rotating basis wrt. an arbitrary inertial basis.

 

[Dale]

Maybe I watched too many movies where I thought afterwards that rotation is a nice alternative to gravitation but it is not.

Actually, locally the centrifugal force is a nice alternative to the force of gravity. Einstein’s equivalence principle, his happiest thought, is that locally gravity is equivalent to an inertial force. It is only over sufficiently large distances and times that the differences between gravity and inertial forces becomes apparent.

 

[waross]

While we're at it, let's swap the sign on the electron charge so electron flow matches conventional current!

To late. That has been done. More than once.
I'm so old that I have seen electricity go three ways.
In high school I was taught that electricity flowed from positive to negative.
Later in trade school, I was taught that electricity was a movement of electrons which moved from negative to positive.
Some years later I went back to trade school as an instructor and electricity was now again flowing from positive to negative.
I heard speculation that too many text books would have to be rewritten if electricity was allowed to remain flowing from negative to positive.

 

[sophiecentaur]

To late. That has been done. More than once.

Electric current has always been the flow of positive charge. As it happens. in most conductors we deal with, the charge carriers are negatively charged electrons.
Your instructors may have thought they were helping you but all they succeeded in doing was clearly to confuse you.

 

[Dale]

I was taught that electricity was a movement of electrons which moved from negative to positive

It always bugs me when teachers in introductory EM classes focus on the movement of electrons or use the term “conventional current”. It is a complete waste of time and effort for both teachers and students.

 

[sophiecentaur]

It always bugs me when teachers in introductory EM classes focus on the movement of electrons or use the term “conventional current”. It is a complete waste of time and effort for both teachers and students.

I got my introduction to Physics before 'new teaching' came along. At a good middle of the road school, I was told that 'Electric Current' goes from + to - and, when we asked about electrons, we were told 'just wait'. A bit later it all made sense and there were no contradictions or confusions.

 

[Dale]

I was told that 'Electric Current' goes from + to - and, when we asked about electrons, we were told 'just wait'. A bit later it all made sense and there were no contradictions or confusions.

Exactly, it is better to postpone that topic until the foundation is ready. Electrons don’t need to be discussed in introductory circuits or EM classes*. They are needed in chemistry, solid state physics, and quantum mechanics.

* The only major exception is the Hall effect, but that usually isn’t covered at all or is covered relatively late.

 

[sophiecentaur]

* The only major exception is the Hall effect, but that usually isn’t covered at all or is covered relatively late.

Even in the case of Hall effect, the charge carriers can be positive or negative in semiconductors.

 

[hutchphd]

Electrons don’t need to be discussed in introductory circuits or EM classes*

I believe there are aspects of tubes that made it more important to identify the carriers than it does now. Cathode rays no longer abound ion our living rooms !

 

[Dale]

Even in the case of Hall effect, the charge carriers can be positive or negative in semiconductors.

Yes, which is another reason not to fixate on electrons too early. There are currents of positive charge carriers

 

[sophiecentaur]

Yes, which is another reason not to fixate on electrons too early.

And the same is true of the dreaded photons..

 

[Vanadium 50]

tubes

What are these "tubes" of which you speak?

 

[hutchphd]

Small particle accelerators purportedly used by ancient civilizations in their communications devices. (Evidence for Alien intervention in early technology)

 

[kuruman]

Exactly, it is better to postpone that topic until the foundation is ready. Electrons don’t need to be discussed in introductory circuits or EM classes*. They are needed in chemistry, solid state physics, and quantum mechanics.

* The only major exception is the Hall effect, but that usually isn’t covered at all or is covered relatively late.

What about conductors? The idea that they contain charges free to move about in response to external electric fields is essential in understanding electrostatics and Lenz's law. Of course we can pretend that these charges are positive but then a smart student would note that only nuclei contain positive charges and they are certainly not free to move. You can't win this battle.

 

[Vanadium 50]

Small particle accelerators purportedly used by ancient civilizations in their communications devices

Preposterous! Next you'll be telling me that in case of suspected failure they had then checked out at a pharmacy!

 

[anorlunda]

What about conductors? The idea that they contain charges free to move about in response to external electric fields is essential in understanding electrostatics and Lenz's law.

It's a matter of learning to crawl before you walk. It is very possible to learn a lot of useful things about circuits and circuit analysis without acknowledging fields or charges.

The assumptions in circuit analysis include "no fields outside of conductors" and "no accumulation of charges at nodes". Things like inductors and capacitors are just components with specific behaviors; it's not necessary to learn about their physics in the first course.

Electrostatics and dynamics and fields can come in a later course.
Since Maxwell's equations require more math, it also makes sense to save the second course until the prerequisite math is taught.

 

[Dale]

What about conductors? The idea that they contain charges free to move about in response to external electric fields is essential in understanding electrostatics and Lenz's law.

A conductor is defined by Ohm’s law. No need to discuss electrons. Particularly since not all conductors have mobile electrons.

a smart student would note that only nuclei contain positive charges and they are certainly not free to move. You can't win this battle.

I absolutely can win. I would tell the students at the beginning that they should forget about electrons until they are ready for quantum mechanics. Any student asking about electrons would then be given an assignment on what electrons actually are in QED. After they completed that they would be allowed to ask about electrons during office hours.

 

[kuruman]

A conductor is defined by Ohm’s law. No need to discuss electrons. Particularly since not all conductors have mobile electrons.

Given Ohm's law, how would you explain charging by induction?

 

[Dale]

Given Ohm's law, how would you explain charging by induction?

I wouldn’t. I would use Faraday’s law instead.

 

[kuruman]

I wouldn’t. I would use Faraday’s law instead.

Sorry, I meant this kind of charging by induction.

Sorry,

 

[Dale]

Sorry, I meant this kind of charging by induction.

View attachment 321483
Sorry,

What do you think would be the problem? The only difference in how I would teach it would be in figure (b). I would show current going to ground. That would in fact make it easier to teach.

Electrostatic induction works the same regardless of the sign of the charge carriers. Do you think it is necessary for the grounded conductor to be an electrical wire? Couldn’t it just as well be the ocean or some other grounded electrolyte with positive charge carriers? For that matter the ball could be an electrolyte also.

 

[kuruman]

A conductor is defined by Ohm’s law. No need to discuss electrons. Particularly since not all conductors have mobile electrons.

I did not exactly understand what you meant. I took the above to mean that there is no need to discuss any kind of charge carriers free to move inside a conductor. I see now by your statement

The only difference in how I would teach it would be in figure (b). I would show current going to ground.

that you assert the existence free positive charges inside the conductor. More precisely these would be absences of negative charge (dare I say holes?) which of course should also not be mentioned to students. I'm OK with that. However, how we got to this point considering the title of this thread is a source of wonderment.

 

[sophiecentaur]

but then a smart student would note

A really smart student would appreciate that there is more to the subject than the water analogy would suggest. 'Smart' would imply some ability with Maths and an awareness that 'a physical interpretation' is a false friend. The teacher has responsibility here.

A conductor is defined by Ohm’s law.

Hmmm. 'Ohm's Law' describes how metals behave. I know I'm a voice in the wilderness but the expression R=V/I is only a 'law' when a system behaves linearly; otherwise it is a definition of a handy quantity that is often constant over a range of conditions and which we refer to as Resistance. (Do we call v=s/t the velocity law?)

 

[vanhees71]

While we're at it, let's swap the sign on the electron charge so electron flow matches conventional current!

The most confusing concept is to introduce "conventional current" instead of simply using current density, which is a vector with a magnitude and direction given by the flow of the particles making up the "fluid of charged matter": $\vec{j}=q n \vec{v}$, where $q$ is the charge of the particles ($-e$ for electrons), $n$ the particle-number density, and $\vec{v}$ the fluid-velocity field. Then there's no confusion about the direction of the flow of electric charge and no need for fictitious "conventional currents".

A current is more complicated then current densities anyway, because the sign is not only determined by the flow of the charged medium and the sign of the charges of the particles but also by the arbitrary choice of direction of surface-normal elements of the surface you integrate over to get the current,
$$I=\int_{A} \mathrm{d}^2 \vec{f} \cdot \vec{j}.$$

 

[sophiecentaur]

The most confusing concept is to introduce "conventional current" instead of simply using current density, which is a vector with a magnitude and direction

Problem is that kids minds have already been polluted long before they can grasp vectors or current density. The only safe way is to frown on (you can't 'forbid' these days) using electrons until they are capable of dealing with this stuff.

 

[A.T.]

The only safe way is to frown on (you can't 'forbid' these days) using electrons until they are capable of dealing with this stuff.

"You want electrons? You can't handle the electrons!"

 

[Dale]

However, how we got to this point considering the title of this thread is a source of wonderment.

Yes, we are rather far off topic at this point. But nobody has complained yet so “no harm no foul”

 

[Dale]

'Ohm's Law' describes how metals behave.

Ohm’s law describes how conductors behave. Metals are conductors, but so are electrolytes. I understand your objection to calling it a law. To me that is just a historical accident.

 

[vanhees71]

Problem is that kids minds have already been polluted long before they can grasp vectors or current density. The only safe way is to frown on (you can't 'forbid' these days) using electrons until they are capable of dealing with this stuff.

Hm, but with the fluid picture of electric currents everything gets more transparent. Of course, point particles in classical electrodynamics should be avoided, but fluids are fine and very intuitive.

What I found most confusing was the use of the integral formulation of Maxwell's equations, which seems to be still the standard didactic approach in highschool even today more than 30 years later. For me reading the Feynman lectures which finally introduced me to the local form, was a revelation. Particularly all these sign issues become much more simple. You just have to learn how to orient the boundaries of volumes (surfaces) relative to these volumes (boundary-surface-normal vectors out of the volume) and surfaces (boundary path oriented relative to the sufrace-normal vectors according to the right-hand rule), i.e., as in the standard use for the Gauss and Stokes integral theorems.

 

[anorlunda]

but the expression R=V/I is only a 'law' when a system behaves linearly;

But it is also very useful for piecewise linear analysis in nonlinear regions. When I say "it" I mean not just Ohm's law but KVL, KCL, and all the circuit analysis techniques.

Consider numerical solutions to circuit differential equations. Our main task is to calculate the differential changes in state variables, given the existing states as initial conditions. We can almost always calculate those with the linear methods despite nonlinearities in the components.