Don't Ever Mention "Centrifugal Force" to Physicists

[anorlunda]

@sophiecentaur , you may be surprised that I agree with you, but only partially. See my Insights article:

Learn Why Ohm’s Law Is Not a Law

Reference: https://www.physicsforums.com/insights/ohms-law-mellow/

 

[waross]

Ohm's Law.
No just a good idea;
It's the law!

 

[waross]

Centrifugal force,
Centripetal force.
Centripedal force. A force that encourages walking.
Nancy "Boots" Sinatra was influenced by this force.

 

[waross]

The best reason to avoid the use of the word "centrifugal" is that use leads to endless futile discussions such as this one.
May I suggest futile?

 

[vanhees71]

One has to understand that the "constitutive laws" we usually learn in the introductory electrodynamics lecture are not fundamental laws but are derived from the fundamental laws in terms of "many-body physics". The best theory we have is, of course, quantum theory, and you can derive the constitutive laws indeed by using quantum-many body theory. For standard household matter (aka electrical engineering purposes) non-relativistic many-body theory will do, and at the ususal linear level what you use is linear-response theory as the most simple approach, i.e., you consider external electromagnetic fields which are much smaller than the intrinsic electromagnetic fields holding the electrons, atomic nuclei/molecules together in your macroscopic piece of matter.

For a piece of metal a simple but not too bad model is the "Jellium Model", i.e., you consider the (conduction) electrons as a gas of negatively charged particles moving in a continuous positive-charge distribution. Astonishingly it's not too bad to even simplify this to treat them as an ideal highly degenerated Fermi gas, and then you can as what happens when I apply an electromagnetic field to the metal. Then you can simplify everything to a magnetostatic or quasistationary approximation, and you'll get out "Ohm's Law",
$$\vec{j}=\sigma \vec{E},$$
where ##\sigma## is a typical transport coefficient, which depends on the material (which kind of metal) and the temperature, i.e., you have an effective macroscopic model, derived from the underlying fundamental microscopic physics. That's what condensed-matter theorists do with great success, and the practical use of such effective models like "Ohm's Law" needs not to be emphasized.

For a very nice presentation of "macroscopic electrodynamics", see Landau&Lifhsitz vol. 8. There they often even use classical models, which are also not too bad. More emphasis on the quantum approach is given in vols. 9 and 10.

 

[losbellos]

That is not correct. The force required to keep an object on a circular path must be directed towards the center of the circle. The centrifugal force, as the name suggests, is directed away from the center.

So they oppose and have the exactly the same values... So it is correct! That in vector it is pointed inwards or outwards that something else, you havent seen that in the equation did you??

 

[kuruman]

I agree with you abut Ohm's, law that it's just a ratio. It probably started at its inception as general rule for different materials and retained its name for historical reasons as more and more "non-Ohmic" materials were discovered.

And, btw, KVL and KCL are different cases. They are Identities, rather than Laws

Here I beg to differ. I would not call them identities but consequences of equations that are based on empirical evidence, laws if you wish.

KVL is a direct consequence of Faraday's "law" in the static case as expressed by Maxwell's equation for the curl of the electric field. It is essentially an energy conservation equation because the electric field is conservative. Formally, starting with Faraday's law when there is no time-varying magnetic field, $$ \mathbf{\nabla}\times\mathbf{E}=0\implies \oint \mathbf{E}\cdot d\mathbf{l}=0\implies -\sum_i\Delta V_i=0.$$ KCL is a result of the "law" of charge conservation which is written as $$\mathbf{\nabla} \cdot \mathbf{J}+\frac{\partial \rho}{\partial t}=0$$ Construct a closed Gaussian surface enclosing any part of the circuit, multiply by a volume element ##dV## and integrate over the volume to get $$\int_V \mathbf{\nabla} \cdot \mathbf{J}~dV+\int_V \frac{\partial \rho}{\partial t}~dV=0.$$ Use the divergence theorem to transform the first volume integral into a surface integral and rearrange to get $$\int_S \mathbf{J}\cdot~\mathbf{\hat n}~dA=- \frac{\partial}{\partial t}\int_V\rho~ dV.$$The left hand side represents the total current coming out of the surface of volume ##V## because ##\mathbf{\hat n}## is the outward normal. If there are ##N## locations on the surface where current comes out, the left hand side can be written as $$I_{\rm{out}}=\sum_{i=1}^{N}\int_{S_i} \mathbf{J_i}\cdot~\mathbf{\hat n}~dA=\sum_i^N I_{\rm{out,i}}$$ The right hand side is the rate of change of the total charge enclosed within the volume. Thus, we write $$\sum_i^N I_{\rm{out,i}}=- \frac{dq_{\rm{encl.}}}{dt}.$$ That's the general form of KCL. We note that

1. When as much current goes into the volume as comes out, the derivative on the RHS is zero and ##\sum_i I_{\rm{out,i}}=0## with the understanding that charge going in the ##i##th location on the surface is added as ##-I_{\rm{out,i}}##. Of course in this case the other side of the equation is zero so the sign doesn't matter as long as charge out has opposite sign to charge in.

2. The sign does matter when the enclosed charge is changing. Consider, for example, the case of volume ##V## enclosing only the positive plate of a discharging capacitor through resistor ##R##. There is only one location where charge can come out, i.e. ##N=1##. Then ##\frac{dQ}{dt}## is a negative quantity which makes ##I_{\rm{out}}## positive. The current in the circuit must be drawn from the positive plate to the resistor before applying KVL.

I know I'm not saying anything new here, but it's nice to see that what might be considered "obvious" can be traced back to fundamental equations and principles that apply in general.

Edit: Minor typo fix.

 

[Dale]

So they oppose and have the exactly the same values... So it is correct!

No, your statement was not correct, for the reason pointed out by @kuruman in post 104.

Please do not try to push incorrect physics on this forum. That is not tolerated here. Simply learn and move on.

 

[kuruman]

So they oppose and have the exactly the same values... So it is correct!

In addition to @Dale's comments in post #113, you should realize that you have undermined your own argument if your statement quoted above is correct. When two opposing forces of equal magnitude act on a moving object at the same time, the object cannot move in a circle but in a straight line at constant velocity.

 

[vanhees71]

So they oppose and have the exactly the same values... So it is correct! That in vector it is pointed inwards or outwards that something else, you havent seen that in the equation did you??

You have to clearly distinguish which forces are present in which frames. In the inertial frame of reference there are only "true forces" (i.e., due to interactions, for everyday matter usually electromagnetic and gravitational ones only), i.e., there's a centripetal force, which keeps the particle on its circular trajectory.

In the rest-frame of the particle, i.e., in a rotating non-inertial frame and only in this frame you have the inertial forces in addition.

 

[A.T.]

centrifugal force = force required to keep and object on circular path

No, that would be centripetal not centrifugal.

Centrifugal (inertial / fictitious) force is merely introduced to make Newtons 2nd Law work in a rotating frame of reference.

So they oppose and have the exactly the same values...

Centrifugal (inertial / fictitious) force and centripetal force have the same magnitude only in special cases, not in general.

 

[sophiecentaur]

Here I beg to differ. I would not call them identities but consequences of equations that are based on empirical evidence, laws if you wish.

I agree with you but perhaps only to some extent. I could be wrong but weren't Kirchhoff's 'laws' based on circuits, currents and voltages, originally? At a deeper level, there is a crossover into Maxwell but isn't it true to say that trying to solve for time varying situations actually takes you beyond KVL and KCL? (Shaky results about Induction when used on their own.)
In a practical sense and, for the majority of students, Kirchhoff is a neat trick for solving DC circuit problems.

In as far a KVL: and KCL kick off by using a definition of R and that. along with definitions of Current and Voltage leads to what I would call two Methods, rather than laws. I guess that, in as far as they are Falsifiable propositions, you could say they are scientific laws. (as opposed to "ohms Law" which is only half stated by most of its users.

 

[anorlunda]

using a definition of R and that.

My point of disagreement is that Ohm's law necessitates a range in which R is constant. It works perfectly well where there is no linear range of R.

 

[kuruman]

I could be wrong but weren't Kirchhoff's 'laws' based on circuits, currents and voltages, originally?

I would say so. Experiments with circuit, currents, magnetic needles etc. provided the basis for Maxwell's synthesis that showed how all these are related and can be derived from four equations plus the conservation of charge equation. My objection was to labeling KVL and KCL as "identities". I think "special cases of general principles" would be a more appropriate label.

 

[sophiecentaur]

I think "special cases of general principles" would be a more appropriate label.

Yes - that's fair enough but they are stated in complete terms - unlike Ohm's Law. They don't actually involve explicit resistance.
We are agreeing.

 

[neilparker62]

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 think he said "Oh centrifugal"

 

[sophiecentaur]

My point of disagreement is that Ohm's law necessitates a range in which R is constant. It works perfectly well where there is no linear range of R.

Why do you put it that way round? Ohm stated the experimental condition that it's temperature that remains constant and he was talking about metals - not diodes etc.. The Physics of metals describes why Ohm got it right (luck and a lot of careful measurements). Semiconductor Physics shows that his law doesn't apply over even very small variations of current and temperature.

The ratio R is valid (of course) and we can use it in our calculations but why is it referred to as "Ohm's Law"? We are happy to use other 'laws' and to include the "all other things being equal" clause - for instance in the subsets of the Gas Law, Boyle's Law and Charles' Law, in which one of the three variables is stated (assumed) to be constant.
But for some reason (familiarity and bad teaching?) we carry on exposing newcomers to two versions of Ohm's Law. And so it continues.

In the case of Centrifugal Force, it's clear why our education starts with "there's no such thing". It's to knock on the head the mistaken idea that the ball 'flies outwards' when the string is cut. That's a misapprehension along the lines of 'things always slow down' and it's what we all experience (or think we experience). It's all a matter of the order in which things need to be taught appropriately on the way to improved understanding. The concept of a reactive force demands a formal level of thought which we lack early on (except for those PF members who seem to remember having grasped all of Physics first time round at school).

I think that Science shares the same problem that politician have, the fear of the U turn and dealing with the complaint that 'you taught us wrong', when we teach better models. Kids do their early learning at a concrete level and they appreciate concrete thoughts. We are not letting them down by not plunging into String Theory when they first ask us about simple Mechanics.