What exactly is centrifugal force

[sophiecentaur]

Wrong. In the rotating frame the centrifugal reaction force can push an object outwards, just like the inertial centrifugal force can.

But will 'flee' along a tangent and not a radius, when you cut the string. That was why the word was not 'permitted'. Of course, they failed to mention that a tangent takes you further from the centre, too.

 

[sophiecentaur]

It is really not that confusing if you make clear which reference frame you consider.

We didn't 'do' astronauts when I was at school (they hadn't been invented - except for Dan Dare) and the term 'reference frame' was University stuff at the time.

Having tried those ideas on teenagers, not long ago, I did find it worked with some. It didn't work with others but, so what? They'll have ended up in banking or as 'TV personalities'.

 

[A.T.]

In the rotating frame the centrifugal reaction force can push an object outwards, just like the inertial centrifugal force can.

But will 'flee' along a tangent and not a radius, when you cut the string.

I was talking about about the rotating frame, where it flees along the radius.

 

[sophiecentaur]

I was talking about about the rotating frame, where it flees along the radius.

See my post - just above.

 

[stevendaryl]

Yeah, you can always replace a simple approach with a mathematically equivalent, but more complicated one.

That's what introducing the idea of "centrifugal force" does. It makes things unnecessarily complicated and confusing.

 

[stevendaryl]

Yeah, you can always replace a simple approach with a mathematically equivalent, but more complicated one.

Really, you have things completely backwards here. The SIMPLE approach is to use vector equations:

1. In the absence of any forces, $\frac{\stackrel{\rightarrow}{dU}}{dt} = 0$
2. In the presence of an external force $m \frac{\stackrel{\rightarrow}{dU}}{dt} = \stackrel{\rightarrow}{F}$
3. If one object exterts a force $\stackrel{\rightarrow}{F}$ on another, then the second object exerts a force $-\stackrel{\rightarrow}{F}$ on the first.

There is nothing confusing about these rules, and there are no exceptions for "fictitious forces" or "noninertial frames". The only complicated thing is that you need to realize that a vector can change for two reasons: (1) the components change, or (2) the basis vectors change. It might be simpler to pretend that (2) never happens, but it's a falsehood, and you're doing physics in a crippled way when you do it.

 

[stevendaryl]

That's what introducing the idea of "centrifugal force" does. It makes things unnecessarily complicated and confusing.

Actually, different people disagree about what is "complicated". I consider it complicated when you have lots of ad hoc rules that apply in specific circumstances: If you are using inertial Cartesian coordinates, do this, if you're using curvilinear coordinates, do that, if you're using noninertial coordinates, do that. I'd rather have a fundamental set of principles that apply in all those circumstances, even if working out the details might be complicated.

 

[ZealScience]

It appears because of choice of coordinates and reference frame, and yes it does not exist in inertial reference frame.

 

[Andrew Mason]

It's not a concept. The concept here is Newtons 3rd Law: A pair of equal but opposite force acting at the interface of two objects: one inwards (centripetal) the other outwards (centrifugal)

Ok. But it gets confusing to students.

Example: there is no centrifugal reaction force to the weight of a car sitting on a road on the equator, even though the car is whipping around at 1000 mph. as the Earth turns and even though it's weight bears on the Earth surface. Ques. What about the normal force? Do we call that a centrifugal force? Answer: no. Ques. But it is directed away from the centre of rotation (ie. up). Answer: Yes, but we do not call it centrifugal. Ques. Why not? Answer: My answer would be: We don't call it centrifugal because it does not cause anything to flee the centre of rotation. I am not sure what your answer would be. Should we call it centrifugal?

This describes the potential effects of the inertial centrifugal force as seen in the rotating frame.

Yes, but the point is that it means "fleeing the centre".

Wrong. In the rotating frame the centrifugal reaction force can push an object outwards, just like the inertial centrifugal force can.

But that is a fictitious centrifugal force, not the "centrifugal reaction force". Give us an example - just one example where the reaction force to a centripetal force causes matter to flee the centre of rotation.

AM

 

[rcgldr]

There is no centrifugal reaction force to the weight of a car sitting on a road on the equator, even though the car is whipping around at 1000 mph.

A more generalized version of this would be 2 body system in outer space, free of external forces, each object orbiting about a common center of mass due to gravity or opposite charge. The Newton third law pair of forces are the two attractive forces between the objects and directed towards a common center of mass. If the orbits are circular, then the two attractive forces are also centripetal forces. In this situation, there are no reactive centrifugal forces.

Change this 2 body system to one where there are no attractive forces, and the two objects are connected by a string and rotate in a circular path about a common center of mass. Both objects exert a reactive centrifugal force on the ends of the string (assuming that the common center of mass is not located within one of the objects, in which case only one end of the string experiences a reactive centrifugal force).

 

[Andrew Mason]

Actually, different people disagree about what is "complicated". I consider it complicated when you have lots of ad hoc rules that apply in specific circumstances: If you are using inertial Cartesian coordinates, do this, if you're using curvilinear coordinates, do that, if you're using noninertial coordinates, do that. I'd rather have a fundamental set of principles that apply in all those circumstances, even if working out the details might be complicated.

The principles and the laws of physics are the same. The problem is that nature makes a distinction between non-inertial and inertial frames of reference.

AM

 

[Andrew Mason]

Change this 2 body system to one where there are no attractive forces, and the two objects are connected by a string and rotate in a circular path about a common center of mass. Both objects exert a reactive centrifugal force on the ends of the string (assuming that the common center of mass is not located within one of the objects, in which case only one end of the string experiences a reactive centrifugal force).

And how would the objects produce a centrifugal acceleration of the ends of the string?

AM

 

[A.T.]

It might be simpler to pretend that (2) never happens,

It is simpler, that’s why inertial forces are widely used.

but it's a falsehood, and you're doing physics in a crippled way when you do it.

It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.

 

[dextercioby]

In classical mechanics we treat the Coriolis force, the translation inertial force and the centrifugal force on equal footing.

I wonder why only the centrifugal force is poorly understood by people, since it's the only inertial force generating multi-page debates o PF...

 

[stevendaryl]

It is simpler, that’s why inertial forces are widely used.

No, inertial forces are NOT simpler. They may seem simpler to people who prefer to memorize formulas instead of understanding them.

 

[stevendaryl]

No, inertial forces are NOT simpler. They may seem simpler to people who prefer to memorize formulas instead of understanding them.

Can someone write down what are the equations for inertial forces, and what are the rules for using them? It seems to me that it amounts to this:

1. Write down the equations of motion using inertial Cartesian coordinates.
2. Transform to curvilinear, noninertial coordinates.
3. Note that there are extra terms in the equations of motion that were not present in the inertial Cartesian case.
4. Call these extra terms "inertial forces".

Surely, the last step isn't doing anything for you. Calling them "forces" doesn't help anything. 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. Calling them forces is a confusion--it's not a simplification. There is nothing that becomes simpler because of that choice of names.

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. It's just not true. It's true for inertial Cartesian coordinates, but not for other coordinates. It's not a "simplification" to assume something that is provably false.

 

[A.T.]

No, inertial forces are NOT simpler...

Then I'm sure you will soon have convinced anyone to stop using them. Let us know when all the books have been revised.

That's just bad mathematics. It's just not true...

It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.

 

[rcgldr]

Change this 2 body system to one where there are no attractive forces, and the two objects are connected by a string and rotate in a circular path about a common center of mass. Both objects exert a reactive centrifugal force on the ends of the string (assuming that the common center of mass is not located within one of the objects, in which case only one end of the string experiences a reactive centrifugal force).

And how would the objects produce a centrifugal acceleration of the ends of the string?

They wouldn't. The net force on each object is inwards. The objects (and the ends of the string) are accelerated "inwards" by the tension in the string. The outwards force exerted by the objects onto the ends of the string is a reaction (to acceleration) force, not a net force, equal in magnitude and opposing the tension at the ends of the string.

 

[sophiecentaur]

Then I'm sure you will soon have convinced anyone to stop using them. Let us know when all the books have been revised.

It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.

This thread reads like something out of Gulliver's Travels, actually. Anyone would think that there is some actual 'reality' in it all. People don't acknowledge that Science is the pragmatic business of predicting things - all the rest is faith.

 

[Dale]

Just throwing in my 2 cents worth.

That is why I prefer the terms "inertial forces" and "interaction forces".

I agree with A.T. here. Fictitious forces do most things that you expect real forces to do, including do work in the non-inertial frame in which they exist.

The true reaction to a centripetal force is another centripetal force.

This can be true in certain circumstances, but it is not generally true.

So some people would take this to mean "Newton's laws only apply in an inertial frame". I don't like that conclusion. If you view them as vector equations, then they apply in all circumstances, not just inertial frames.

Interesting idea. I was aware of this in terms of gravity in GR, but hadn't thought clearly about the advantage for Newtonian physics also. As we discussed in that other thread, I am not convinced about this because of the double-degeneracy of the metric in Newtonian physics. But I haven't looked at it closely (for that same reason).

There is nothing about the "centrifugal reaction force" that causes anything to flee from the centre. Nothing.

This is simply wrong. If you look at A.T.'s little astronaut cartoon, suppose that the astronaut is standing on a section of the floor supported by bolts which can be suddenly cut. If they are suddenly cut then the reactive centrifugal force will accelerate the section of the floor away from the center. It is only the presence of the bolt forces which prevents the floor from fleeing the center under the influence of the centrifugal reaction force.

 

[rcgldr]

Suppose we have two spherical moons orbiting a spherical planet and both moons are directly opposite each other (ie. a line through the moons' centres passes through the planet's centre) on identical orbits. Would you say that that the reaction forces of each moon on the planet are centrifugal?

In this situation, there is no reaction force, because there is nothing to exert a reaction force onto. The only forces are gravitational. The only "outwards" force would be exerted onto the surface of the planet, but that force is due to gravity, not a reaction force. In this situation, the reaction to gravitational force is a change in the path of the moons as they orbit.

If you look at A.T.'s little astronaut cartoon, suppose that the astronaut is standing on a section of the floor supported by bolts which can be suddenly cut. If they are suddenly cut then the reactive centrifugal force will accelerate the section of the floor away from the center. It is only the presence of the bolt forces which prevents the floor from fleeing the center under the influence of the centrifugal reaction force.

A reactive force is a response to acceleration of an object wrt inertial frame. In an inertial frame, once the floor is cut, the astronaut and the floor cease to accelerate, so there is no reactive centrifugal force. In a rotating frame, the reactive centrifugal force also vanishes (the astronaut ceases to exert a force onto the floor), and the fictitious centrifugal force now changes into a combination of fictitious centrifugal and coriolis forces that correspond to an object moving at constant velocity wrt inertial frame, as observed from a rotating frame.

 

[stevendaryl]

Then I'm sure you will soon have convinced anyone to stop using them. Let us know when all the books have been revised.

There are lots of bad ideas that are taught to beginning students of physics that have to be "untaught" to advanced students. Inertial forces is one of them. "Relativistic mass" is another.

It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.

It doesn't lead to ANYTHING. Calling something a "force" when it's not is just bad terminology. It's not an alternative approach to doing physics.

 

[stevendaryl]

This thread reads like something out of Gulliver's Travels, actually. Anyone would think that there is some actual 'reality' in it all. People don't acknowledge that Science is the pragmatic business of predicting things - all the rest is faith.

The claim that "Science is the pragmatic business of predicting things - all the rest is faith" is itself a philosophical position, and is therefore, not science.

 

[A.T.]

It doesn't lead to ANYTHING.

It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.

 

[stevendaryl]

It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.

Calling something a "force" doesn't lead to ANYTHING. If you think otherwise, give an example of how something follows from the fact that you call certain terms "forces".

 

[stevendaryl]

It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.

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.

 

[A.T.]

The claim that nothing matters other than quantitative predictions...

...in physics.

It's funny that the people who bring up "that's just philosophy" as an argument...

The argument is "The rest is philosophy, so there is no point arguing about it on a physics forum".

 

[stevendaryl]

The argument is "The rest is philosophy, so there is no point arguing about it on a physics forum".

But that's basically this entire thread. The physics part is nothing more than:

"If one uses noninertial, curvilinear coordinates, then additional terms appear in the equations of motion."

One sentence. Everything else is an argument for a particular way of looking at those additional terms.

 

[A.T.]

give an example of how something follows from the fact that you call certain terms "forces".

All forces are just "certain terms". So I don't see how this is an argument against inertial forces specifically.

 

[stevendaryl]

It leads to the same quantitative predictions, which is all that matters in physics. The rest is philosophy.

I also want to point out that connection coefficients (the preferred, in my opinion, way to deal with noninertial, curvilinear coordinates) are essential to understanding General Relativity.

 

[stevendaryl]

All forces are just "certain terms". So I don't see how this is an argument against inertial forces specifically.

No, they're not. Real forces have certain properties that the fake forces don't:
(1) They are vector quantities, meaning that they exist in EVERY coordinate system. The components change when you change coordinate systems, but a vector is a geometric quantity that is independent of coordinates.
(2) Real forces have corresponding reaction forces, leading to conservation of momentum.

In contrast, "inertial forces" are artifacts of a particular choice of coordinates. They don't have corresponding reaction forces. They can be made to disappear by choosing the appropriate coordinate system.

 

[A.T.]

In a rotating frame, the reactive centrifugal force also vanishes (the astronaut ceases to exert a force onto the floor),

You can easily find examples where reactive centrifugal force pushes things outwards in the rotating frame. Two blocks on a turntable. An outer light one with high friction. An inner massive one on rollers. The inner block applies a centrifugal interaction force to the outer block, which pushes the outer block away from the center in the rotating frame.

But all of that is not relevant to the "centrifugal"-label for the reason I state in post #64.

 

[A.T.]

Real forces have certain properties...

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

 

[sophiecentaur]

The claim that "Science is the pragmatic business of predicting things - all the rest is faith" is itself a philosophical position, and is therefore, not science.

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. So far, we have found this as our experience has been that Science, and its models, continuously changes to fit new evidence.
It has to be true that Science endeavors to avoid saying what things 'really are' because there are so many examples of two or more, equally valid 'realities'. (Note, I write "Science" and not 'Scientists' - who are human and fallible and seldom view things without the distraction of some sort of faith).

 

[Andrew Mason]

This is simply wrong. If you look at A.T.'s little astronaut cartoon, suppose that the astronaut is standing on a section of the floor supported by bolts which can be suddenly cut. If they are suddenly cut then the reactive centrifugal force will accelerate the section of the floor away from the center. It is only the presence of the bolt forces which prevents the floor from fleeing the center under the influence of the centrifugal reaction force.

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