What exactly is centrifugal force

[sophiecentaur]

Words like "fictitious force" and "particle" should have a warning sign on them when they're used for public consumption. If you can feel the effect then it's not really fictitious so a different word should really be used to describe it. Likewise, calling a photon a particle is just asking for the sort of misinterpretations we read every day. A term like quasi-force or quasi-particle would at least ring warning bells for people who might want to rush off and think in terms of conventional meanings.

 

[A.T.]

That is quite true, but you are only looking at part of the picture.

"Part of the picture" is fully sufficient for Newtons 3rd Law and local interactions. You don't have to consider all forces acting on a object or the net acceleration of the object, to tell that an individual force acting on it is centrifugal (points away from the rotation center) and forms a 3rd Law pair with a centripetal force acting on a different object.

 

[Andrew Mason]

Because you are considering only the most trivial cases, like:

So where is the concept of a centrifugal reaction force used? It cannot ever produce a centrifugal acceleration. So all it does is explain the tension.

In the other thread we gave you plenty examples where a reactive centrifugal force exists.

My quibble is not with the force per se but with the name "centrifugal" in conjunction with the term "force". A force is something that is capable of producing an acceleration of an object. The acceleration that this reaction force produces is always centripetal ie. opposite to the direction of the force.

The term "centrifugal" has nothing to do with producing acceleration. It simply means that the force points away from the center of rotation. Acceleration is a matter of net force, not just one centrifugal force.

From Wikipedia:
Centrifugal force (from Latin centrum, meaning "center", and fugere, meaning "to flee") is the apparent outward force that draws a rotating body away from the center of rotation.

There is nothing about the "centrifugal reaction force" that causes anything to flee from the centre. Nothing. The only thing that causes a rotating object and rotating rope to "flee" the centre is inertia, not a force.

AM

 

[sophiecentaur]

"Part of the picture" is fully sufficient for Newtons 3rd Law and local interactions. You don't have to consider all forces acting on a object or the net acceleration of the object, to tell that an individual force acting on it is centrifugal (points away from the rotation center) and forms a 3rd Law pair with a centripetal force acting on a different object.

Using the term 'Centrifugal Force' when I was at school was verboten. It was regarded as worse than talking about sex in front of your parents.

 

[A.T.]

So where is the concept of a centrifugal reaction force used?

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)

From Wikipedia:
Centrifugal force (from Latin centrum, meaning "center", and fugere, meaning "to flee") is the apparent outward force that draws a rotating body away from the center of rotation.

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

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

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

 

[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".