Argument on centrifugal force

[Alpharup]

My grade 11 textbook never mentioned about inertial frame, non- inertial frame, rotating frame of reference and so son.The derivation of centripetal acceleration was very intuitive.This derivation was given after Laws of Inertia and other Newton's laws of motion.Ideas like cross product and dot product are not clearly given in the textbook
After the not-so-explanatory derivation of centripetal acceleration and the corresponding force, we have the discussion of centrifugal force...

"Centifugal Reaction
According to Newton’s third law of motion, for every action there
is an equal and opposite reaction. The equal and opposite reaction to the
centripetal force is called centrifugal reaction, because it tends to take the
body away from the centre. In fact, the centrifugal reaction is a pseudo
or apparent force, acts or assumed to act because of the acceleration
of the rotating body.
In the case of a stone tied to the end of the string is whirled in
a circular path, not only the stone is acted upon by a force (centripetal
force) along the string towards the centre, but the stone also exerts an
equal and opposite force on the hand (centrifugal force) away from the
centre, along the string. On releasing the string, the tension disappears
and the stone flies off tangentially to the circular path along a straight
line as enuciated by Newton’s first law of motion.
When a car is turning round a corner, the person sitting inside
the car experiences an outward force. It is because of the fact that no
centripetal force is supplied by the person. Therefore, to avoid the
outward force, the person should exert an inward force."
Something is wrong with this explanation.First there is no reference about rotating frame which is a non-inertial frame.The author talks about validity of Newton's laws without the concern of the nature of frame.I think this is weak description..Iam a high school passout and I have found some conceptual errors.
Physics is taught the worst possible way in my textbook. I myself took the initiative to learn about frames of references. I have given the link to my textbook..Please rate this textbook.

http://www.textbooksonline.tn.nic.in/Books/11/Std11-Phys-EM-1.pdf

Also, if there is some logical inconsistency of this explanation, please point it.I want to take up the matter to the educational officers concerned..

 

[WannabeNewton]

The book seems to be incorrectly mixing and matching the so called "reactive centrifugal force" http://en.wikipedia.org/wiki/Reactive_centrifugal_force with the much more common use of the term centrifugal force, that being the inertial force that arises in rotating reference frames. The two are different concepts.

 

[D H]

"Centifugal Reaction
According to Newton’s third law of motion, for every action there
is an equal and opposite reaction. The equal and opposite reaction to the
centripetal force is called centrifugal reaction, because it tends to take the
body away from the centre. In fact, the centrifugal reaction is a pseudo
or apparent force, acts or assumed to act because of the acceleration
of the rotating body.

This is very bad. It is conflating the fictitious centrifugal force with the real reaction force. This is not just bad. It is wrong, wrong wrong. Wronger than wrong. Fictitious forces are not subject to Newton's third law. There is no equal but opposite reaction to the fictitious centrifugal force.

How one would classify the equal but opposite reaction to a real centripetal force -- that depends on the circumstances, and on what one deems to be the center.

In the case of a stone tied to the end of the string is whirled in
a circular path, not only the stone is acted upon by a force (centripetal
force) along the string towards the centre, but the stone also exerts an
equal and opposite force on the hand (centrifugal force) away from the
centre, along the string.

Here the reaction to the force exerted by the string on the rock is indeed centrifugal. That's just a label applied to one force acting at a tiny part of the string at the very end of the string. The rest of the string also exerts a force on that little part of the string, and this is centripetal. The net force *has* to be centripetal because the end of the string is undergoing uniform circular motion.

In fact, the only way in which the reaction force to a centripetal force is a real centrifugal force is when multiple forces are involved.

For a counter example, look at two objects orbiting one another gravitationally. Objects A and B are orbiting one another about their common center of mass. Both objects are undergoing centripetal motion. The equal but opposite force to gravitation is gravitation. It's a centripetal force no matter which object you look at.

 

[Alpharup]

The book seems to be incorrectly mixing and matching the so called "reactive centrifugal force" http://en.wikipedia.org/wiki/Reactive_centrifugal_force with the much more common use of the term centrifugal force, that being the inertial force that arises in rotating reference frames. The two are different concepts.

Yes, the author seems to be confused.Thanks for the link. I never read the applications in the Wiki page but I would mention one which I had encountered in a TV show. A car was tied to a metal pole with a rope. It was made to revolve around the pole with a very high constant velocity(i suppose it is 60 km/hour)..Due to the reactive centrifugal force(I suppose), the pole broke off..
I may be wrong in my understanding in reactive centrifugal force..Please correct me if the newly-found explanation for a phenomena, by the theory given by you is wrong..

 

[Alpharup]

This is very bad. It is conflating the fictitious centrifugal force with the real reaction force. This is not just bad. It is wrong, wrong wrong. Wronger than wrong. Fictitious forces are not subject to Newton's third law. There is no equal but opposite reaction to the fictitious centrifugal force.

How one would classify the equal but opposite reaction to a real centripetal force -- that depends on the circumstances, and on what one deems to be the center.

.

Yes you are right...But intuitively, it appears that the author is right to the students. Your reasoning in second paragraph is also right.
Your explanation is far more satisfying than mine. I live in India and this is a book of a state board. Like USA, India is divided into states(division into state is based on language). Each state has different education syllabus. My state may have the worst among them..I have not posted all that is wrong with the textbook..You may yourself see it.

The comical part is that teachers teach this way. When you approach them they say that this book was written by "Phd" person and that we must not question them. I think these persons have definitely rigged to get their Phds.. Leave alone, the teachers themselves must have rigged the syllabus. The exam system is also worse. I have given the explanation which is given in the book. You have to memorise it and vomit in exams. If you change the sentence or wordings, you may get low scores or you may fail. You should write as it is in the textbook. I hate this system here.

I have finished my school. So, I won't have much problem in pointing out the conceptual errors. Thanks for you explanation

 

[A.T.]

According to Newton’s third law of motion, for every action there
is an equal and opposite reaction. The equal and opposite reaction to the
centripetal force is called centrifugal reaction, because it tends to take the
body away from the centre. In fact, the centrifugal reaction is a pseudo
or apparent force,

As others said, this is wrong. Apparent forces do not obey Newtons's 3rd Law. The Author is confusing centrifugal reaction:
http://en.wikipedia.org/wiki/Reactive_centrifugal_force
with centrifugal inertial force:
http://en.wikipedia.org/wiki/Centrifugal_force_(rotating_reference_frame)

Here is a table comparing the two:
http://en.wikipedia.org/wiki/Reactive_centrifugal_force#Relation_to_inertial_centrifugal_force

And here a picture I once made about a rotating space station:

 

[Alpharup]

@A.T..thanks for the diagram.Now, Iam a little confused about all the forces concerning rotational motion. I want to test my understanding of inertial centrifugal force again. Now a body 'A' is moving around a point 'O' in circular motion with a constant velocity 'v' and radius 'r'..
In the rotating frame of reference of 'A', there is centripetal force..But the linear velocity and angular velocity is zero..This contradicts Newton's second law because the body is at rest though it is still acted upon by centripetal force..So, we have to assume a pseudo-force called inertial centrifugal force which has the same magnitude of centripetal force and acts in the opposite direction on 'A'..Thus the net force on the body is zero and the body remains in rest..

 

[A.T.]

@A.T..thanks for the diagram.Now, Iam a little confused about all the forces concerning rotational motion. I want to test my understanding of inertial centrifugal force again. Now a body 'A' is moving around a point 'O' in circular motion with a constant velocity 'v' and radius 'r'..
In the rotating frame of reference of 'A', there is centripetal force..But the linear velocity and angular velocity is zero..This contradicts Newton's second law because the body is at rest though it is still acted upon by centripetal force..So, we have to assume a pseudo-force called inertial centrifugal force which has the same magnitude of centripetal force and acts in the opposite direction on 'A'..Thus the net force on the body is zero and the body remains in rest..

Yes, this is the whole idea behind inertial (aka fictitious, pseudo, apparent) forces: Make Newtons 1,2 Law work in non-inertial frames. But you cannot make the 3 Law work for them, only "real" interaction forces are part of 3rd Law pairs. Therefore the inertial centrifugal force F_icf is not a reaction force to anything, and it exists only in the rotating frames. The centrifugal reaction F_cfr is a "real" interaction force that exists in any frame.

 

[pgardn]

As others said, this is wrong. Apparent forces do not obey Newtons's 3rd Law. The Author is confusing centrifugal reaction:
http://en.wikipedia.org/wiki/Reactive_centrifugal_force
with centrifugal inertial force:
http://en.wikipedia.org/wiki/Centrifugal_force_(rotating_reference_frame)

Here is a table comparing the two:
http://en.wikipedia.org/wiki/Reactive_centrifugal_force#Relation_to_inertial_centrifugal_force

And here a picture I once made about a rotating space station:

I like this diagram.
The only problem is if someone asks about the space station wall and sees only one force present on that wall they might be tempted to ask why is the wall not accelerating out. In the inertial frame diagram.

Would you then go on to explain there must be a force between the wall space station atoms that is larger that the force of the astronaut on the wall of the space station and directed in?

 

[A.T.]

I like this diagram.
The only problem is if someone asks about the space station wall and sees only one force present on that wall they might be tempted to ask why is the wall not accelerating out. In the inertial frame diagram.

Would you then go on to explain there must be a force between the wall space station atoms that is larger that the force of the astronaut on the wall of the space station and directed in?

Yes, there are obviously internal forces that hold the space station together. There are also internal forces in the legs of the astronaut, which prevent his upper body from hitting the wall. But drawing all the internal forces is hardly possible.

 

[Andrew Mason]

This has been discussed on other threads.

In a rotating body or system, the accelerations are all toward the centre of rotation. There is nothing wrong with the textbook saying that the perceived centrifugal force is fictitious IF one is talking simply about a force as a mass x its acceleration. All of those forces are centripetal. If the forces between the parts of a rotating body disappear suddenly, the parts of the body just continue their motion at the time the forces disappeared - no outward acceleration.

To talk about centrifugal force simply causes confusion, as we see here. The textbook should not be suggesting that the reaction force to a centripetal force is a fictitious force. It is a real force. Whether it is centrifugal or centripetal is another matter.

So what is the "reaction force" to the centripetal force on a piece, ψ, of a rotating body of mass m and a distance r from the centre of rotation (F_ψ = ma = -mω²r)? Since that centripetal force on ψ is supplied by the rest of the body of which it is a part, the reaction force to F_ψ must be the mass x acceleration of the rest of the body in the direction opposite.

But is that opposite direction centrifugal? That is a matter of how one defines the direction of a radial force. It is definitely radial. And it is opposite to the direction of the acceleration of ψ. But the acceleration of each part of the rest of the body is also toward the centre of rotation. So the reaction force applying to the rest of the rotating body is the force supplying the centripetal acceleration of the rest of the body. To call that centrifugal would be incorrect.

My advice is to forget about the term centrifugal. It just causes confusion and does not add any insight into the physics of rotating bodies. It applies only to tensions that do not and cannot cause acceleration. It makes some sense only if you divide the rotating body up into more than two parts. If you consider the centripetal force of a part as being supplied only by the parts of the body that are in contact with it rather than the entire rest of the body, it might make sense. But that just obscures the physics. The only reason the parts that are in contact can supply the centripetal force because they are connected to the rest of the rotating body.

AM

 

[A.T.]

But is that opposite direction centrifugal? That is a matter of how one defines the direction of a radial force...To call that centrifugal would be incorrect.

It is neither correct nor incorrect. It just depends on which definition of "centrifugal" is used, as you just stated yourself.

It makes some sense only if you divide the rotating body up into more than two parts.

Which is a perfectly valid way to analyze the system. There no law stating that any system must be analyzed as exactly two parts.

 

[Alpharup]

I like this diagram.
The only problem is if someone asks about the space station wall and sees only one force present on that wall they might be tempted to ask why is the wall not accelerating out. In the inertial frame diagram.

Would you then go on to explain there must be a force between the wall space station atoms that is larger that the force of the astronaut on the wall of the space station and directed in?

Yes, there are obviously internal forces that hold the space station together. There are also internal forces in the legs of the astronaut, which prevent his upper body from hitting the wall. But drawing all the internal forces is hardly possible.

I think that frictional force between the astronaut and the space station may also contribute in some way to the internal force...

 

[A.T.]

I think that frictional force between the astronaut and the space station may also contribute in some way to the internal force...

If the angular velocity is constant, and astronaut doesn't run along the walls, there should be no tangential friction, just radial contact forces.

 

[Alpharup]

If the angular velocity is constant, and astronaut doesn't run along the walls, there should be no tangential friction, just radial contact forces.

Can these contact radial forces act as centipetal force?

 

[A.T.]

Can these contact radial forces act as centipetal force?

Yes, the force by the wall on the shoes is centripetal.

 

[Dale]

Since that centripetal force on ψ is supplied by the rest of the body of which it is a part, the reaction force to F_ψ must be the mass x acceleration of the rest of the body in the direction opposite.

This makes two unnecessary assumptions. First, it assumes that the body is isolated, i.e. there are no external forces acting on the body. Second, it assumes that the analysis of the body divides it into only 2 parts. Neither of these assumptions is mandated by Newtonian physics and the rest of your conclusions fail if either is violated.

 

[pgardn]

Yes, there are obviously internal forces that hold the space station together. There are also internal forces in the legs of the astronaut, which prevent his upper body from hitting the wall. But drawing all the internal forces is hardly possible.

I was just thinking of drawing a FBD of the wall of the station at the place where the astronaut is.

It seems there would be two forces on the wall, the internal forces holding the wall together (electromagnetic I guess), and the force of the astronaut on the wall(this force is what accelerates the astronaut towards the center).

The internal wall forces must be greater or that section of the wall would not accelerate towards the center. So if a student was asked to draw a FBD of that section of the wall, both would be drawn, with the net force being (internal wall - astronaut force on wall) = centripetal force.

Is the above reasonable if asked to draw a FBD of the wall?

 

[Andrew Mason]

This makes two unnecessary assumptions. First, it assumes that the body is isolated, i.e. there are no external forces acting on the body.

Yes. But an external force would not be supplying centripetal force. So, assuming the body is rigid, if there are external forces you would just add the mass x acceleration of the centre of mass - not difficult.

Second, it assumes that the analysis of the body divides it into only 2 parts. Neither of these assumptions is mandated by Newtonian physics and the rest of your conclusions fail if either is violated.

Similarly, there no requirement that forbids analysing it in terms of two parts (1. a part of the rotating body and 2. the rest of the rotating body). You can always do that for any rotation. You cannot always break a rotating system into more than two parts.

AM

 

[A.T.]

Similarly, there no requirement that forbids analysing it in terms of two parts

Nobody forbids it, but doesn't make much sense to base general naming conventions on this one special case. It is also a bad idea to base the names of forces on accelerations, because it fails for static forces. It is much simpler and more general to base the distinction on the direction of the force and its point of attack.

 

[A.T.]

I was just thinking of drawing a FBD of the wall of the station at the place where the astronaut is.

It seems there would be two forces on the wall, the internal forces holding the wall together (electromagnetic I guess), and the force of the astronaut on the wall(this force is what accelerates the astronaut towards the center).

The internal wall forces must be greater or that section of the wall would not accelerate towards the center. So if a student was asked to draw a FBD of that section of the wall, both would be drawn, with the net force being (internal wall - astronaut force on wall) = centripetal force.

Is the above reasonable if asked to draw a FBD of the wall?

Yes, if you cut the space station in segments, you have to include the forces between the segments in a FBD.

 

[Andrew Mason]

Nobody forbids it, but doesn't make much sense to base general naming conventions on this one special case.

Naming conventions? Centrifugal means "fleeing the centre" and Centripetal means "centre seeking".

It is also a bad idea to base the names of forces on accelerations, because it fails for static forces. It is much simpler and more general to base the distinction on the direction of the force and its point of attack.

The tensions within a rotating body act in all directions, not just radially. So centrifugal/centripetal is not really the best way to describe tensions. What you are interested in are the accelerations. All accelerations are centripetal.

The point of all this is to teach students about forces. It does not help to confuse them by introducing them to two types of centrifugal forces, neither of which are capable of producing acceleration and one of which is not a real force.

AM

 

[A.T.]

Naming conventions? Centrifugal means "fleeing the centre" and Centripetal means "centre seeking".

Yes, and in regards to forces this can be interpreted as:

centrifugal : (point_of_attack - center) parallel to force
centripetal : (point_of_attack - center) anti-parallel to force

This is simple. It doesn't require the knowledge about accelerations, so it works for static forces too. It doesn't require the knowledge about the whole system. It doesn't depend on the way you cut the system into bodies.

Good luck convincing anyone to drop this and adopt your more dependent and less general convention.

 

[Dale]

We have already had this argument in full:

https://www.physicsforums.com/showthread.php?t=668756

No need to re-hash it.