What exactly is the reactive centrifugal force (split)

Andrew Mason

You have quoted only part of what I said. The "net" force IS ALWAYS the mass x its acceleration. The astronaut's entire reaction force is equal and opposite to its mass x its acceleration and that is exactly equal to the mass x acceleration of the space station. It is by its very nature a "net" force.

AM

A.T.

No, it is not the same. They have a different point of attack. See post #76.

Andrew Mason

I don't see the significance of the point of attack.

Maybe I am missing something here. Stop me if you think I am saying anything that is incorrect.

1. For a rigid body that is not rotating and whose centre of mass is not accelerating, the sum all forces acting on it is 0. Since no part of the body is accelerating, the sum of all forces acting on each part of such a body is 0.

2. For a rigid body that is rotating and whose centre of mass is not accelerating, the sum of all forces acting on it is 0. Since each part of the body is accelerating, the sum of all forces acting on each part of the body is equal to the mass of such part multiplied by its (centripetal) acceleration. (Since the sum of all such mass x accelerations must be 0, a rotating free body always rotates about an axis through its centre of mass).

3. The space station with the single astronaut lying on the floor (as I described in my post #73) is a rotating rigid body whose centre of mass is not accelerating. Therefore:

• the sum of all forces acting on each part is equal to the centripetal acceleration of that part multiplied by the mass of such part.
• For any arbitrary division of the space station (including contents) into two parts, the sum of all forces acting on each part is equal to the mass of such part multiplied by its (centripetal) acceleration and
• The sum of the mass x (centripetal) acceleration of each of the two parts = 0.
• Thus, the mass x (centripetal) acceleration of any part is equal and opposite to the mass x centripetal acceleration of the other part.

4. Therefore the mass x acceleration of the astronaut = -mass x acceleration of the rest of the space station

5. Since the force applied by the space station to the astronaut = the mass x the (centripetal) acceleration of the astronaut, the equal and opposite force applied by the astronaut to the space station = the mass x (centripetal) acceleration of the rest of the space station = sum of all the forces acting on all the parts of the rest of the space station.

AM

A.T.

It's a naming convention, not a matter of great significance. See post #85 for my reasons to prefer the common convention over yours.

DaleSpam

This is not generally true. If you take two parts which are near each other or two parts which are opposite but not equally massive then their change in momentum may not be equal and opposite.

This is true if you consider the opposite astronaut to be part of the space station (which is valid). In that case the centrifugal reaction force applied by the right astronaut to the space station is indeed equal to the mass x centripetal acceleration of the "space station & left astronaut".

The statement is not true if you consider the opposite astronaut not to be part of the space station (which is also valid). In that case the centrifugal reaction force applied by the right astronaut to the spact station is not equal to the mass x centripetal acceleration of the space station.

A.T.

Since the extended body aspect seems to be a reason for confusion, I propose to use an even simpler example:

A space ship is moving on a circular path, by firing its engines continuously to provide the centripetal acceleration. The astronaut inside the ship exerts a reactive centrifugal force on the ship's wall.

DaleSpam

I think that we should go ahead with the current example in your drawing. Andrew Mason has a valid point that in certain perfectly legitimate analyses of perfectly reasonable circumstances the centrifugal reaction force can cause centripetal acceleration.

The point remains that whenever a centripetal force has a 3rd law pair which is directed away from the center of rotation that force is called the "centrifugal reaction force". That is the definition of the term and it is a common enough term that people should know what it means.

In some cases the centrifugal reaction force causes only centrifugal effects (material stresses, accelerations, etc.), but sometimes it causes centripetal effects. The naming convention refers to its direction, and not to its effects. Andrew Mason has every justification to dislike the naming convention (I dislike it for a different reason), but nevertheless it is well defined and well established.

Andrew Mason

The ONLY effect that the centripetal force applied by a part of a rotating free body can have on the COM of the rest of the body is a centripetal acceleration of that COM. There is no other possible effect. It does not matter how you cut it or how the force is applied. There can NEVER be a centrifugal acceleration of the other part or ANY part of that other part.


In any rigid body there are, by definition, static tension forces everywhere. We don't concern ourselves with those forces. We cannot possibly know what those forces are doing at any moment because they operate at atomic levels and the atoms are constantly undergoing thermal motion. We can only look at the forces that cause acceleration.

Whose "naming convention"? Give me a cite. No physics text that I have ever read refers to "centrifugal reaction force". The only book that I have found that references it is Mook and Vargish "Inside Relativity" (1987):

"As a result of the force acting on the ball, the ball deviates from uniform motion and follows a circular path, just as the planet docs when acted upon by the sun's gravity, But by Newton's third law, if you exert a force on the ball, the ball must exert an equal and opposite force on your hand, and it does. You feel this force as the " tug" of the ball on the string you hold. It is not necessary to posit a centrifugal force. What is sometimes called a "centrifugal force" is a reflection of the force you are exerting on the ball to keep it in a circular path. Similarly, the sun will feel such a reactive, centrifugal force from each of the planets that it holds in an orbit by its force of gravity."

There is absolutely no difference between this "reactive centrifugal force" ("rcf") and the "fictitous centrifugal force" ("fcf"). The rcf/fcf is the outward pull on the other end of the system (person) which is created to explain the fact that the guy is pulling the ball but the ball does not appear to be accelerating it toward him. The reaction to that fictitious force - the pull of the guy on the ball - is real. In actual fact, both bodies are accelerating about a common centre of rotation and there is no outward force.

AM

A.T.

I think it is beaten to death. Everyone agrees what happens there. The disagreement about the naming convention (by force direction or by force effect) cannot be resolved. It is a matter of personal preference.
Yes. It doesn't depend on how you define the objects. It doesn't depend on other forces that are eventually contributing to the acceleration. It is local and doesn't force you to analyze the acceleration of a larger part. It is more general and practical.

A.T.

It does. The COM of the space station doesn't accelerate, if you treat it as 3 objects. And your convention depends on this acceleration.
What is "in the body" and what is an external force depends on how you cut it.
Acceleration of what? Where the COMs are, and how they accelerate, depends on how you cut it.
Don't look at me. I call my forces: F₁, F₂... But if I had to choose, I would prefer this simple convention, over your effect reasoning.
You are back to page one of the previous thread. Here the differences between FCF and RCF again:
http://en.wikipedia.org/wiki/Reactiv...trifugal_force

Andrew Mason

I should have made it clear that I was referring to any arbitrary division of the space station and contents into two parts.

I was referring to the space station with one astronaut - eg. the single astronaut lying on the "floor" as described in my post #73. In this case there is just the space station itself whose centre of mass is not the centre of rotation (the centre of rotation being the geometric centre).

In the symmetrical station with 2 identical astronauts opposite each other, the reaction force applied by the right astronaut would be equal to the mass x centripetal acceleration of the other astronaut [+ 0 (which is the total centripetal acceleration of just the space station)].

AM

Andrew Mason

Perhaps you could provide a cite for where this term is used - please do not cite Mook and Vargish, Inside Relativity.

A cite would be helpful.

Can you give us an example of how an the centrifugal reaction force cause anything to undergo centrifugal acceleration? I don't see that. It would be like the normal force of the earth causing a person to jump. Or the force on the seat back of a person sitting in a car that is accelerating forward causing the car or the car seat to accelerate backward. As soon as he car or car seat stops accelerating forward the reaction force ends.

AM

A.T.

So you demand the we:
- always consider the whole isolated system
- always cut it in exactly two parts
and you call this "arbitrary"? Sorry, but this is not what everybody wants/needs to do in an analysis. So I don't think many will want to use a naming convention based on that.

The nice thing about the naming convention you oppose, is that it doesn't rely on effects like acceleration. Newtonts 3rd (the current mainstream interpretation) doesn't care about accelerations and their causes. But if you want an example, here it is:

A space ship is moving on a circular path, by firing its engine continuously to provide the centripetal acceleration. The burned fuel is exerting a centripetal force on the ship, which causes a centripetal acceleration of the ship. The ship is exerting a centrifugal force on the burned fuel, which causes a centrifugal acceleration of the burned fuel.

DaleSpam

OK, under that restriction your statement is true, but no longer general. In fact, even requiring the system to be isolated makes it not general.

Yes. Note however that the reaction force is applied to the space station and not the other astronaut. The 3rd law pair is the force on the astronaut from the floor and the force on the space station floor from the astronaut, not the forces on the two astronauts.

DaleSpam

Nonsense. The whole subject of statics is concerned with these forces. We know a great deal about them, and we can easily use strain gauges to know what they are doing at any moment even when there is no acceleration (i.e. constant strain).

You are completely misreading their statement. It is clearly not the same as the fictitious centrifugal force.

DaleSpam

Sure:

http://en.wikipedia.org/wiki/Reactive_centrifugal_force
http://en.wikipedia.org/wiki/Centrif...trifugal_force
http://physnet.org/modules/pdf_modules/m17.pdf
http://books.google.com/books?id=QnJ...gal%22&f=false
http://books.google.com/books?id=4Gm...ion%22&f=false
http://books.google.com/books?id=eF-...rce%22&f=false
http://books.google.com/books?id=tvk...ion%22&f=false
http://books.google.com/books?id=xvS...ion%22&f=false

A.T. recently proposed an example with a rocket, the centrifugal reaction force of the engine on the exhaust causes centrifugal acceleration of the exhaust. I also previously proposed an example with rapidly cutting bolts on a section of the floor. I am sure other similar examples could be constructed. I don't know if you want to count your dent formation examples since in those cases the acceleration is only centrifugal in the rotating frame.

Also, in all cases the centrifugal force causes the object on which it is exerted to have less centripetal acceleration than if the centripetal force were unopposed. That in itself is a centrifugal effect although not centrifugal acceleration.

Look, Andrew, this is pointless. The terminology is well-defined. You do have good reasons for not liking it, but it is common enough that people should know about it. You don't need to use it if you don't like it, but others surely will, so you should know what it is. All of your complaining about situations where it causes centripetal acceleration, while correct, doesn't make the term go away. The term is well-defined, and sufficiently common to be taken as standard terminology.

Andrew Mason

Strain gauges do not measure the actual static forces between the molecules of the body. They measure the response of the material to an applied external force. For a steel beam floating in space the strain gauge would measure 0 strain. But we know that there are enormous forces holding the steel molecules together.

My point was that when analysing the physics of the rotating rigid body, we assume it is rigid and able to remain perfectly rigid as it rotates. We don't have to be concerned with the static forces within the body to analyse the physics of rotation.

Not only is it not "clearly" not the same as the fictitious centrifugal force, there is no clarity at all to the entire explanation of what "centrifugal force" means.

The only way that a planet's force on the sun could be called centrifugal is if you ignore the fact that the sun and other planets/asteroids etc are actually rotating around the centre of mass of the solar system. The pull of the earth on the sun is NOT centrifugal in an inertial frame of reference. So if it is "centrifugal" it is because it is seen as force in the direction away from the perceived centre of rotation (the centre of the sun) in the non-inertial frame of reference of the sun. That is the fictitious centrifugal force.

As far as the swinging ball is concerned, the authors do no talk about the force of the ball on the rope. They talk about the force of the ball on the person. For a person to be swinging a ball the person has to rotate about the common centre of mass. For a small ball it may be hard to see this. But look at how an Olympic hammer thrower has to lean backward as he swings the hammer ball. The centre of rotation is between the thrower and the ball and both rotate around it.

AM