Is the concept of reactive centrifugal force valid?

[Andrew Mason]

Wrong. If one assumes an inertial frame, then there are no inertial forces, per definition. Whether the inertial frame assumption is valid is another question, and depends what you want to investigate.


Wrong. The "reactive centrifugal force" is a consequence of Newtons 3rd Law which does not apply to inertial forces.

If you assume that a non-inertial frame of reference is inertial you will observe what you will interpret to be forces but which are simply inertial effects.

AM

 

[Dale]

That's physics 101: by means of a coordinate transformation I can derive the acceleration wrt that frame

Right, and what is the expression for the acceleration in that frame?

 

[harrylin]

Exactly. So the reaction to a centripetal force is a real force. Centrifugal "forces" are not real forces. So the reaction to a centripetal force cannot be a centrifugal force.

You seem to have misunderstood the point I was making.

AM

The point that I tried to make: you pretended to ask a question. However, instead you seem to be trying to make a point, and all our efforts to explain you that a centrifuge creates a real force of the clothes on the tub are wasted on you.

Here's my last try, centrifugal:
http://dictionary.reference.com/browse/centrifugal

Good luck
Harald

 

[harrylin]

I also look forward to his refutation of Einstein's modern view.

Einstein's view is not modern anymore. See the physics FAQ: "modern usage demotes the uniform "gravitational" field back to its old status as a pseudo-field"
http://www.desy.de/user/projects/Physics/Relativity/SR/TwinParadox/twin_gr.html

 

[A.T.]

I think this is partly a semantic problem.

I agree. Some seem totally stuck at this "centrifugal" specifier in "reactive centrifugal force", which is not important at all, but rather a trivial additional bit of information. But it seems to cause more confusion than it's worth.

 

[A.T.]

If you assume that a non-inertial frame of reference is inertial you will observe what you will interpret to be forces but which are simply inertial effects.

Yes, but the "reactive centrifugal force" is not such a force. It appears in all reference frames. If the reaction to centripetal force is not acting away from the rotation center, then the term "reactive centrifugal force" is simply not used, or at least not with the "centrifugal" specifier.

 

[harrylin]

I agree. Some seem totally stuck at this "centrifugal" specifier in "reactive centrifugal force", which is not important at all, but rather a trivial additional bit of information. But it seems to cause more confusion than it's worth.

Yes, it seems to be a debate between language purists ("centrifugal" has a precise generic meaning) and jargon purists ("centrifugal force" can only mean what is in vogue).

 

[harrylin]

Right, and what is the expression for the acceleration in that frame?

See Wikipedia*; I asked you how you derive the path of your inertial object with the use of fictive forces.

*http://en.wikipedia.org/wiki/Fictitious_forces#Rotating_coordinate_systems

 

[Andrew Mason]

The point that I tried to make: you pretended to ask a question. However, instead you seem to be trying to make a point, and all our efforts to explain you that a centrifuge creates a real force of the clothes on the tub are wasted on you.

My question was: am I missing something? You are persuading me that I wasn't.

If you put the washing machine in space and put it in spin cycle to spin the clothes, what happens? (let's assume there is electrical power somehow and let's assume that the machine is much heavier than the drum and clothes). The drum containing the clothes spins. But the rotating drum and clothes causes the washing machine to prescribe a circular motion about a point at or very close to the centre of the post on which the drum is centred (depending on how evenly the mass is distributed). In fact, both the drum and the rest of the machine are rotating (differently - at different angular speeds) about a common point. There is no centrifugal reaction force. There are only centripetal forces. The centripetal forces all sum to zero, since there is no net force on the machine as a whole. Where is the centrifugal force (I did not say centrifugal effect)?

Now keep increasing the mass of the washing machine until it has a mass of 6 x 10^24 kg. What, fundamentally, changes? If nothing changes fundamentally, then where does a "real" centrifugal reaction force arise?

AM

 

[K^2]

Andrew, in this case, the opposing centripetal forces are each-other's reaction forces. Reaction force is just another name for a constraint force. You constrain the clothes to move along the curve. Hence the force on whatever provides the constraint. Nothing else to it.

 

[JeffKoch]

Einstein's view is not modern anymore. See the physics FAQ: "modern usage demotes the uniform "gravitational" field back to its old status as a pseudo-field"
http://www.desy.de/user/projects/Physics/Relativity/SR/TwinParadox/twin_gr.html

You'll have to explain how your interpretation of this link refutes the point of view that in general, boiled down, there are no special frames of reference, and what is "real" and what is "pseudo" depends on which frames of reference you are comparing and which one you prefer.

 

[Dale]

See Wikipedia*; I asked you how you derive the path of your inertial object with the use of fictive forces.

*http://en.wikipedia.org/wiki/Fictitious_forces#Rotating_coordinate_systems

Exactly. So in the rotating frame we have:

m \mathbf{a}= \mathbf{F}_{\mathrm{fict}} +\mathbf{F}_{\mathrm{real}}
where
\mathbf{F}_{\mathrm{fict}} = <br /> - 2 m \boldsymbol\Omega \times \mathbf{v}_{B} - m \boldsymbol\Omega \times (\boldsymbol\Omega \times \mathbf{x}_B ) - m \frac{d \boldsymbol\Omega }{dt} \times \mathbf{x}_B

You have to use the fictitious forces in the rotating frame, otherwise you get the wrong trajectory. It doesn't matter if you do your dynamics in the inertial frame and then transform the result to the rotating frame or if you do your dynamics in the rotating frame directly. Either way the trajectory in the rotating frame has coordinate accelerations that are not attributable to the real forces and require fictitious forces to explain.

 

[Andrew Mason]

Andrew, in this case, the opposing centripetal forces are each-other's reaction forces. Reaction force is just another name for a constraint force. You constrain the clothes to move along the curve. Hence the force on whatever provides the constraint. Nothing else to it.

Exactly. The reaction force is another centripetal force. It is a real force. It is not a centrifugal force.

AM

 

[A.T.]

The reaction force is another centripetal force.

If that's the case, then you simply don't use the term "reactive centrifugal force". But in other scenarios the reaction to centripetal force is centrifugal (away from rotation center), so some use the term "reactive centrifugal force".

It is a real force. It is not a centrifugal force.

"Real" and "centrifugal" are not mutually exclusive. You have been given many examples where the real reaction force to centripetal force is centrifugal (away from rotation center):

O-------->==> +

O : mass
--- : string
>==> : rocket
+ : rotation center of the whole arrangement

Here the rocket exerts a centripetal force on the mass, and the mass exerts a centrifugal reaction force on the rocket . The reactive centrifugal force acting on the rocket is a real force that appears in every frame.

Merry-go-round

Interaction forces that obey Newtons 3rd, and appear in every reference frame:
- centripetal force on the child, by the seat
- centrifugal force on the seat, by the child

Inertial force that doesn't obey Newtons 3rd, and appears only in the rotating reference frame:
- centrifugal force on the child

 

[harrylin]

My question was: am I missing something? You are persuading me that I wasn't.

If you put the washing machine in space and put it in spin cycle to spin the clothes, what happens? (let's assume there is electrical power somehow and let's assume that the machine is much heavier than the drum and clothes). The drum containing the clothes spins. But the rotating drum and clothes causes the washing machine to prescribe a circular motion about a point at or very close to the centre of the post on which the drum is centred (depending on how evenly the mass is distributed). In fact, both the drum and the rest of the machine are rotating (differently - at different angular speeds) about a common point. There is no centrifugal reaction force. There are only centripetal forces. The centripetal forces all sum to zero, since there is no net force on the machine as a whole. Where is the centrifugal force (I did not say centrifugal effect)?

Now keep increasing the mass of the washing machine until it has a mass of 6 x 10^24 kg. What, fundamentally, changes? If nothing changes fundamentally, then where does a "real" centrifugal reaction force arise?

AM

I thought that what you were missing are the definitions of "centrifugal" and "force". However, now it seems that what you miss is more fundamental, related to the meaning of Newton's third law and the way he applied it.
Amazingly, you seem to deny that the clothes push against the drum! Perhaps it's useful if you explain what you think that Newton meant with the citations that I gave you, for your convenience here they are again (Motte's translation):

"To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts."
[..]
"This is the centrifugal force, with which the body impels the circle; and to which the contrary force, wherewith the circle continually repels the body towards the centre, is equal."Harald

 

[harrylin]

Exactly. So in the rotating frame we have:

m \mathbf{a}= \mathbf{F}_{\mathrm{fict}} +\mathbf{F}_{\mathrm{real}}
where
\mathbf{F}_{\mathrm{fict}} = <br /> - 2 m \boldsymbol\Omega \times \mathbf{v}_{B} - m \boldsymbol\Omega \times (\boldsymbol\Omega \times \mathbf{x}_B ) - m \frac{d \boldsymbol\Omega }{dt} \times \mathbf{x}_B

You have to use the fictitious forces in the rotating frame, otherwise you get the wrong trajectory. It doesn't matter if you do your dynamics in the inertial frame and then transform the result to the rotating frame or if you do your dynamics in the rotating frame directly. Either way the trajectory in the rotating frame has coordinate accelerations that are not attributable to the real forces and require fictitious forces to explain.

The starting point for you is the result of my derivation from a coordinate transformation without the use of fictitious forces: it's
a_B in the derivation on the page that I mentioned.

This coordinate acceleration is the result of (and attributed to) the rotation of the frame; it really doesn't make any sense to attribute them to fiction. And as we already have the equation of motion, there is also no reason to next introduce forces - let alone fictitious ones - for the determination of the trajectory.
The only thing to do is not forget that your frame rotates; else what you get is magic and fiction.Harald

 

[harrylin]

You'll have to explain how your interpretation of this link refutes the point of view that in general, boiled down, there are no special frames of reference, and what is "real" and what is "pseudo" depends on which frames of reference you are comparing and which one you prefer.

I didn't make the claims that you put in my mouth. In contrast, your claim concerning the use of non-inertial frames, that you "also look forward to his refutation of Einstein's modern view" sounds very much in disagreement with demoting Einstein's uniform "gravitational" field back to its old status as a pseudo-field.Harald

 

[Andrew Mason]

If that's the case, then you simply don't use the term "reactive centrifugal force". But in other scenarios the reaction to centripetal force is centrifugal (away from rotation center), so some use the term "reactive centrifugal force".


"Real" and "centrifugal" are not mutually exclusive. You have been given many examples where the real reaction force to centripetal force is centrifugal (away from rotation center):

The centrifugal effect in those examples is the result of a body's inertia. It is not a real force since it produces no acceleration.

The problem here may be with the concept of a "fixed" centre of rotation. The only fixed centre of rotation is a centre of mass. The reaction force to centripetal acceleration of mass on one side of that centre of mass is the centripetal force on the mass on the opposite side. That has to be the case in every rotation. There is no "real" centrifugal force or "reactive centrifugal force". A real centrifugal force would provide an acceleration away from the centre of mass of rotation. There is no acceleration away from the centre of mass.

AM

 

[A.T.]

It is not a real force since it produces no acceleration.

Acceleration of an object depends on the sum of all forces, not just the reactive centrifugal force, acting here on the rocket / seat. The forces on the rocket(by the mass) and on the seat(by the child) are real interaction forces, as defined in Newtons 3rd law. The net acceleration of rocket / seat is completely irrelevant for this consideration.

A real centrifugal force would provide an acceleration away from the center of mass of rotation.

Only if it was the only force acting, which is not the case in the scenarios.

 

[rcgldr]

The problem here may be with the concept of a "fixed" centre of rotation.

You could have a inertial (non-rotating) frame of reference with it's origin at center of rotation of a rotating frame of reference, assuming the center of the rotating frame does not have a linear component of acceleration.

There is no acceleration away from the centre of mass.

From an inertial frame of reference, the center of mass of a closed system can't accelerate, for example a rocket and it's expelled mass (spent fuel). If the rocket were in space free of external forces, and using it's engine to move in a circular path, then the rocket would experience centripetal force, and the exhaust, centrifugal force. In a frame of reference centered at the center of the circular path and rotating at the same speed as the rocket, the rocket would appear to be at rest, and the exhaust (and center of mass of rocket and exhaust) would appear to be moving "outwards".

 

[JeffKoch]

The centrifugal effect in those examples is the result of a body's inertia. It is not a real force since it produces no acceleration.

Only if you aren't in the rotating frame. If you are sitting on the merry-go-round, there is indeed a force, you will accelerate if the force is not balanced e.g. by you clinging to the pole that's impaling your wooden horsey, and if you do move then the force will have done work. If it looks like a duck, walks like a duck, and quacks like a duck...

 

[A.T.]

Only if you aren't in the rotating frame.

No, we are not talking about the inertial centrifugal force in the in the rotating frame. We are talking about the reactive centrifugal force that acts on a different object and appears in every frame.

See scenarios here:
https://www.physicsforums.com/showpost.php?p=3470239&postcount=74

 

[Dale]

The starting point for you is the result of my derivation from a coordinate transformation without the use of fictitious forces: it's
a_B in the derivation on the page that I mentioned.

Obviously. Nobody is saying that there are fictitious forces in the inertial frame.

This coordinate acceleration is the result of (and attributed to) the rotation of the frame; it really doesn't make any sense to attribute them to fiction.

I don't know what you are talking about. They are named "fictitious forces" they aren't attributed to fiction. I don't even know how you could attribute a force to a body of literature. Perhaps you just don't like the term "fictitious forces" and would prefer the term "inertial forces" or "pseudo forces". My preference is "inertial forces".

And as we already have the equation of motion, there is also no reason to next introduce forces - let alone fictitious ones - for the determination of the trajectory.

The point is that the equation of motion is not f=ma, there are additional terms, and those additional terms are the fictitious forces. It doesn't matter if you start with the equations of motion in the non-inertial frame, or if you transform from the inertial frame into the non-inertial frame. Once you get to the non-inertial frame there are fictitious forces. You cannot remove those fictitious forces and correctly determine the trajectory.

 

[Andrew Mason]

You could have a inertial (non-rotating) frame of reference with it's origin at center of rotation of a rotating frame of reference, assuming the center of the rotating frame does not have a linear component of acceleration.

Provided the centre of rotation was also the centre of mass of the rotating system. For example in the earth/moon system, the inertial frame of reference (ignoring the orbit around the sun and gravitational effects of other planets) would be the centre of mass of the earth/moon system which is between the centre of the Earth and centre of the moon.

From an inertial frame of reference, the center of mass of a closed system can't accelerate, for example a rocket and it's expelled mass (spent fuel). If the rocket were in space free of external forces, and using it's engine to move in a circular path, then the rocket would experience centripetal force, and the exhaust, centrifugal force. In a frame of reference centered at the center of the circular path and rotating at the same speed as the rocket, the rocket would appear to be at rest, and the exhaust (and center of mass of rocket and exhaust) would appear to be moving "outwards".

How would you get the rocket to prescribe a circular path without using tangental rocket thrust?

AM

 

[A.T.]

How would you get the rocket to prescribe a circular path without using tangental rocket thrust?

Circular motion at constant speed requires only a centripetal acceleration which acts radially. No tangential thrust is needed once the rocket has the right linear and angular velocity.

 

[Andrew Mason]

Circular motion at constant speed requires only a centripetal acceleration which acts radially. No tangential thrust is needed once the rocket has the right linear and angular velocity.

That is not a problem if the rotation is about the centre of mass. How can the rocket rotate about a point other than its centre of mass and still have angular momentum being conserved here? You have to take into account the rocket gases flying out the rear of the rocket.

AM

 

[Andrew Mason]

Only if you aren't in the rotating frame. If you are sitting on the merry-go-round, there is indeed a force, you will accelerate if the force is not balanced e.g. by you clinging to the pole that's impaling your wooden horsey, and if you do move then the force will have done work. If it looks like a duck, walks like a duck, and quacks like a duck...

I am not trying to suggest that the centrifugual effect is imagined. It is quite apparent. It is just that it is not a real force.

But my point is that the reaction force to the centripetal force that is applied to the merry-go-round rider is not a centrigufal reaction force. Rather it is always an equal and opposite centripetal force toward the centre of mass of the rotating system. If the centre of rotation of the merry-go-round is its centre of mass, then there is no force on the Earth and the reaction force to the centripetal force on the rider is the centripetal force keeping mass on the opposite side of the merry-go-round rotating.

AM

 

[A.T.]

How can the rocket rotate about a point other than its centre of mass and still have angular momentum being conserved here? You have to take into account the rocket gases flying out the rear of the rocket.

Yes, if you take into account the rocket gases the total momentum is conserved, while the rocket rotates around some point, other than the rockets COM. And the force applied to the gases by the rocket is called reactive centrifugal force, because it points away from that center of rotation.

 

[Doc Al]

But my point is that the reaction force to the centripetal force that is applied to the merry-go-round rider is not a centrigufal reaction force. Rather it is always an equal and opposite centripetal force toward the centre of mass of the rotating system.

Would you not agree that the merry-go-round must exert a centripetal force on the rider? If so, then the rider exerts and equal and opposite (in this case, outward) force on the merry-go-round. Simple as that. (Call that force what you will.)

 

[A.T.]

But my point is that the reaction force to the centripetal force that is applied to the merry-go-round rider is not a centrigufal reaction force.

The force on the seat, by the rider is centrifugal (= away from the center of rotation).

Rather it is always an equal and opposite centripetal force toward the centre of mass of the rotating system.

The specifiers centripetal & centrifugal refer to the center of rotation, not to the center of mass of some closed system for which momentum is conserved.

But if you are so obsessed with the center of mass, just put a second rider of equal weight on the opposite side. Both riders will exert reactive centrifugal forces on their seats. These forces point away from :
- the center of rotation
- the center of mass
You can't get more centrifugal than that.