# Reactive Centrifugal Force

#### Andrew Mason

Homework Helper
I came across this http://en.wikipedia.org/wiki/Reactive_centrifugal_force" [Broken]

I think this is Wikipedia nonsense. There is only one centrifugal "force" and it is the inertial effect or "pseudo force" or "fictitious force" observed in a non-inertial frame of reference.

The authors of these articles seem to be forgetting that in the interaction between two bodies, A and B in which A applies a force to B the reactive force (Newton's Third Law) acts on A not on B. So in the case of the moon in gravitational orbit around the earth, the reaction to the centripetal force of the earth on the moon is the gravitational force of the moon on the earth, which is TOWARD the centre of mass of the moon-earth system. In simple terms, the reaction force to a centripetal force is itself a centripetal force. It is not directed away from the centre. So calling it a centrifugal reaction force is simply wrong.

Am I missing something?

AM

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#### rcgldr

Homework Helper
In simple terms, the reaction force to a centripetal force is itself a centripetal force.
Not always, that wiki article for reactive centrifugal force shows an example where the reactive force results in an outwards force on a "immovable post". There was a prior diagram that was more complicated, but I think did a better job, showing the Newton third law pair of forces at the interface between string and ball, the string exerts a centripetal force on the ball, and the ball exerts a reactive centrifugal force on the string. Another example would be a rocket in space where there are no external forces. The rocket is using it's engine to travel in a circular path. At the engine, there's a centripetal force on the rocket and an equal and opposing centrifugal force on the ejected fuel mass, and both forces could be considered "reactive" forces in this case.

The wiki article for centrifugal force now includes both usages:

http://en.wikipedia.org/wiki/Centrifugal_force

There had been an ongoing debate about terminology, but I had the impression it was settled, at least with the people involved with the Wiki articles. Take a look at the discussion pages if you want to see the history of this debate. I don't think anyone will confuse the meanings of fictitious centrifugal force with reactive centrifugal force regardless of context as long as the qualifiers fictitious and reactive are used.

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#### A.T.

There is only one centrifugal "force"
"Centrifugal" just means "away from the center". It depends on the contex which force is actually meant.

and it is the inertial effect or "pseudo force" or "fictitious force" observed in a non-inertial frame of reference.
That is one very common use of term. Apparently the Wiki authors came to the conclusion that the other one is quite common too.

The authors of these articles seem to be forgetting that in the interaction between two bodies, A and B in which A applies a force to B the reactive force (Newton's Third Law) acts on A not on B. So in the case of the moon in gravitational orbit around the earth, the reaction to the centripetal force of the earth on the moon is the gravitational force of the moon on the earth, which is TOWARD the centre of mass of the moon-earth system. In simple terms, the reaction force to a centripetal force is itself a centripetal force. It is not directed away from the centre. So calling it a centrifugal reaction force is simply wrong.
I agree that article is suboptimal, because it implies that the reaction to centripetal force is always centrifugal, which is not the case as you point out.

#### rcgldr

Homework Helper
I agree that article is suboptimal, because it implies that the reaction to centripetal force is always centrifugal, which is not the case as you point out.
The main exception is when a force between two bodies does not involve physical contact between the two bodies. This would include gravity, electrical, and magnetic forces, so a lot of exceptions. Perhaps this could be mentioned in the discussion page and the article updated to note this exception.

#### Andrew Mason

Homework Helper
The main exception is when a force between two bodies does not involve physical contact between the two bodies. This would include gravity, electrical, and magnetic forces, so a lot of exceptions. Perhaps this could be mentioned in the discussion page and the article updated to note this exception.
But "contact" forces are simply electromagnetic forces.

Consider a rotating mass whose centripetal force is supplied by a mechanical force supplied by tension in a rope: the molecules in the end of the rope in "contact" with the rotating object apply a centripetal force to the object through electromagnetic attractive bonds. The rotating object, in turn, exerts an equal and opposite electromagnetic attractive force on the molecules in the rope. This chain of electromagnetic force is repeated all the way down the string to the pole to which the rope is attached. The molecules in the end of the pole then apply electromagnetic force to the rope molecules that are in contact with the pole. The chain of electromagnetic force repeats all the way down to, and through, the earth to which the pole is attached.

Ultimately (let's just ignore the rope's mass for simplicity) the rotating object exerts an electromagnetic pull on the earth and the earth exerts an electromagnetic pull on the mass toward a common point located somewhere in between the centre of mass of the earth and the centre of mass of the rotating object.

So this idea that there is a "reactive centrifugal force" that is different than the "pseudoforce that appears in a noninertial, rotating frame of reference" seems to me to be incorrect. The centrifugal "force" is the same inertial effect in all cases.

AM

#### rcgldr

Homework Helper
But "contact" forces are simply electromagnetic forces.
True, but a 2 body system where objects orbit due to gravity is different than a 2 body system with no gravity and the objects orbit due to a string that connects them. In the gravity case, both objects only experience centripetal force. In the string case, each string end experiences a reactive centrifugal force from the body attached to that end of the string.

So this idea that there is a "reactive centrifugal force" that is different than the "pseudoforce that appears in a noninertial, rotating frame of reference" seems to me to be incorrect.
It's my understanding that "pseudo forces" in a rotational frame may correspond to non-forces (zero force) in an inertial frame, and are used to compensate for the rotating frame. Gravity would be a real force in an inertial or rotational frame. In a frame that rotates at the same speed as two objects in a circular orbit due to gravity, the two objects appear at rest within the rotational frame. Gravity is a real force, and fictitious centrifugal force is what keeps those objects from accelerating towards each other. For each object, gravity + fictitious centrifugal force = 0 in this frame. For the string case, tension would be real, and fictitious centrifugal force would be keeping the objects apart, but in this case the centrifugal force is real (from the string's perspective).

A better example would be a time lapse camera at either north or south pole of the earth oriented straight "up". The stars are at rest (zero force) in an inertial frame, but appear to be orbiting from the camera's rotating frame of reference. In this case, fictitious corilios froce is double in magnitude and opposite of fictitious centrifugal force, resulting in apparent fictitious centripetal force.

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#### A.T.

Ultimately (let's just ignore the rope's mass for simplicity) the rotating object exerts an electromagnetic pull on the earth and the earth exerts an electromagnetic pull on the mass toward a common point located somewhere in between the centre of mass of the earth and the centre of mass of the rotating object.
If you use the rest frame of Earth the reaction to the centripetal force is a real centrifugal force acting on the central pole. But it could just as well be a rocket in space that creates the centripetal force, and experiences an centrifugal reactive froce:

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.
So this idea that there is a "reactive centrifugal force" that is different than the "pseudoforce that appears in a noninertial, rotating frame of reference" seems to me to be incorrect.
It is a direct consequence of Newtons 3rd Law. The reaction to a real centripetal force is also a real force that appears in inertial frames, and is sometimes centrifugal.

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#### Andrew Mason

Homework Helper
True, but a 2 body system where objects orbit due to gravity is different than a 2 body system with no gravity and the objects orbit due to a string that connects them. In the gravity case, both objects only experience centripetal force. In the string case, each string end experiences a reactive centrifugal force from the body attached to that end of the string.
I don't think that is correct. The only force acting on the rope is the centripetal force required to keep the rope rotating. If you ignore the mass of the rope, there would be no net force on the rope at all.

Since the pole is rigid and not rotating (or otherwise accelerating), there is no net force on the pole. There is only a net force on the earth (assuming it is rigid) and that force is equal to its mass times the acceleration of its centre of mass and it is directed toward the centre of the object/earth rotation (which, due to the mass of the earth is very near its centre of mass).

It's my understanding that "pseudo forces" in a rotational frame may correspond to non-forces (zero force) in an inertial frame, and are used to compensate for the rotating frame. Gravity would be a real force in an inertial or rotational frame. In a frame that rotates at the same speed as two objects in a circular orbit due to gravity, the two objects appear at rest within the rotational frame. Gravity is a real force, and fictitious centrifugal force is what keeps those objects from accelerating towards each other. For each object, gravity + fictitious centrifugal force = 0 in this frame. For the string case, tension would be real, and fictitious centrifugal force would be keeping the objects apart, but in this case the centrifugal force is real (from the string's perspective).
The string can only experience a real net force if it has mass and if it is accelerating. That force would vary along the length of the rope since the acceleration is a function of the distance from the centre (ie radius). If we say the mass is negligible, the force on the rope is negligible.

All I am saying is that the centrifugal "force" that the rope observes is the same kind of centrifugal force that the rotating object at the end of the rope feels.

AM

#### A.T.

Since the pole is rigid and not rotating (or otherwise accelerating), there is no net force on the pole.
Who cares about the net force on the pole? We are only interested in the force from the string on the pole, which is a real force, and is centrifugal in the rest frame on the pole. This force is called reactive centrifugal force. The fact that there are other forces on the pole, yielding a zero net force, is completely irrelevant here.

All I am saying is that the centrifugal "force" that the rope observes is the same kind of centrifugal force that the rotating object at the end of the rope feels.
No. In the non rotating rest frame of the pole there is no centrifugal force at the rotating object at the end of the rope. But there still is a real centrifugal force at the pole from the string.

#### rcgldr

Homework Helper
A 2 body system ... no gravity ... where objects orbit due to a string that connects them.
The only force acting on the rope is the centripetal force required to keep the rope rotating. If you ignore the mass of the rope, there would be no net force on the rope at all.
The forces exerted at each end of the string are equal and opposing, so there is no net force on the string, but those "outward" forces do produce a tension in the string.

#### harrylin

I came across this http://en.wikipedia.org/wiki/Reactive_centrifugal_force" [Broken]

I think this is Wikipedia nonsense. There is only one centrifugal "force" and it is the inertial effect or "pseudo force" or "fictitious force" observed in a non-inertial frame of reference.

The authors of these articles seem to be forgetting that in the interaction between two bodies, A and B in which A applies a force to B the reactive force (Newton's Third Law) acts on A not on B. So in the case of the moon in gravitational orbit around the earth, the reaction to the centripetal force of the earth on the moon is the gravitational force of the moon on the earth, which is TOWARD the centre of mass of the moon-earth system. In simple terms, the reaction force to a centripetal force is itself a centripetal force. It is not directed away from the centre. So calling it a centrifugal reaction force is simply wrong.

Am I missing something?

AM
Yes, what you write is simply wrong - and even in several ways.

Centrifugal force is directed away from the centre (such as the force that your wash exerts on your washing machine), and the only proper use of such a term is if it points to a real force. And inertial forces are not "pseudo" at all but very real. The third law of Newton does not concern two centripetal forces in the way you describe, as then the earth and the moon would crash into each other - you actually forgot the inertial centrifugal forces that balance the centripetal forces!

As many people use the same expression for a pseudo force, quite some people want to ban that term altogether - which would leave us without a translation and proper understanding of some of Newton's Principia. :tongue2:

PS, from the "horse's mouth": "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."
- http://gravitee.tripod.com/booki2.htm

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#### Andrew Mason

Homework Helper
The forces exerted at each end of the string are equal and opposing, so there is no net force on the string, but those "outward" forces do produce a tension in the string.
Yes. One end the force pulls the object toward the earth and the other end pulls the earth toward the object. Both pulling forces are centripetal forces. It is a little more difficult to see with the earth because the earth does not appear to accelerate. But it does - just a tiny little bit.

AM

#### Andrew Mason

Homework Helper
Yes, what you write is simply wrong - and even in several ways.

Centrifugal force is directed away from the centre (such as the force that your wash exerts on your washing machine), and the only proper use of such a term is if it points to a real force. And inertial forces are not "pseudo" at all but very real.
So what is your definition of force? The one I use is F = dp/dt. What "force" is causing the water to move to the outside of a spinning washer? Does a water droplet that leaves a piece of clothing accelerate?

The third law of Newton does not concern two centripetal forces in the way you describe, as then the earth and the moon would crash into each other - you actually forgot the inertial centrifugal forces that balance the centripetal forces!
I take it you are not serious..?

As many people use the same expression for a pseudo force, quite some people want to ban that term altogether - which would leave us without a translation and proper understanding of some of Newton's Principia. :tongue2:

PS, from the "horse's mouth": "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."
- http://gravitee.tripod.com/booki2.htm
The centrifugal "force" that is experienced by the rotating observer (so long as he is not rotating because he is in gravitational orbit) is equal and opposite to the centripetal force measured by an inertial observer. But this centrifugal "force" is apparent to him only because he is not in an inertial frame of reference.

I am not trying to say anything new about centrifugal "force". I am just trying to show that there are not two distinct types of centrifugal "force".

AM

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#### harrylin

So what is your definition of force? The one I use is F = dp/dt. What "force" is causing the water to move to the outside of a spinning washer? Does a water droplet that leaves a piece of clothing accelerate?

I take it you are not serious..?

The centrifugal "force" that is experienced by the rotating observer (so long as he is not rotating because he is in gravitational orbit) is equal and opposite to the centripetal force measured by an inertial observer. But this centrifugal "force" is apparent to him only because he is not in an inertial frame of reference.

I am not trying to say anything new about centrifugal "force". I am just trying to show that there are not two distinct types of centrifugal "force".

AM
Like Newton I do not use fictitious forces but only real forces; I do favour a ban on confused "rotating observers" with their fictitious forces. Newton did not use such fictions, instead he used reference systems in rectilinear motion. I have the same definitions of force as Newton and as you saw, according to him - if he'd lived to see one - it is the centrifugal force with which the water impels the circular tub. Surely you do admit that the clothes are not pushing towards the centre of the tub!

If you don't see the error of your example of two centripetal forces without a reaction force, just compare it with the following situation: two non-rotating objects attract each other with a force F.
1. What happens to them, and what is the cause that they do not hit each other at infinite speed?
2. Next, what force causes at sufficient rotation speed that the two objects do not collide? Do you really think that this is a centripetal force?

#### Andrew Mason

Homework Helper
Like Newton I do not use fictitious forces but only real forces; I do favour a ban on confused "rotating observers" with their fictitious forces. Newton did not use such fictions, instead he used reference systems in rectilinear motion. I have the same definitions of force as Newton and as you saw, according to him - if he'd lived to see one - it is the centrifugal force with which the water impels the circular tub. Surely you do admit that the clothes are not pushing towards the centre of the tub!
It depends on what you mean by the clothes pushing. Their momentum vector is constantly changing. They are being constantly pushed toward the centre of rotation.

If you don't see the error of your example of two centripetal forces without a reaction force, just compare it with the following situation: two non-rotating objects attract each other with a force F.
1. What happens to them, and what is the cause that they do not hit each other at infinite speed?
They will hit each if they have no angular momentum. They will not hit at infinite speed. Meteors collide with earth all the time with less than infinite speed.

2. Next, what force causes at sufficient rotation speed that the two objects do not collide? Do you really think that this is a centripetal force?
No force is required. Just initial angular momentum. That is how the earth came to orbit the sun, for example. The only forces acting on the earth are from other gravitating bodies such as the sun and moon and other planets. None of these are centrifugal.

AM

#### rcgldr

Homework Helper
The forces exerted at each end of the string are equal and opposing, so there is no net force on the string, but those "outward" forces do produce a tension in the string.
Yes. One end the force pulls the object toward the earth and the other end pulls the earth toward the object. Both pulling forces are centripetal forces.
My example wasn't one based on gravity, but instead one where gravity can be ignored and the primary centripetal force is the string. Each end of the string pulls inwards on one of the two bodies, and each body pulls outwards on one of the ends of the string. I and some others call these force pairs centripetal and reactive centrifugal.

It's not much different than a linear acceleration situation where a force accelerates a massless string attached to some object. You have equal and opposing forces, the force that accelerates the system, and the opposing reactive force from the accelerating object.

The third law of Newton does not concern two centripetal forces ... earth and moon.
In a 2 body system, where gravity is causing the objects to orbit in a circular path, the Newton third law pair of forces is the gravity force that each object exerts on the other. From each object's perspective, the gravity force that accelerates each object is towards the center of the orbit, so both gravity forces are centripetal. The situations changes if a string is supplying the force instead of gravity, in which case the objects exert reactive centrifugal force on the ends of the string.

#### Andrew Mason

Homework Helper
In a 2 body system, where gravity is causing the objects to orbit in a circular path, the Newton third law pair of forces is the gravity force that each object exerts on the other. From each object's perspective, the gravity force that accelerates each object is towards the center of the orbit, so both gravity forces are centripetal.
So we agree there is no centrifugal "force" observed.

The situations changes if a string is supplying the force instead of gravity, in which case the objects exert reactive centrifugal force on the ends of the string.
The string is used to conduct the force, but it does not supply it.

What if the string is not attached to a large mass (such as the earth)? eg. a 1 kg mass tethered by a string to a 10 kg mass. The two masses would rotate or precess about a common point. Where is the centrifugal reactive force? How is it away from that common point?

The only difference is that in the above case the larger mass is only 1 order of magnitude more massive than the "rotating" object instead of 24 orders of magnitude greater. The principles are still the same.

AM

#### A.T.

What if [some scenario]. Where is the centrifugal reactive force?
What is actually your point? That there are some scenarios/reference frames where there is no centrifugal reactive force. That was never denied. But there are other scenarios where the term centrifugal reactive force is applicable. I gave you a very simple one in post #7.

What if the string is not attached to a large mass (such as the earth)? eg. a 1 kg mass tethered by a string to a 10 kg mass. The two masses would rotate or precess about a common point. Where is the centrifugal reactive force?
In the rest frame of the 10 kg mass, for example.

Note: The fact that this frame is not inertial, does not mean that the centrifugal reactive force is an inertial force. It is a real force that acts on the 10 kg mass in every frame. But the specifier "centrifugal" applies to this force only in some frames. The senario in post #7 has a centrifugal reactive force in an inertial frame.

#### Andrew Mason

Homework Helper
What is actually your point? That there are some scenarios/reference frames where there is no centrifugal reactive force. That was never denied. But there are other scenarios where the term centrifugal reactive force is applicable. I gave you a very simple one in post #7.
I wish to make only one point: there is no material fundamental distinction between "centrifugal force" and "centrifugal reaction force". That distinction is made by the Wikipedia articles to which I refer. The "centrifugal reaction force" is no more "real" than any other centrifugal force. The are both inertial effects and not real forces.

In the rest frame of the 10 kg mass, for example.

Note: The fact that this frame is not inertial, does not mean that the centrifugal reactive force is an inertial force. It is a real force that acts on the 10 kg mass in every frame. But the specifier "centrifugal" applies to this force only in some frames. The senario in post #7 has a centrifugal reactive force in an inertial frame.
That is where I disagree. In the inertial frame of the centre of mass, both masses experience a force toward a common point. That point does not change.

The rate of change in momentum of the 10 kg mass as observed in an inertial frame must be equal in magnitude and opposite in direction to the rate of change of momentum of the 1 kg mass. Both forces are always directed toward a fixed point in the rest frame of the centre of mass of the two masses. Because if not, the forces (the force on the 1 kg mass and the force on the 10 kg mass) do not sum to zero (there being no external forces) and this would violate Newton's third law.

AM

#### rcgldr

Homework Helper
There is no material fundamental distinction between "centrifugal force" and "centrifugal reaction force".
Trying to find a case where there is a difference is difficult, but I think what I describe next is an example where there is a difference.

A frictionless and very long cylinder is rotating end over end at a constant rate in space, with it's mid point attached to a very huge mass at rest in an inerital frame (so a virtually immovable center point), with a power source to maintain the cylinders rate of rotation. There's a relatively light object inside the cylinder, initially slightly offset from the center, that slides outwards over time due to the (ever increasing) tangental force from the inner walls of the cylinder. From an inertial frame of reference, there are no centripetal or centrifugal forces involved, only a tangental force. From a frame of reference that rotates at the same speed as the cylinder, there's a truly "fictitious" centrifugal force.

One possible issue with this scenario is although the force is always tangental at any moment in time, what is a tangental force at one point in time is an outwards force at a bit later moment in time. I'm not sure if that force should be considered to have a centrifugal force component over time. If it is considered as such, then this would be a case where the centrifugal force compnent is real, and the rate of outwards acceleration component would correlate to a centripetal reaction force component.

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"Reactive Centrifugal Force"

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