Is the concept of reactive centrifugal force valid?

[A.T.]

Good luck in trying to explain to a physics student why physicists do not call that a centripetal force.

That is simple: Because it points away from the center of rotation.

BTW: Here is a nice table listing the differences between the real and inertial centrifugal force.
http://en.wikipedia.org/wiki/Reactive_centrifugal_force#Relation_to_inertial_centrifugal_force

 

[Andrew Mason]

That is simple: Because it points away from the center of rotation.

Which centre of rotation? There are two centres of rotation about which both masses are prescribing circular motion.

BTW: Here is a nice table listing the differences between the real and inertial centrifugal force.
http://en.wikipedia.org/wiki/Reactive_centrifugal_force#Relation_to_inertial_centrifugal_force

Interesting that you should point that out in support of your argument. There are several incorrect or, at best, misleading statements there.

This statement, for example, relating to the "reactive centrifugal force" suggests that the body upon which the "centrifugal reaction force" acts is not undergoing centripetal acceleration itself, which would not be correct:

The object(s) causing the curved motion, not upon the body in curved motion

The chart also says that the "centrifugal reaction force" is exerted by bodies moving in
curved paths. While that is true, this reaction force (which, for reasons I have given, I say is not centrifugal) is not exerted by all masses moving in curved paths. It is not exerted by a mass moving in a curved path that is outermost from the centre of rotation.

AM

 

[Dale]

This statement, for example, relating to the "reactive centrifugal force" suggests that the body on which the "centrifugal reaction force" is not undergoing centripetal acceleration itself, which would not be correct:

That is not what it says.

The chart also says that the "centrifugal reaction force" is exerted by bodies moving in
curved paths. While that is true, this reaction force (which for reasons I have given in a I say is not centrifugal) is not exerted by all masses moving in curved paths. It is not exerted by a mass moving in a curved path that is outermost from the centre of rotation.

This is not correct, in your recent example the mass exerts a centrifugal reaction force on the rope and the mass is outermost.

 

[A.T.]

Which centre of rotation?

The same that "centripetal force" refers to.

This statement, for example, relating to the "reactive centrifugal force" suggests that the body on which the "centrifugal reaction force" is not undergoing centripetal acceleration itself, which would not be correct:

No, from the context it's clear that "the body in curved motion" specifically means the body on which the paired centripetal force acts. It simply restates that 3rd law pairs act on two different objects.

 

[Andrew Mason]

This is not correct, in your recent example the mass exerts a centrifugal reaction force on the rope and the mass is outermost.

So explain to me (perhaps again - if so I apologize for being so boneheaded) in the passenger/space station example, how the space station exerts a reactive centrifugal force on anything.

The space station is prescribing curved (rotational) motion about the passenger/space station centre of mass. What is causing that centripetal acceleration? There is nothing else besides the passenger to cause the centre of mass of the space station to accelerate. So according to this http://en.wikipedia.org/wiki/Reactive_centrifugal_force#Relation_to_inertial_centrifugal_force", the space station must exert a centrifugal reaction force on the passenger. Where is it?

AM

 

[Andrew Mason]

Regarding the Wikipedia article which spawned this whole thread. In the first sentence of the first paragraph it says "This reactive force is directed away from the center of rotation". Which I think we all agree is incorrect in general since there are cases where the reaction to a centripetal force is also centripetal (e.g. two bodies under a central force).

Unfortunately, that sentence has a reference which is clearly incorrect:
http://books.google.com/books?id=Qn...nepage&q="reactive centrifugal force"&f=false

Does anyone have a reference that we could use to counteract this and point out the fact that sometimes the reaction to a centripetal force is also centripetal. We can then put a "there is controversy" section in.

This was what prompted my initial post on this thread. I doubt that there are many physics texts out there that use the term. In four years of university physics I never encountered reactive centrifugal force in texts or in lectures. Mind you, that was a while ago and we never went into the example of two radially tethered balls rotating about a central point.

AM

 

[Dale]

So explain to me (perhaps again - if so I apologize for being so boneheaded) in the passenger/space station example, how the space station exerts a reactive centrifugal force on anything.

The space station is prescribing curved (rotational) motion about the passenger/space station centre of mass. What is causing that centripetal acceleration? There is nothing else besides the passenger to cause the centre of mass of the space station to accelerate. So according to this http://en.wikipedia.org/wiki/Reactive_centrifugal_force#Relation_to_inertial_centrifugal_force", the space station must exert a centrifugal reaction force on the passenger. Where is it?

The centrifugal force is exerted by the astronaut (who moving in a curved path) upon the space station (which is the object causing the curved motion of the astronaut). As we have discussed, there isn't always a reactive centrifugal force, but AFAIK whenever there is it does follow the chart. The chart is correct.

 

[Andrew Mason]

The centrifugal force is exerted by the astronaut (who moving in a curved path) upon the space station (which is the object causing the curved motion of the astronaut). As we have discussed, there isn't always a reactive centrifugal force, but AFAIK whenever there is it does follow the chart. The chart is correct.

So only one of the two objects in this example exerts a centrifugal reactive force? So what is the reaction force for the centripetal force supplied TO the space station (ie the one that causes its centre of mass to accelerate toward the centre of mass of the station/passenger system)? What is it exerted on and what direction is it?

AM

 

[Dale]

There is only one pair of forces in that example. The centripetal force on the astronaut and the centrifugal force on the space station. Because of the geometry, the centrifugal force causes the centripetal acceleration of the space station. There is no centripetal force applied to the space station.

 

[A.T.]

So what is the reaction force for the centripetal force supplied TO the space station (ie the one that causes its centre of mass to accelerate toward the centre of mass of the station/passenger system)?

There is no individual centripetal interaction force acting on the space station. Only the net force on the space station is centripetal, hence centripetal acceleration of it's center of mass.

The reactive centrifugal force and the net force on the station happen to have the same direction & magnitude in this special case, but they still have different points of application:
- The reactive centrifugal force acts at the contact patch with the astronaut
- The net force is assumed to act at the center of mass
Since those two points of application lie on opposite sides of the center of rotation, one force is centrifugal and one is centripetal.

In more general terms: The net force does not contain all the information about the individual forces, it ignores their points of application. So even if there is just one individual force acting, the net force is not equivalent to that single force if that single force doesn't act at the center of mass.

 

[harrylin]

So only one of the two objects in this example exerts a centrifugal reactive force? So what is the reaction force for the centripetal force supplied TO the space station (ie the one that causes its centre of mass to accelerate toward the centre of mass of the station/passenger system)? What is it exerted on and what direction is it?

AM

First (as I originally understood your question), ignoring the little imbalance caused by the astronaut, there is no centripetal force on the space station. When it rotates, its molecular adhesion forces allow the space station to stay in one piece and to accelerate the astronaut. In order to maintain the centripetal acceleration of the astronaut by the space station, the floor of the space station must exert a centripetal force on the astronaut. And of course, the astronaut exerts a centrifugal counter force on the floor of the space station.

But as you correctly noticed, it is a quite a bit trickier when we look, not at the motion of the floor, but at the motion of the centre of mass of the space station. Good one.

As you indicated, the centrifugal force that is exerted on the floor will cause a slight imbalance that results in a little circular motion of the centre of mass of the space station. It can only be the centrifugal force that is exerted on one point on the floor that takes care of the centripetal acceleration of the centre of mass of the space station (in the same direction: for example the centre of mass of the space station can be slightly to the left of the centre of the system while the astronaut is exerting centrifugal pressure on the floor on the right).

 

[rcgldr]

Regarding the Wikipedia article which spawned this whole thread. In the first sentence of the first paragraph it says "This reactive force is directed away from the center of rotation".

In both Wiki articles, that statement is made in reference to a mass being accelerated by direct contact (implied) with some other object, not by a field (electrical, gravitational, magnetic):

This centripetal acceleration is caused by a force exerted on the mass by some other object. In accordance with Newton's third law of motion, the mass exerts an equal and opposite force on the object.

So the statements as written are OK, but it should be noted that when centripetal acceleration is due to a field (and not direct contact with an object), then both forces are usually centripetal. This has already been mentioned in the wiki discussion page for centrifugal force.

 

[sankalpmittal]

In both Wiki articles, that statement is made in reference to a mass being accelerated by direct contact (implied) with some other object, not by a field (electrical, gravitational, magnetic):

This centripetal acceleration is caused by a force exerted on the mass by some other object. In accordance with Newton's third law of motion, the mass exerts an equal and opposite force on the object.

So the statements as written are OK, but it should be noted that when centripetal acceleration is due to a field (and not direct contact with an object), then both forces are usually centripetal. This has already been mentioned in the wiki discussion page for centrifugal force.

If you whirl a stone tied to a string , then the restoring force of string which acts towards the centre and acts on the stone is centripetal force.

But since you know Newton's third law , there must be opposite reaction too existing in pairs. This opposite reaction is mentioned as Reactive centrifugal force. It acts on your hand equal and opposite to the direction of centripetal force.
However my text refers that opposite reaction must not be confused with the name of centrifugal force.

In rotating frame of reference , there is no centripetal force. The only force which acts is inertial centrifugal force, unlike whirling frame of reference.
Your inertia makes you stable there.

 

[D H]

In rotating frame of reference , there is no centripetal force. The only force which acts is inertial centrifugal force, unlike whirling frame of reference.

The centripetal force is a real force. It is present in all frames of reference. The centrifugal force is only present in rotating frames.

Your inertia makes you stable there.

No, it doesn't.

Care is needed here with regard to which rotating frame is being referenced. Presumably you are talking about a frame in which the moving object (moving as viewed from the point of view of an inertial frame) appears to be at rest.

What does Newton's first law tell you about the net force on an object that is at rest?