Centrifugal force and Newton 3rd law

[D H]

First I was chastized for viewing things only in an inertial reference frame. So I then viewed things in a rotating refreence frame, and now I'm guilty of only considering objects rotating with the frame. Whether I explain in inertial or rotating frames I'm excluding something!

In Newtonian mechanics, the acceleration of a fixed-mass object as viewed from the perspective an inertial reference is given by Newton's second law,
m\,\mathbf a = \mathbf{F}_{\text{ext}}
Things get just a bit hairier when things are viewed from the perspective of rotating, accelerating reference frame:
m\,\mathbf a = \mathbf{F}_{\text{ext}}<br /> \;-\; m\, \mathbf{\omega}\times(\mathbf{\omega} \times \mathbf{r})<br /> \;-\; 2 m\, \mathbf{\omega}\times \mathbf{v}<br /> \;-\; m\,\frac{d\mathbf{\omega}}{dt} \times \mathbf{r}<br />
In general, yech. Yet at times it does make more sense to use a rotating frame. We live on a rotating frame, for example. The circular restricted three body problem is also easier to solve in a rotating frame.

Every attempt to counter my view results in contradictions among the people arguing with me. Then we go off on the tangent "is gravity force REAL?"!

That was not a tangent. The gravitational force is no more "REAL" than is the centrifugal force.

By the way, gravity is REAL. Some time ago, not far from my home, a despondent jilted lover took a leap from a local bridge. The personnel who had to tend to the situation and his survivors are quite convinced that the gravitational force and acceleration acting on him was indeed real. Peace.

It was the normal force that kept the lover from sinking into the Earth at the end of the fall, not the gravitational force, that killed the despondent lover.

 

[cmos]

Every attempt to counter my view results in contradictions among the people arguing with me. Then we go off on the tangent "is gravity force REAL?"!

It would seem to me that tiny-tim, DH, and myself are more or less backing each other up with the slight deviation in our views on gravity. Perhaps I will think of this more and make a new post somewhere in the forum; my apologies for helping to start the tangent.

Can we simplify to a two body system? The moon revolves around the earth. It has a velocity tangential to its path. I know already that orbits are slightly elliptic, but the eccentricity is generally less than 0.02 so that ucm is approx. valid. The moon's force/acceleration keeping it from departing its Earth orbit is purely *centripetal*. The moon also attracts the earth. The Earth encounters a force towards the moon and like its counterpart is due to gravity. Thus gravity accounts for the centripetal force/accel and the moon's velocity is always tangential to the path.

In the moon's ref frame, it feels a force of gravity towards the Earth and is there a counter force?

Regarding the last sentence, the Newton's third law force pair is the gravitational attraction of the moon acting on the Earth and the gravitational attraction of the Earth acting on the moon. Is this what you are trying to get at?

Keeping with the two body system, let's simplify the problem to a geosynchronous satellite, i.e. a satellite that stays over the same piece of ground at all times (satellite's orbital period is equal to the Earth's rotational period).

If we analyze this system from an inertial reference frame, then yes, as you said, the centripetal acceleration will be equal to the gravitational field of the Earth. That is, the only force present is the gravitational force.

However, if we analyze this system from the non-inertial reference frame which we take to be on the satellite, what do we see? We see that the satellite does not move and we see that the Earth does not move. So from this frame of reference we see that the gravitational force due to the Earth is exactly balanced by the centrifugal force.

 

[cabraham]

It would seem to me that tiny-tim, DH, and myself are more or less backing each other up with the slight deviation in our views on gravity. Perhaps I will think of this more and make a new post somewhere in the forum; my apologies for helping to start the tangent.



Regarding the last sentence, the Newton's third law force pair is the gravitational attraction of the moon acting on the Earth and the gravitational attraction of the Earth acting on the moon. Is this what you are trying to get at?

Keeping with the two body system, let's simplify the problem to a geosynchronous satellite, i.e. a satellite that stays over the same piece of ground at all times (satellite's orbital period is equal to the Earth's rotational period).

If we analyze this system from an inertial reference frame, then yes, as you said, the centripetal acceleration will be equal to the gravitational field of the Earth. That is, the only force present is the gravitational force.

However, if we analyze this system from the non-inertial reference frame which we take to be on the satellite, what do we see? We see that the satellite does not move and we see that the Earth does not move. So from this frame of reference we see that the gravitational force due to the Earth is exactly balanced by the centrifugal force.

The centripetal force is that of gravity. But there is no source for centrifugal. Where does it come from? A free body diagram of the satellite includes only centripetal. In the inertial frame of the satellite there is an attractive force of gravity. There is no centrifugal. In the satellite ref frame, it is still and the Earth moves towards it due to gravity. In order to do so an attractive force is needed. This is the force due to gravity. No counter force is present. The action-reaction or force-pair at work here is not centripetal-centrifugal, but Earth attracts satellite and satellite attracts earth. But, you seem to indicate that because the satellite is attracted to Earth due to gravity, yet it does not accelerate to earth, that there must be an equal and opposite counter force. Using this logic, since the Earth does not accelerate towards the satellite, there must be a counter force directing the Earth away from said satellite. Where does this come from.

Many feel compelled to balance every force with a counter force. Hence centripetal must have its balancing counterpart in the form of centrifugal. But in classical mechanics, I was taught (were my profs mistaken or did I misinterpret them?) that when the forces summed on a body did not balance, then the "ma" vector closes the force polygon. For a satellite in space, the force is gravity directed inwards, or centripetally, and its own velocity tends to follow a tangent. The sum of these 2 tend to maintain ucm. No balancing force is present or needed. A rotating frame has Coriolis force cs. an inertial frame which doesn't. Those who insist on looking at the rotational reference frame viewpoint have ignored Coriolis. Projectiles fired on Earth ae influenced by Coriolis force. You can't treat a geosat (geosynchronous satellite) as an inertial frame. The geosat and the Earth attrct each other due to gravity, yet do not accelerate towards each other, so there MUST BE another force counterbalancing the centripetal. Oh well.

I'll re-examine the equivalence principle, but from memory I don't think a geosynchronous satellite's inertial frame of reference is equivalent to 2 stationary objects. If I'm wrong I'll accept correction, but rotating frames are not the same as translating frames.

As far as the despondent lovers leap is concerned "it wasn't gravity that killed him, it was normal force", my answer is "get real!"

 

[cmos]

cabraham,

You're on the right track; you have valid arguments but you are not following them all the way. As you stated (or rather Newton) F=ma. So for the geosync. satellite-Earth system, when viewed in an inertial reference frame,
F=ma=G\frac{Mm}{r^2} .
If it helps to visualize, think of this reference frame as a point hovering over the orbital plane of the two-body system.

But if you view the events from on the satellite (this being a non-inertial reference frame), then you see that you do not move and you see that the Earth does not move. Therefore the acceleration, thus net force, is equal to zero:
F=ma=0=G\frac{Mm}{r^2}-|F_{centrifugal}|
where the centrifugal force as equal in magnitude to the gravitational force.

I want to note that philosophers, prior to Newton, held the second view that the centrifugal force must balance the centripetal force to keep the planets in the heavens. Their view wasn't necessarily wrong, it just took the view of a non-inertial observer.

Newton's laws require an inertial system and by invoking that, we get the first view that there is no balancing of forces for the above system and that the net force does not equal zero.

In solving problems, it is sometimes convenient to resort to the "old view" and work the problem in a non-inertial frame. Being more enlightened than the old philosophers, we invoke the use of "fictious" forces realizing that they are only manifested because we are using a non-inertial frame.

 

[cmos]

A rotating frame has Coriolis force cs. an inertial frame which doesn't. Those who insist on looking at the rotational reference frame viewpoint have ignored Coriolis. Projectiles fired on Earth ae influenced by Coriolis force.

The Coriolis force requires that something be moving with respect to a rotating frame of reference. I have been careful in my examples to make sure that the Coriolis force can be neglected.

Excuses me if I may, but if you have no problem with invoking the Coriolis force, then why so much scrutiny to the centrifugal force? Both are fictious forces that are manifested in a rotating frame.

 

[D H]

The centripetal force is that of gravity.

A free-falling object is following a geodesic in space-time. You get a fictitious centripetal force when you use a non-inertial frame.

But there is no source for centrifugal. Where does it come from? A free body diagram of the satellite includes only centripetal. In the inertial frame of the satellite there is an attractive force of gravity.

You are using Newtonian mechanics and you are assuming that it is perfectly true. It is not. General relativity is a better (more accurate) model, and gravity is not a force in general relativity. It arises from the use of a non-inertial frame.

Look at it this way. Suppose you are designing a spacecraft or an airplane that uses accelerometers as a part of its inertial navigation system. The flight software will have to augment the accelerometer readings with estimates of the gravitational force to have any chance of making the propagated state reflect reality for the simple reason that accelerometers measures all real forces acting on a body except for gravity. This, of course is the Newtonian mechanics view of accelerometers. From a general relativistic viewpoint, the viewpoint is simple: Accelerometers measures all real forces acting on a body, period.

As far as the despondent lovers leap is concerned "it wasn't gravity that killed him, it was normal force", my answer is "get real!"

People jump out of planes on a regular basis. The free-fall period is, from what I have been told, very exhilarating. The act of free-fall itself doesn't kill. Hitting the ground sure does.

 

[cabraham]

A free-falling object is following a geodesic in space-time. You get a fictitious centripetal force when you use a non-inertial frame.

You are using Newtonian mechanics and you are assuming that it is perfectly true. It is not. General relativity is a better (more accurate) model, and gravity is not a force in general relativity. It arises from the use of a non-inertial frame.

Look at it this way. Suppose you are designing a spacecraft or an airplane that uses accelerometers as a part of its inertial navigation system. The flight software will have to augment the accelerometer readings with estimates of the gravitational force to have any chance of making the propagated state reflect reality for the simple reason that accelerometers measures all real forces acting on a body except for gravity. This, of course is the Newtonian mechanics view of accelerometers. From a general relativistic viewpoint, the viewpoint is simple: Accelerometers measures all real forces acting on a body, period.


People jump out of planes on a regular basis. The free-fall period is, from what I have been told, very exhilarating. The act of free-fall itself doesn't kill. Hitting the ground sure does.

I don't believe what I'm reading. I am an EE, not a pure physicist, and I make no claims as to being a physics expert. But, those who are debating me don't seem to be experts either. I can't believe what I'm reading. Now you are arguing that centripetal force is fictitious. Also presented is that Coriolis is fictitious. Previously it was stated that gravity is fictitious. My dear contrarian friends, is there any force in the universe that is "real", other than your cherished beloved centrifugal force. That's real, all others are fictitious.

"Free fall doesn't kill, hitting the ground does" is so ludicrous it doesn't deserve a response. But I'll give one. How hard you hit the ground depends on how long the "fictitious gravity force" was acting on you. You don't need an advanced physics degree to know that.

In an attempt to "prove" that cf is "real", my opponents have collectively reduced gravity, centripetal, and Coriolis forces to the status of "fictitious". Amazing!

Nothing personal, but now is the time to get on my horse and ride off into the sunset. Best wishes to all. ---sound of horse hoofs ----

Claude

 

[D H]

Nobody but you has said the centripetal force is an inertial force. So please stop with the straw man arguments.

If you are going to college, go ask a physics professor. If you're not going to school, you should have enough money as an EE to buy a book or two on general relativity aimed at the layman.

Regarding things the centrifugal force, the coriolis force, gravity, and other inertial forces: They result solely because of the reference frame of the observer. In the sense that a real force is what an accelerometer reads, none of these forces are real.

 

[tiny-tim]

real and fictitious centripetal force

Now you are arguing that centripetal force is fictitious.

A free-falling object is following a geodesic in space-time. You get a fictitious centripetal force when you use a non-inertial frame.

Hi cabraham!

No … D H was saying that this particular centripetal force … gravitation … is fictitious … because it is absent in genuine inertial coordinates.

Centripetal force due to friction, or to a string, or to reaction from a track, is undeniably real … it is present in any coordinate system.

 

[cmos]

I think DH and tiny-tim have said enough in response to cabraham. It just amazes me that you claim to be an engineer but still misinterpret what we are saying to the point that you start making up what we say. Are you even reading our responses thoroughly?

We have all taken the time to give very good examples, sometimes with the pertinent mathematics. Go back a read through our posts and then you may speak knowledgeably. Either that or realize that engineering technologist is not the same as an engineer...

 

[cabraham]

I think DH and tiny-tim have said enough in response to cabraham. It just amazes me that you claim to be an engineer but still misinterpret what we are saying to the point that you start making up what we say. Are you even reading our responses thoroughly?

We have all taken the time to give very good examples, sometimes with the pertinent mathematics. Go back a read through our posts and then you may speak knowledgeably. Either that or realize that engineering technologist is not the same as an engineer...

Engineering TECHNOLOGIST! Who are you? I'm a full EE and a Ph. D. candidate. What I posted was based on the teachings of Ph.D. physics professors while an undergrad studying **full EE**, NOT EET. What are you, just for the record? Where do you even get off talking in such an uppity manner? Are you a Ph.D. physicist? If not, then you are arguing with profs who are more qualified than you. What are your credentials? You think that I am a mere EET, but you don't state what you are "cmos". Please enlighten us.

 

[D H]

On the Coriolis effect: This is a very good example of how the name fictitious force is a bit misleading. The Coriolis effect is a real phenomenon. All one has to do is look at a hurricane or cyclone: Coriolis effect. So, how to explain this very real phenomenon?

Anyone who tries to do planetary atmospheric modeling from a general relativistic perspective is insane, or will go insane while trying to solve the problem. Atmospheric modeling assumes Newtonian mechanics, which means treating gravity is treated as a real force.

Another way to go insane is to model the Earth's atmosphere from the perspective of an inertial reference frame. No meteorologist or climatologist in their right mind would think of modeling a large rotating ball of gas that co-rotates with a large plastic object (the Earth) from the perspective of an inertial frame. It makes a whole lot more sense to model things from the perspective of an accelerating and rotating reference frame.
This means various pseudo forces will need to be modeled to make Newton's second law appear to apply. Since the Earth's rotation rate is nearly constant, these are pseudo forces are

• Earth acceleration due to other bodies in the solar system. The typical approach is to compute the difference between the gravitational acceleration at some point toward these other bodies and the gravitational acceleration of the Earth toward these other bodies. The difference between these accelerations are called third-body gravity effects. Third body effects are roughly proportional to the inverse of the cubes of the distances to the other bodies. These effects appear in the form of ocean and solid body tides.
• Centrifugal force. For objects located at some position \mathbf r with respect to the center of the Earth, the centrifugal force is \mathbf{\omega} \times (\mathbf r \times \mathbf{\omega}) (see post #31). This effect is typically combined with the gravitation acceleration caused by the Earth to form the acceleration due to gravity. Geodesists distinguish the terms gravitation and gravity to mean the acceleration that results from Newton's law of gravitation and the combined effects of Earth gravitation and centrifugal acceleration due to the Earth's rotation. Acceleration due to gravity is largest at the poles and smallest at the equator. The difference is small.
• Coriolis force. For objects moving with a velocity \mathbf v with respect to the rotating Earth, the Coriolis force is 2 \mathbf v \times \mathbf{\omega} (see post #31). The Coriolis effect in the atmosphere arises directly from the Coriolis force when the Earth's atmosphere is modeled from the perspective of an Earth-fixed frame.

Suppose instead you want to model the flight of a shell fired from a large gun. This can be done from the perspective of an inertial reference frame, and no Coriolis force is needed to model the flight of the shell. The Coriolis force only needs to be introduced if one wants to model the flight of the shell from the perspective of an observer fixed with respect to the Earth.

 

[D H]

I don't believe what I'm reading. I am an EE, not a pure physicist, and I make no claims as to being a physics expert. But, those who are debating me don't seem to be experts either. I can't believe what I'm reading.

Either that or realize that engineering technologist is not the same as an engineer...

Engineering TECHNOLOGIST! Who are you? I'm a full EE and a Ph. D. candidate.

You two need a time out. Stop the name calling right now.

FYI Cabraham, tiny tim is a PhD physics candidate. I am a physicist who has worked in the field of aerospace engineering for 30+ years.

 

[cabraham]

You two need a time out. Stop the name calling right now.

FYI Cabraham, tiny tim is a PhD physics candidate. I am a physicist who has worked in the field of aerospace engineering for 30+ years.

Tiny Tim isn't the one who called me a technologist, cmos was. I have not engaged in any name calling. I was the target of such and simply reacted. I have not, to this point downgraded anybody's knowledge, experience, or academic credentials. When mine were challenged, I gave my background, and only asked that the other party do the same. That is not name calling.

BTW, I worked in aerospace engr for a decade, then in commercial engr where I still practice, totalling 30 yrs. But my specialty is EE, not physics. Having 30 yrs. experience in EE and returning to grad school for PhD after 26 yrs since the MSEE program does not make me a physics expert. My position is based on PhD physics prof teachings, not my own opinions. Regarding physics, esp. modern (relativity, quantum mech) I only had one course at the undergrad level from the physics dept as a senior EE elective. We covered SR, QM, and kinetic theory of matter. Only one couse, so I do not claim to be an expert. If you'd rather that I not post in this forum, just say so.

 

[D H]

We are here to answer questions. Ask away!

The post by cmos was out-of-line. Then again, your post where you questioned our expertise was a bit inflamatory as well. Bottom line: ask away, keep it civil.

A couple web references on the Coriolis effect:

Wikipedia, http://en.wikipedia.org/wiki/Coriolis_effect.

"In physics, the Coriolis effect is an apparent deflection of moving objects when they are viewed from a rotating frame of reference. ... The Coriolis force is an example of a fictitious force (or pseudo force), because it does not appear when the motion is expressed in an inertial frame of reference, in which the motion of an object is explained by the real impressed forces, together with inertia."​

Wikipedia is not the most reliable of sources. The University of Illinois hosts the weather world 2010 project. From
http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml" ,

"Coriolis Force
an artifact of the Earth's rotation
Once air has been set in motion by the pressure gradient force, it undergoes an apparent deflection from its path, as seen by an observer on the earth. This apparent deflection is called the "Coriolis force" and is a result of the Earth's rotation."​

 

[cmos]

I do sincerely apologize. My previous posts was meant to exemplify a fact: it is very infuriating to be publicly misrepresented; this being in reference to post #37. With the example made, I do again apologize. I think we can all agree that we should get back to the physics?

Is it possible we are dwelling down an argument of semantics? The term fictious force does not mean that the so-called force has no effect. It simply means that when viewed from an inertial frame, the force disappears. Only when viewed from a (specific) non-inertial frame does the force prevail. Hence we refer to it as a fictious or psudo-force.

I refer you to my post #34. In the non-inertial frame, the fictious centrifugal force prevails and balances the gravitational force. When viewed inertially, the centrifugal force disappears and all that remains is the gravitational force. Note that this is a classical argument, i.e. we consider the gravitational force as "real" since we do not want to bring Einstein into play (as noted by DH).

Similarly, in reference to DH's post #45, when viewed on Earth, the Coriolis force is a dominant mechanism in the dynamics of weather. In this case the Earth is a non-inertial frame. We may however take our view point from some point in space at which point we can consider our frame to be inertial and we will see no sign of the Coriolis force. Instead, this will be accounted for by our observations of the Earth's movement.

 

[D H]

Some levity

Looks like the time-out period worked. Thanks, guys.

Before we go back to physics, some levity thanks to http://xkcd.com" :

Edit:
Hey! What's the deal with [noparse][/noparse] tags? Why does the image link show up as a link rather than an image?

 

[cabraham]

I do sincerely apologize. My previous posts was meant to exemplify a fact: it is very infuriating to be publicly misrepresented; this being in reference to post #37. With the example made, I do again apologize. I think we can all agree that we should get back to the physics?

Is it possible we are dwelling down an argument of semantics? The term fictious force does not mean that the so-called force has no effect. It simply means that when viewed from an inertial frame, the force disappears. Only when viewed from a (specific) non-inertial frame does the force prevail. Hence we refer to it as a fictious or psudo-force.

I refer you to my post #34. In the non-inertial frame, the fictious centrifugal force prevails and balances the gravitational force. When viewed inertially, the centrifugal force disappears and all that remains is the gravitational force. Note that this is a classical argument, i.e. we consider the gravitational force as "real" since we do not want to bring Einstein into play (as noted by DH).

Similarly, in reference to DH's post #45, when viewed on Earth, the Coriolis force is a dominant mechanism in the dynamics of weather. In this case the Earth is a non-inertial frame. We may however take our view point from some point in space at which point we can consider our frame to be inertial and we will see no sign of the Coriolis force. Instead, this will be accounted for by our observations of the Earth's movement.

Apology accepted.

Regarding the moon orbiting earth, no one has even touched that one. Where, oh where, my learned friends, is centrifugal force? I'm from Missouri (figuratively) so you must show me. The centripetal is due to gravity. It is directed towards the center. From either the moon or Earth frame of ref, centripetal shows up in both free body diagrams. Where is centrifugal? Sorry to be so insistent, but please show me.

Regarding the geosat example, an observer stationary on the geosat sees the Earth and the geosat as two non-moving bodies. Since gravity tends to attract the 2 towards each other, there must be a counter force to neutralize said force, since the 2 don't attract. Such is labeled "centrifugal". But I don't think that you can draw such a conclusion. The centripetal is an artifact of gravity, a known phenoenon. Where does cf originate from? If the geosat and the Earth were both stationary, the gravity force is still there. But "cf" isn't. Where did it come from and where did it go.

If I'm on a geosat, looking towards the earth, and observe no relative motion between the 2, I would NOT conclude that the gravity is canceled by a counter force, preventing attraction, but rather that one body is orbiting the other. The geosat IS FALLING. Its inertia tends to carry it out in space along a tangent line to its orbit. It also "falls" towards earth. The reason that the geosat does not fall to the Earth is due to its own velocity, tangential to the orbit, accelerated towards the center of the orbit due to gravity. The centripetal/gravity is always there regardless of whether the geosat is still or orbiting the earth.

At best, I would regard cf as a "fictitious", "virtual", or "pseudo-" force. When examining forces and accelerations of bodies in ucm, centripetal is always there. Centrifugal is just a mental concept. It is not an active phenomena which exerts influence on bodies. It is like the "bubble" in a carpenter's level, akin to a "hole" in semiconductors. A void has no mass, velocity, energy, wavelength, etc. But we can treat such as a real entity. If we tilt the level downwards to the right, the bubble moves upward towards the left. Inside the fluid we can regard the bubble as an actual entity. Outside the tube, should it break and the fluid exit, the concept of bubble is not valid.

If cf is regarded as something perceived which can be regarded as an actual entity under specific conditions, then I don't think there is a problem accepting it as such. It does not however, enjoy the same status as gravity, centripetal, or Coriolis. Peace and best regards to all.

Claude

 

[George Jones]

I have taught first-year physics several times, and, each time I presented Newtonian gravity as a real force.

I have taught second and third-year mechanics (for physics majors) several times, and, each time I presented centrifugal force and Coriolos force as fictitious forces. When working through some problems it is convenient to think (fictiously?) of these forces as real, but when push come to shove, I would have to stick with the fictitious classification.

I have taught very introductory general relativity once (based on the book Exploring Black Holes by Taylor Wheeler), and I presented gravity as a fictitious force. (More on why later; on my out the door.)

In my experience at a number of universities, these choices are fairly standard in physics departments.

 

[D H]

cabraham: I am going to address the issues you raised in your post out of order. I want to deal with the Newtonian mechanics first.

At best, I would regard cf as a "fictitious", "virtual", or "pseudo-" force. ... It does not however, enjoy the same status as gravity, centripetal, or Coriolis.

The Coriolis force is no more real, and no more unreal, than is the centrifugal force. I supplied two references on the Coriolis effect. Read them, please. The Coriolis effect is a "fictitious force". Since you are going to school, you have access to a library. Look at any junior-level classical mechanics physics text. I have Classical Dynamics, J. Marion, 1970 right in front of me. Goldstein is another. Whichever book you look at, it will inevitably have a detailed treatment of motion in a noninertial reference frame. Here is what Marion says:

It is important to realize that the centrifugal and Coriolis forces are not "forces" in the usual sense of the word; they have been introduced in an artificial manner as a result of our arbitrary requirement that we be able to write an equation which resembles Newton's equation and which at the same time is valid in a noninertial reference frame.​

I think we are all agreed that gravity is a real force in Newtonian mechanics. It is not viewed as such in general relativity.

The geosat IS FALLING. Its inertia tends to carry it out in space along a tangent line to its orbit. It also "falls" towards earth. The reason that the geosat does not fall to the Earth is due to its own velocity, tangential to the orbit, accelerated towards the center of the orbit due to gravity. The centripetal/gravity is always there regardless of whether the geosat is still or orbiting the earth.

You are implicitly assuming Newtonian mechanics here. That is not how things are viewed in general relativity. In general relativity, an object in free-fall follows a geodesic in space-time. The four-acceleration of an object following a geodesic is zero. There is no acceleration, so no centripetal force. So, why use such a theory that stupidly says an object in free-fall is not "accelerating"? Simple. It works, and works better than does Newtonian mechanics. One reason general relativity was accepted so quickly is because it explained a phenomenon that had been vexing physicists for quite some time: the precession of Mercury's orbit. General relativity is a more accurate (better) model than is Newtonian mechanics.

 

[Doc Al]

Regarding the moon orbiting earth, no one has even touched that one. Where, oh where, my learned friends, is centrifugal force? I'm from Missouri (figuratively) so you must show me. The centripetal is due to gravity. It is directed towards the center. From either the moon or Earth frame of ref, centripetal shows up in both free body diagrams. Where is centrifugal? Sorry to be so insistent, but please show me.

Viewed from a rotating frame in which the moon is at rest, there is no acceleration. The Earth still exerts its gravitational pull on the moon (here I take the simple Newtonian view of gravity as a "real" force--no need for general relativity), which is counterbalanced by the outward centrifugal force. (I use the modern definition of centrifugal force as a pseudoforce needed to apply Newton's law in a rotating frame.)

Of course, for a simple problem such as this there is no advantage to using a non-inertial frame, but as has been pointed out several times in this thread there are many kinds of problems in which a rotating frame is the only practical one to use.

Note that both centrifugal and coriolis are "pseudoforces" that arise from using a rotating frame of reference.

 

[cmos]

Regarding the moon orbiting earth, no one has even touched that one. Where, oh where, my learned friends, is centrifugal force? I'm from Missouri (figuratively) so you must show me. The centripetal is due to gravity. It is directed towards the center. From either the moon or Earth frame of ref, centripetal shows up in both free body diagrams. Where is centrifugal? Sorry to be so insistent, but please show me.

The reason I created the geosynchronous satellite example was because it is a simpler example to work with but still marvelously exemplifies the details we are trying to point out.

Regarding the geosat example, an observer stationary on the geosat sees the Earth and the geosat as two non-moving bodies. Since gravity tends to attract the 2 towards each other, there must be a counter force to neutralize said force, since the 2 don't attract. Such is labeled "centrifugal". But I don't think that you can draw such a conclusion. The centripetal is an artifact of gravity, a known phenoenon. Where does cf originate from? If the geosat and the Earth were both stationary, the gravity force is still there. But "cf" isn't. Where did it come from and where did it go.

Newton's second law: F=ma. Since none of the bodies accelerate, we must conclude that all the forces are balanced to zero. The gravitational attraction between the observer and the satellite is balanced by the normal force between the two. But what balances the Earth-satellite gravitational attraction? This being a non-inertial reference frame we must invoke the use of the fictious centrifugal force to balance the Earth-satellite attraction. This is the second equation in my post #34.

That is why the force is termed fictious; it is because it is only manifested as a result of using a non-inertial reference frame. It has no physical manifestation in the sense that is gravity or electromagnetisim.

If I'm on a geosat, looking towards the earth, and observe no relative motion between the 2, I would NOT conclude that the gravity is canceled by a counter force, preventing attraction, but rather that one body is orbiting the other. The geosat IS FALLING. Its inertia tends to carry it out in space along a tangent line to its orbit. It also "falls" towards earth. The reason that the geosat does not fall to the Earth is due to its own velocity, tangential to the orbit, accelerated towards the center of the orbit due to gravity. The centripetal/gravity is always there regardless of whether the geosat is still or orbiting the earth.

This is the view from an inertial reference frame. It requires that you view the system from a point in space where you see that, in reality, the satellite orbits the Earth with a period equal to the Earth's rotational period. Here, the Earth-satellite attraction is not balanced. This is the first equation in my post #34.

At best, I would regard cf as a "fictitious", "virtual", or "pseudo-" force. When examining forces and accelerations of bodies in ucm, centripetal is always there. Centrifugal is just a mental concept. It is not an active phenomena which exerts influence on bodies. It is like the "bubble" in a carpenter's level, akin to a "hole" in semiconductors. A void has no mass, velocity, energy, wavelength, etc. But we can treat such as a real entity. If we tilt the level downwards to the right, the bubble moves upward towards the left. Inside the fluid we can regard the bubble as an actual entity. Outside the tube, should it break and the fluid exit, the concept of bubble is not valid.

Bingo! This is precisely what we have been trying to say.

If cf is regarded as something perceived which can be regarded as an actual entity under specific conditions, then I don't think there is a problem accepting it as such. It does not however, enjoy the same status as gravity, centripetal, or Coriolis. Peace and best regards to all.

Wrong; the Coriolis force is another fictious force. It is manifested due movement with respect to a rotating (non-inertial) frame of reference. If you were to view the Earth from a point in space, you would see that the Earth rotates and that it orbits the sun. This would account for what would otherwise be the Coriolis force when viewed form the surface of the Earth. So in the inertial frame, there is no Coriolis force either.

 

[rcgldr]

It seems like the situation is being made far more complicated than it needs to be, Newton's 3rd law is simple enough, you can't apply a force to an object without that object responding with an equal and opposite force.

Going back to the simple example of a person twirling an object around while holding a string, it's clear that the person will experience a real outwards force due to tension in the string. The person applies countering inwards force on the string. Note that the person is in a non-rotating frame of reference.

At the string to object contact point, the string applies a centripetal force to the object, and the object applies a reactive centrifugal force to the string.

 

[Doc Al]

At the string to object contact point, the string applies a centripetal force to the object, and the object applies a reactive centrifugal force to the string.

Anyone using "centrifugal force" to mean a real, reactive force--instead of the standard definition as a "fictitious" force--should add a disclaimer in bold red letters: This is not standard physics usage--read at your own risk!

Seriously, many of the posts in this thread confuse this very issue and that makes the discussion very hard to follow. If you want to use the term in that that fashion, make it clear that you are using a different definition than most of the other posters. (Otherwise we are bogged down in semantics.)

 

[D H]

Space war!

A science fiction setting:

Two fiercely competitive species find an airless, spinning planet chock full of metals. Each builds an armed mining outpost, only to discover the other species has also found the planet. One species fires first, consistently missing their enemy. The commander asks the science officer whether the firing system models the Coriolis force. The science officer says it's not modeled and won't budge when told to incorporate it because "It's not a real force". The commanding officer finds another solution: Make the guns aim at where the enemy outpost will be when the missiles hit rather than where it is when the missiles are launched. The science officer agrees to this, but says that this will take some time.

Meanwhile, the other species retaliate. They come from a rapidly spinning world and have the Coriolis force factored in. It doesn't matter to them that the force is not real; the effect is real. Their guns are deadly accurate.

========================================================

All of this debate on whether the centrifugal and Coriolis effects are "real" misses the mark. Hurricanes form because of the Coriolis effect, and gravity varies with latitude in part because of the centrifugal force. These very real effects are explainable without the aid of fictitious forces from the point of view of an inertial observer. Sometimes an inertial perspective happens to be extremely inconvenient. Atmospheric modeling is one such example.

 

[rcgldr]

Anyone using "centrifugal force" to mean a real, reactive force--instead of the standard definition as a "fictitious" force--should add a disclaimer in bold red letters: This is not standard physics usage--read at your own risk!

Well maybe you should update or delete the wiki reference to "reactive centrifugal force".

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

I for one prefer to use non rotational, non accelerating frame of references, and centrifugal force should have a meaning in a more common frame of reference.

Getting back to that person that is twirling an object, what do you call the outwards and rotating force that person applies at the contact patch between his feet and the ground (either a platorm on a frictionless plane, or the earth)?

 

[Doc Al]

Well maybe you should update or delete the wiki reference to "reactive centrifugal force".

In general, I would not use Wiki as a serious reference. Pick up any intermediate classical mechanics textbook instead.

I for one prefer to use non rotational, non accelerating frame of references, and centrifugal force should have a meaning in a more common frame of reference.

Use a different word then. But don't use a word that already has a standard meaning in a nonstandard way. (And try analyzing large scale atmospheric effects from an inertial frame--good luck!)

Getting back to that person that is twirling an object, what do you call the outwards and rotating force that person applies at the contact patch between his feet and the ground (either a platorm on a frictionless plane, or the earth)?

Why does it need a special name? You twirl a rock on a string, the string pulls on you, you pull back on the string. (I'd call those forces string tension.) The ground exerts a friction force on you to prevent slipping (and you, of course, exert an equal and opposite friction force on the ground).

 

[cabraham]

So it appears to be that we agree that centrifugal is a fictitious or virtual force created to balance centripetal in a specific ref frame. I still take issue with those who say Coriolis is not a real force. My understanding is as follows.

If we regard Earth as a ref frame and wish to fire a projectile from the equator northward, we must account for rotation of the earth. When the projectile is fired, it has the velocity eastward equal to that at the equator. As it traverses its path northward, it maintains its eastward linear velocity while the Earth underneath maintains its eastward angular velocity. When the missile lands north of the equator, its eastward velocity is greater than the eastard *linear* velocity of that spot on Earth north of the equator. Hence the missile lands *east* of its intended target spot had Coriolis not been accounted for.

I've always regarded Coriolis as a "correction term" that must be computed to account for the above phenomenon. While the missile is airborn, of course there is no literal "Coriolis force" acting on it to accelerate it eastwardly. From the Earth ref frame, if we treated the Earth as stationary then the missile won't land where we thought it should have. What "knocked the missile off course?" We add the Coriolis term as a correcting factor. The Coriolis component is not an actual force acting on the airborn missile deviating its path. Rather it is a correction term accounting for the fact that a rotating ref frame cannot be equated to a stationary one.

There is no literal Coriolis force actively influencing the missile trajectory, but rather it is a correction term accounting for the deviation AS IF THERE WAS a "real" Coriolis force. The force is not literal, but the missile's path deviation is absolutely real. Coriolis force is a virtual force mathematically defined to account for A VERY REAL NON-FICTITIUOS path deviation.

That's my understanding of the "Coriolis component" using my undergrad physics prof Dr. M terminology. Dr. M knew his stuff. In 3 decades of EE R & D, his teachings never once failed me. He was brilliant. Dr. M, wherever you are, "you da man!"

 

[cmos]

cabraham,

That's exactly why it is a fictious force. It is manifested only to correct for the fact that your frame of reference is non-inertial.

In firing a projectile (such as a missile) over long distances over the Earth surface, the Coriolis force will play a significant role. This is the non-inertial view.

But if your launch center was from a point in space, you wouldn't have to worry about the Coriolis force; you'd just have to account for the fact that you are firing at a moving target (the Earth). This is the inertial view.

 

[D H]

The force is not literal, but the missile's path deviation is absolutely real. Coriolis force is a virtual force mathematically defined to account for A VERY REAL NON-FICTITIUOS path deviation.

Bingo! The Coriolis force is a fictitious force. When viewed by an inertial observer, a balistic missile flies in a plane. There is no curvature of the path.

There is an easy test of whether a force is real or fictitious: Can you build a black box to measure the force? Fictitious forces arise from the observer's perspective rather than from some real force that truly does act on the body. Can we measure the normal force? Sure. You step on a scale every morning. Can we measure tension? Sure. Can we measure a centrifugal force or Coriolis force: Nope. These are observer-dependent. They aren't real.

One such measuring device is an accelerometer. The Newtonian view of a perfect accelerometer is a device that measures all real forces except gravitation acting on some body. Why that "except gravitation" clause? The GR view is "A perfect accelerometer is a device that measures all real forces acting on some body, period. There is no reason to exclude gravity because gravity is not a real force."