centrifugal force

D H

cabraham, why are you harping so on centrifugal force? Everyone has said it is a pseudo-force. A recap:

• Centrifugal force is a pseudo-force that appears only because a rotating observer (i.e., an observer in a non-inertial frame) wants to use Newton's second law to describe observed motions.
  The centrifugal force does not appear only when there is a need to balance forces. This is the freshman physics point-of-view. The centrifugal force arises in a reference frame whenever that reference frame is rotating.
  
  
• The Coriolis force is also a pseudo-force. The Coriolis force arises in a rotating reference frame when the object being observed has a non-zero velocity in that frame.
  
  
• Gravity is a real force in Newtonian mechanics.
  
  
• Gravity is a pseudo-force in general relativity. Newtonian mechanics and general relativity disagree on the underlying concept of what constitutes an inertial reference frame and on the spatial extent of an inertial reference frame.

Note well: Just because these pseudo-forces are not real (have no causative agent) does not mean they do not exist. They certainly do exist in the eye of the observer.

Doc Al

I agree with what D H and cmos haved deftly explained (yet again), but here's my response just the same.
Yes. I've practically been shouting this.
Sounds right. But don't get hung up on the term "centripetal". It just means "acting towards the center". Centripetal force is not a separate force unto itself, it's just a catch-all term for whatever is making something move in a circle. In the case of the moon orbiting the earth, gravity provides the centripetal force; in the case of ball on a string being twirled in a horizontal circle, string tension provides the centripetal force. But those forces are "real": they have agents.

Good!

In all frames there is a gravitational force.

Right.
Right. You are accelerating.
If you choose to analyze your motion from the non-inertial frame of the falling platform, then you must include the inertial forces. Realize that a normal force is a "real" force--either it's there or it isn't in all frames.
Done.

Here's another scenario you might find interesting to analyze. Imagine a railroad car with an object tied to a string hanging from the ceiling of the car. The train accelerates. What angle does the string make with the vertical?

From the inertial frame of the tracks, the object is accelerated. The only forces acting on the object are the string tension and the weight. Both of these forces are "real". Newton's 2nd law applies without modification.

To analyze the situation from the non-inertial frame of the railroad car, one must modify Newton's laws by adding in an inertial pseudoforce. Otherwise you get nonsense. The inertial force is just an artifact of analyzing things from a non-inertial reference frame. (The "real" forces still exist in either frame, of course.)

cabraham

I understand where you're coming from, but still see a problem. So when the demon drop platform and passengers are in free fall, the normal force disappears, and in Doc Al's words because "You are accelerating". Not to nitpick but that is where I see the problem. I have no issue so far. But, if I am accelerating, then we don't need a pseudo force "inertial" to balance gravity. Were my physics and ME profs wrong when they taught me that the summation of forces goes to zero when a body is in static equilibrium, i.e. at rest. But if the body is "accelerating", which I have no dispute with, why do we need a counter force to gravity? The inertial counter or pseudo force is brought into the picture to balance out the gravity to keep the summation of forces at zero. Again, was I taught wrong that the sum of forces is NONZERO in acceleration?

Yes, Doc Al, I am well aware that "centripetal" is a term indicating the direction of a force being radially inward. The part about the string, friction, or gravity providing the centripetal was something I was about to post when you just did. I agree completely.

Maybe now is a good time to check outside resources. I visited MIT physics site, and found a lot about bodies in ucm. Centripetal is discussed in every lecture note, but centrifugal is not mentioned. I asked 2 ME people here at work, BSME education, about it, and they said that centripetal acts inward, and velocity is tangential, but centrifugal is something they don't use. I'll find a Ph.D. physics prof at the university I go to, but school is out for the summer, so it may take a while.

The only thing I'm sure of is what I've believed for years, that accelerated ref frames are very tricky to deal with.

I'll think about the railroad car with the object dangling from a string. But, the gravity in this case is vertical while the train's acceleration is horizontal. The gravity is of course fully present in both R and S ref frames. But in the demon drop, the acceleration is vertical as is gravity, no coincidence.

I've thought about it. When at rest, the dangling object is pulled down by gravity and the string tension counters the g force keeping the object in static equilibrium. When accelerating, the horizontal force is forward coincident with the acceleration, vertical force is still downward due to gravity, and the tension in the string where it is attached counters the horizontal accelerating force and gravity which is vertical. The string angle, I would expect, would be the result of vector summation. Just an off the cuff 2 minute analysis.

Doc Al, further back in this thread, was you stated that when a rock is twirled on a string, the outward force you feel is something you just call as "tension". That is my position precisely. In the train case, I see it as the tension always acting counter to the force. Maybe I, or others, is just making too much out of it and should let it rest.

Good day to all.

Doc Al

As long as you stick to an inertial frame, there's no need to consider pseudoforces. (You certainly don't need to use a non-inertial frame to discuss your "demon drop" platform example!) But the choice of frame in which to analyze a problem is up to you. If for some reason you choose to analyze things from the non-inertial accelerating frame, you must include the inertial forces. (Measured from that accelerating frame, you are at rest thus the net force on you must be zero. You need to add pseudoforces to keep Newton's laws working in that frame.)

These concepts are common knowledge among physics students (and physics professors!), but I can easily imagine them not being used much in mechanical engineering. Go to your university library and browse the physics sections for intermediate/classical mechanics books. Or go to the web: Centrifugal Force.
Most definitely!
That's why I chose this example.
Sure, but since this thread is about pseudoforces and non-inertial reference frame, I thought you might like to understand how one would analyze the problem from a non-inertial frame. You sure don't have to use a non-inertial frame to analyze such a simple problem--I never would, except to illustrate the concepts of inertial forces.
The point of my comment was that the outward force that you feel when twirling the rock is not what we call "centrifugal force". That outward force that you feel is a "real" force caused by tension in the string--nothing "pseudo" about it.
Again, the point of the train problem was not to solve the problem--which is trivial--but to show how you would have to introduce an inertial force if--for some strange reason--you wished to do the analysis strictly from the reference frame of the train.

tiny-tim

Hi Claude!

I won't repeat what others have been saying about the difference between Newtonian and Einsteinian frames.

I'll just say that you're trying to understand centrifugal force, which appears only in rotating frames, by using the demon drop example, which is not a rotating frame.

The extra force in the demon drop is the R-double-dot force.

D H

Sometimes it is easier to do the physics in a non-inertial frame than an inertial frame. Some real examples:

The Earth's atmosphere
Meteorologists model the atmosphere from the perspective of an Earth-fixed frame. Modeling the atmosphere from the perspective of an inertial frame is, simply put, insane. To model the Earth's atmosphere from the perspective of an Earth-fixed frame, meteorologists must incorporate the Earth's rotation in terms of both a centrifugal force and a Coriolis force. It gets even worse because the Earth is accelerating as well rotating. The Earth's oceans and the Earth itself are subject to tidal forces from the Moon and the Sun. These tides affect The Earth's atmosphere, too, and atmosphere modelers must take these tidal effects into consideration.

Sea level
The Earth's rotation reduces the apparent strength of the Earth's gravity. This effect is largest at the equator, non-existent at the poles. The fictitious centrifugal force and gravity are conservative forces, which means they can be expressed as a potential. The mean sea level is an iso-surface of the combined gravitational and centrifugal potentials.

Earth satellites
Satellites orbiting the Earth feel the gravitational force of the Moon, the Sun, Jupiter, etc. One could model Earth satellites from the perspective of a reference frame with origin at the solar system barycenter. This frame is very close to inertial. However, it is much more convenient to model satellites from the perspective of an "Earth centered inertial" frame (you can google that phrase). This ECI frame is not truly inertial because it is accelerating.

SOHO
The Solar and Heliospheric Observatory is in a halo orbit about the Sun-Earth L1 point. It is much easier to model the "restricted elliptical three-body problem" from the perspective of a rotating frame than from an inertial frame. I'm not going to go into details, but I did give you a phrase that you can google to find out more info if you wish to do so.

cabraham

Yes I'm well aware that the demon drop is not a rotating frame. But in formulating centrifugal "pseudo-force" the "inertial force" concept was introduced. I figured that where a rotating frame in ucm has constant speed and changing direction, I used its counterpart "demon drop" with constant direction and changing speed. Demon drop doesn't accelerate in a rotational sense, but in a translational sense. It was mentioned to discuss the concept of inertial force.

By "R-double-dot" I presume you mean acceleration, the 2nd time derivative of position. If so, I agree. The gravitational force vector is countered by what you call r dot dot, or more precisely "ma". No other forces are present. Agreed.

Doc Al: "The point of my comment was that the outward force that you feel when twirling the rock is not what we call "centrifugal force". That outward force that you feel is a "real" force caused by tension in the string--nothing "pseudo" about it."" end quote

Of course! I've never thought otherwise. When I pull on a rope with the other end attached to a heavy object, the tug that I feel is what I've always referred to as tension. Tension is real. Likewise with twirling a rock in ucm on a string. The outward force the string exerts on my hand is tension and nothing more. I don't regard it as centrifugal.

I'll do some research. Sorry to annoy anyone, but the teachings of my profs still seem invincible.

D H

cabraham, what exactly are you arguing here? That centrifugal force is an inertial force, or that it does not exist?

Suppose two spacecraft meet such that one spacecraft sees the other as stationary but rotating, and rotating about an axis normal to the line connecting the spacecraft. The first spacecraft sees this condition persist for some time. The other spacecraft will see the first spacecraft as rotating, but with the axis of rotation directed opposite to the axis seen by the first spacecraft. The other spacecraft will not see the first spacecraft as being stationary. Instead, the other spacecraft will see the first spacecraft as undergoing uniform circular motion. Which point of view is "correct"?

The answer is, both points of view are correct. Just because the first spacecraft's description of the motion is simpler (rotation only) than the other spacecraft's description (rotation plus translation) does not make the first point of view more "correct" than the other. Both spacecraft might be completely passive (no active controls) with the first spacecraft in inertial attitude and the other spacecraft rotating. Alternatively, the first spacecraft might well be continuously firing its thrusters to place itself in a forced orbit around the other spacecraft and continuously rotating so it is always pointed at the other spacecraft. I have not told you which, if any, scenario is the case. The crew on the other spacecraft will conclude the alternate explanation if the gyroscopes and star trackers on that spacecraft indicate zero rotation with respect to inertial.

If, on the other hand, the other spacecraft's inertial navigation system says that they themselves are rotating and the first spacecraft is completely passive. The crew on the other spacecraft can still explain the first spacecraft's motion from the perspective of a frame fixed with respect to the other spacecraft. In this frame, the first spacecraft will have an velocity of [itex]\mathbf v = \mathbf r \times \mathbf {\omega}[/itex]. This velocity will appear to change due an apparent centrifugal acceleration of [itex]\mathbf {\omega} \times (\mathbf r \times \mathbf {\omega})[/itex] and an apparent Coriolis acceleration of [itex]2 \mathbf v \times \mathbf {\omega} = 2 (\mathbf r \times \mathbf {\omega}) \times \mathbf {\omega}[/itex]. While there is no real centripetal force causing the first spacecraft's apparent uniform circular motion, there is an apparent centripetal force equal to the vector sum of the centrifugal and Coriolis forces.

cmos

Have you ever considered that you misunderstood your professor? You have said yourself that you are an EE, which means that the only formal physics you've done is at the elementary level. I have a feeling your professor said something along the lines of, "the centrifugal force is not a real force."

Well, that's more or less what we've been saying all along.

The centrifugal force is NOT usually taught at the elementary level. That's because non-inertial frames are not usually taught at the elementary level. That's because, at this level, we are still trying to get students accustomed to what exactly is a force and the formal concepts of Newton's laws.

(Edit: When I say elementary level, I mean first/second-year physics)

Another thing; it is oft said that one cannot learn nor understand physics without doing physics. Have you tried doing a simple problem (maybe one of the examples myself or others have come up with) yourself to see how much simpler life becomes when you invoke a non-inertial reference frame? Do this and you'll see.

cmos

I check out the MIT OCW out of curiosity. They do not have ANY lecture note on intermediate or advanced mechanics anywhere. This may you cannot find notes on non-inertial frames. But check this out:

http://ocw.mit.edu/OcwWeb/Physics/8-...ings/index.htm

This is schedule for an intermediate/advanced mechanics class. Look at session 15. Non-inertial frames!

Why don't you pick up one of those books, or any book on classical mechanics at your library?

cabraham

I'm going to do just that. No offense, but maybe all of us should do likewise.

As far as misunderstanding my professor goes, that is a possibility. Often I hear people quoting something from a lecture, or a highly esteemed source like Newton, Maxwell, Einstein, etc. and they misunderstood the source. I'm always careful regarding that. However, here are my prof's exact words:

"There is no such thing as centrifugal force."

I guess I must have misconstrued the above statement.

In the final analysis, maybe the viewpoint today, vs. the 1970's, is to give fictitious, or "pseudoforces" due respect as if they were "real", whatever "real" means. If that be the case, well, I don't want to argue that point. I just completed a semiconductor physics course in EE. I took the prerequisite class in Spring 1979 as an MSEE grad student. Back in those days, an electron was regarded as an actual particle, and a hole was "virtual". Anyway, in my Spring 2008 sequel class, the prof mentioned that holes are injected into the base lead of a bjt, and I remarked, "uh, isn't it more like electrons are extracted from the base lead as holes are virtual and do not exist outside the semiconductor?" He rebuked me with "You are using the older viewpoint that holes are not true particles. Today they are viewed as such." I guess I can't argue with whatever the science community regards as "real". It's sort of like Pluto. In my youth Pluto was a full planet. Now, poor Pluto is but a dwarf, 2nd class, reduced in stature. Oh well. Best regards.

D H

No offense, but many of us already have. It is obvious that at least cmos and jospuur have taken the equivalent course. So have I. The texts for the MIT class are Goldstein, Classical Mechanics, 3rd Edition, and Marion & Thornton, Classical Dynamics of Particles and Systems, 4th Edition. Those are exactly the books I recommended in post #50. Jostpuur obviously used the Classical Dynamics of Particles and Systems, 5th Edition. Marion died between the 4th and 5th editions and lost his place as first author but kept his place as a posthumous author. cmos must have used Fowles and Cassiday, Analytic Mechanics. These three books are the standard set of texts for the advanced undergraduate classical mechanics. These texts are so widely used that they are referred to by author rather than name.

Stop generalizing. It makes you come off as a pompous whatever.

Freshman physics instructors sometimes go overboard because the intent of freshman physics is to introduce basic concepts. Things like centrifugal and coriolis forces are distractions in freshman physics. Freshman physics instructors also say that gravity is a real force. So go figure.

The caloric and the luminiferous aether do not exist and as such should never be used in describing thermodynamics and light transmission. Similarly, saying "there is no such thing as centrifugal force" strongly implies that the centrifugal force should never be used in describing behaviors. This is what we are objecting to. None of us has said that fictitious forces are "real". There is, however, a big difference between "fictitious" and "does not exist".

cmos

I think most, if not all, of us who've highly contributed to this thread have studied out of one of those books or some equivalent.

I don't want to get too off topic (but it does to serve a point), regarding the case you brought up of hole injection. A hole is what we refer to as quasi-particle (sort of like a quasi- or fictious force). Does it really exist? Not really (sort of like a fictious force). But it makes the analysis much simpler if we talk about about the hole as if it were a real particle (sort of like a fictious force).

cabraham

Well, what you just stated about a hole being a quasi-particle which does not really exist is what I've believed since the '70's. But, I was just told that holes are now given the same recognition as electrons. The semiconductor physics community, or at least a large number of members, now consider the hole and the electron to be on equal footing. For me that is going to take some getting used to just like considering inertial/centrifugal forces which have always been virtual to now be existant. I'm not averse to accepting new definitions. If holes are now "real" and no longer "virtual", not being a device physics specialist, I am in no position to argue. Likewise with Pluto being downgraded.

As far as freshman physics goes, if centrifugal actually exists, no prof would knowingly say that it doesn't just to keep things simple. They would say that we can neglect it for now, but it appears in more advanced courses. I've never been taught one thing by an engr or physics instructor only to later find out it wasn't so.

The reason I brought up the electron/hole analogy is just to point out that how things are viewed varies as time advances. Maybe Dr. M was putting forward what was the prevailing view at the time, the mid-70's. "Virtual" forces may have been said to be "non-existant" at that time. I'll find out. Incidentally, my 1964 GE transistor manual gives holes as being "virtual" having no existance outside the bulk semiconductor material. My 2005 Sze ref text just used for my recent course makes no mention (or maybe it does but I haven't seen it) about distinguishing "virtual from actual". Holes and electrons are described thoroughly with no mention of which is more significant.

In 40 years, semiconductor behavior didn't change, but how the scientific community views, interprets, and models them did change. That's what I've distilled from this example. BR.

Claude

D H

Sure they do. Even now, freshman physics instructors teach their students that gravity is a real force.

This whole, overdrawn debate hinges on the words "does not exist". That is a very strong phrase in physics. As I mentioned earlier, the caloric and the luminiferous aether do not exist. It would be completely wrong to base any physics education or physics analyses on these falsified concepts. There is a huge difference between "does not exist" and "fictitious". Physicists, meteorologists, engineers, and many others use fictitious forces every day in their work. There is nothing inherently wrong with doing so because there is nothing inherently wrong with the concepts of centrifugal force, coriolis force, etc.

Sure you have. You have been taught that [itex]\mathbf F=m\mathbf a[/itex] (Newton's second law) and that [itex]\mathbf v_\text{rel}=\mathbf v_2 - \mathbf v_1[/itex] (Galilean relativity).

cristo

This debate has been drawn out for long enough, and I can see that things will only be rehashed again and again. This seems a good place to end the discussion, thus I am closing the thread here.