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# Centripetal Force How Does It Relate To Skiing? - Page 4

Quote:
Originally Posted by mdf

Ok, is this bait?

The astronauts really are weightless, in the sense that they do not experience the fictitious force called "gravity."  Gravity, of course, is the fictitious force that corresponds to the real force exerted by the ground on the bottoms of our feet.  That ground force accelerates us relative to a truly inertial trajectory (which is, of course, a geodesic).

(Gravity <--> ground pushing up)  is a pair that is analogous to (centrifugal <--> centripetal).

Are you serious? I really can't tell. From a man who referenced Landau & Lifshitz and was aware of the Copenhagen interpretation of QM, this must be intended as a joke. On the other hand, the absurdity is expressed with such sophistication and eloquence without any hint of irony or sarcasm that some may think it is serious. So, forgive me if I belabor the obvious.

Gravity is as real as an apple (remember the Newton's apple story). Whether you are free falling off a cliff skiing or free falling in orbit (free falling = no forces other than gravity acting on the object), gravity is there. In the latter case, gravity provides the centripetal force for that orbital motion. The ground force is equally real. It stops you from accelerating into the center of the earth when you hit the ground. They are both real, present at the same time, independent of any frame of reference.

Quote:
Originally Posted by Ghost

The astronauts are not weightless.  The very real force of gravity is what keeps them turning in a curved orbit instead going in a straight line into outer space.

Ghost, I'm disappointed you didn't follow my fancy footwork. Maybe I needed to telegraph my punches a little more.  I switched to a general relativistic point of view.

In that context, geodesics are "straight lines" and the astronauts are following one.  They are not accelerating.

Those of us on the ground are constantly accelerating, since the ground pressing up on the bottom of our feet deflects us from following the natural path toward the center of the earth.  Gravity is the fictitious force felt by those of us on the ground in an accelerating reference frame.  The astronauts are not accelerating, and therefore do not experience the fictitious force of gravity.

No acceleration in orbit --> no gravity --> no weight.

Just like the centripetal / centrifugal story.

Quote:
Originally Posted by ChuckT

Are you serious? I really can't tell. From a man who referenced Landau & Lifshitz and was aware of the Copenhagen interpretation of QM, this must be intended as a joke.

Sure it is a joke, but I am still serious.  It is a perfectly valid way of analyzing the situation, even though it is unusual (and inconvenient for calculation).

I take the general equivalence principle very seriously.

Quote:
Originally Posted by Ghost

The only time centrifugal force is imaginary or unreal is when you are describing it from a different frame of reference.

Is the strong nuclear force real or imaginary?  Is it just an imaginary invention to explain why atoms don't fly apart?  What is a force anyway?

When it comes right down to it, the experimental evidence of force rests in the effects of that force.  If you have an object that is accelerating in your chosen frame of reference then there must be a real net force acting on it.  That force may not be real in some other frame of reference.

Thank you, Ghost!

I have a longer post that I had started to write earlier this evening, stating much the same point that Ghost just made, but it will have to wait for a bit. For now, I simply find myself asking the question, "does it take a real force to make a physicist implode, or is a fictitious force sufficient?"

ChuckT--slow down a little--I think that you are starting to lose your scientific objectivity and clarity. If you are now trying to say that there is centripetal force in a situation in which there is no centripetal acceleration (that is, no circular motion--the ski deck skier simply going left and right within the "inertial" frame of reference of the room the deck is in), then you are starting to define terms in some unique ways that I suspect even your physicist peers would question. If that is the way you want to argue now, you are as guilty of conveniently switching frames of reference to suit your needs as anyone. You are right that the technique and thus the forces on that ski deck are virtually identical to the technique on a real slope (which is what I said, and which is the point of the video clip, I believe--you have both agreed with me and called me "unequivocably wrong" on that point). And you are, of course, right that there is, indeed, centripetal acceleration and centripetal force in some frames of reference on that ski deck. There is no problem with switching frames of reference for convenience--we do it all the time, naturally, and for convenience--again, the point I have been trying to make. But when you do it, the rest of your arguments fall apart: centrifugal force is REAL in some frames of reference, and centripetal force is no more than a fictitious force in some frames of reference. If you want to talk about centripetal force on that ski deck, you are either changing the definition of centripetal force to suit your whim, or you are shifting frames of reference and thus supporting my point that "other" frames of reference are equally valid and often more useful for describing motion.

I have often tried to point out that many apparent disagreements on the "facts" of motion and forces are really just misunderstandings or misalignments on the frame of reference used to describe the motion. And that is the case again here. It is really not an argument about whether centrifugal force, or any other force, exists. It does. And it does not. Simultaneously. In different frames of reference. To take a stand on one side of the "it does/it does not exist" line is either just silly, or else it is to say that some frames of reference are more real and more valid than others. I would not expect a real physicist to say that.

As PhysicsMan said (oh, where are you, Tom?), the mountain is just a great big physics lab, with skiing a great and ongoing experiment in applied physics. I submit that the education in physics continues for all of us--well past high school, college, and graduate school--and that, as the Austrians like to say, "ze mountain vill teach you."

Best regards,
Bob
Quote:
Originally Posted by mdf

Sure it is a joke, but I am still serious.  It is a perfectly valid way of analyzing the situation, even though it is unusual (and inconvenient for calculation).

I take the general equivalence principle very seriously.

OK, mdf.

Choosing a non-inertial frame of reference is indeed a perfectly valid way if set up correctly. It is not even unusual and actually convenient to analyze the situation as I applied earlier to Bob's ski ship where I use the accelerating ship as the frame of reference.

Considering another more interesting variation of the ski deck: Describing the trajectory of a skier skiing down a giantic conical slope rotating at a constant angular velocity w. This is most easily done by picking the rotating cone as the FoR and solve the F=ma equation where F is the sum of gravity, snow resistance, and an apparent force = -m*(w*r)^2/2. This force is a more generalized version of the centrifugal force. There is no physical meaning to it, unlike gravity or snow resistance. It is just a good way to solve an otherwise mathematically messy problem. I hope I have convinced you that contrary to claimed made here, I have no trouble picking any frame of reference and my preferred FoR is that which makes the math simplest.

Notice that in all of these cases, I don't pick the skier as the FoR. The reason is that doing so is useless in trying to solve these more complicated problems. For the original discussion of skiing down a stationary hill, picking the skier as the FoR is also meaningless in the sense that you must either know the trajectory of the skier (relative to the hill) to determine the centrifugal force appropriate for this accelerating FoR or you must know the net real force to yield the centrifugal force which is the exact opposite of the net real force (the sum of all must be zero since the skier is stationary in his own FoR). But if you already know either the trajectory of or the net force on the skier, what else is there to describe or worry about? A little math - differentiation with the former, integration with the latter - will tell you everything there is to know.

Choosing the skier as his own FoR only enables us to wave our hands and sound sophisticated and technical without adding any real value. I doubt skiers use their own FoRs either. You mentioned balance, but that is about forces which need no self-refenced frame to describe. I believe when we ski, we do not think of ourselves as stationary, which is what we must do if we are self referencing. In our own frame of reference, the trees, rocks, gates move to and away from us. How many of us think while we ski down a chute that "oops, a rock is moving to me, I have to make this rock move away from me"? Or do we think along the line "oops, I will hit this damn rock if I don't turn now"?

How many racers think, sense, or feel that the slope is moving and rotating underneath their skis as they make SL or GS turns? None, I bet. We all feel, think, and know without any questions that we are moving on a stationary hill. So, all this talk about own frame of reference is fun, but technically and practically useless.

Whoa! Bob!

How do you read that I am "trying to say that there is centripetal force in a situation in which there is no centripetal acceleration"? The ski deck skier is NOT just moving left and right, as in back and forth along a straight line in the room. Of course not, there is of course a curvy motion. I think you said this yourself. Didn't I mention a figure 8? And whenever there is a curved trajectory, there is a centripetal force. You are unequivocally wrong because: it's exactly the same force, exactly the same technique, body position, independent of whatever frame of reference you choose. Any physicist will confirm that for you. This is very elementary, Bob.

I have written enough on this matter, both objectively and with exasperation. I have answered all your questions point by point (and asked you a couple). I don't want to belabor the point any more. But let me make you this offer.

Get any bonafide physicist, sounds like you know a few, to confirm that I am wrong and I will write Epicski, or you, or any charity of your choice a check for \$100 (I'm not as rich as Romney) once I verify his or her credential.

I always put money where my mouth is, even on the internet

Quote:
Originally Posted by Bob Barnes

Thank you, Ghost!
I have a longer post that I had started to write earlier this evening, stating much the same point that Ghost just made, but it will have to wait for a bit. For now, I simply find myself asking the question, "does it take a real force to make a physicist implode, or is a fictitious force sufficient?"
ChuckT--slow down a little--I think that you are starting to lose your scientific objectivity and clarity. If you are now trying to say that there is centripetal force in a situation in which there is no centripetal acceleration (that is, no circular motion--the ski deck skier simply going left and right within the "inertial" frame of reference of the room the deck is in), then you are starting to define terms in some unique ways that I suspect even your physicist peers would question. If that is the way you want to argue now, you are as guilty of conveniently switching frames of reference to suit your needs as anyone. You are right that the technique and thus the forces on that ski deck are virtually identical to the technique on a real slope (which is what I said, and which is the point of the video clip, I believe--you have both agreed with me and called me "unequivocably wrong" on that point). And you are, of course, right that there is, indeed, centripetal acceleration and centripetal force in some frames of reference on that ski deck. There is no problem with switching frames of reference for convenience--we do it all the time, naturally, and for convenience--again, the point I have been trying to make. But when you do it, the rest of your arguments fall apart: centrifugal force is REAL in some frames of reference, and centripetal force is no more than a fictitious force in some frames of reference. If you want to talk about centripetal force on that ski deck, you are either changing the definition of centripetal force to suit your whim, or you are shifting frames of reference and thus supporting my point that "other" frames of reference are equally valid and often more useful for describing motion.
I have often tried to point out that many apparent disagreements on the "facts" of motion and forces are really just misunderstandings or misalignments on the frame of reference used to describe the motion. And that is the case again here. It is really not an argument about whether centrifugal force, or any other force, exists. It does. And it does not. Simultaneously. In different frames of reference. To take a stand on one side of the "it does/it does not exist" line is either just silly, or else it is to say that some frames of reference are more real and more valid than others. I would not expect a real physicist to say that.
As PhysicsMan said (oh, where are you, Tom?), the mountain is just a great big physics lab, with skiing a great and ongoing experiment in applied physics. I submit that the education in physics continues for all of us--well past high school, college, and graduate school--and that, as the Austrians like to say, "ze mountain vill teach you."

Best regards,
Bob

Quote:
I hope I have convinced you that contrary to claimed made here, I have no trouble picking any frame of reference and my preferred FoR is that which makes the math simplest.

You have, Chuck--and thank you. But you'll have to admit that you've shown a definite bias toward inertial frames of reference, particularly the one anchored to the mountain. You have gone to great lengths to deny centrifugal force the status of "real," which in the right frame of reference, as the agent that causes acceleration in that reference frame, it certainly is.

And I'll still argue with you about your point in this paragraph:
Quote:
Choosing the skier as his own FoR only enables us to wave our hands and sound sophisticated and technical without adding any real value. I doubt skiers use their own FoRs either. You mentioned balance, but that is about forces which need no self-refenced frame to describe. I believe when we ski, we do not think of ourselves as stationary, which is what we must do if we are self referencing. In our own frame of reference, the trees, rocks, gates move to and away from us. How many of us think while we ski down a chute that "oops, a rock is moving to me, I have to make this rock move away from me"? Or do we think along the line "oops, I will hit this damn rock if I don't turn now"?

How many racers think, sense, or feel that the slope is moving and rotating underneath their skis as they make SL or GS turns? None, I bet. We all feel, think, and know without any questions that we are moving on a stationary hill. So, all this talk about own frame of reference is fun, but technically and practically useless.

You're right--we "sense" our motion on the hill--and we know it's happening. We think in terms of that frame of reference about our path on the mountain, and if we were inclined to analyze our motion, the math would be simplest with that frame of reference. You have pointed out how silly it would be to visualize or describe our forward progress and curvy path on the hill from our accelerated frame of reference, and I agree completely.

However, I have also pointed out how commonly we do describe motion--particularly when referring to ski technique and the movements we make on our skis--from our own accelerated frame of reference. Quoting from my own post #19 above,
Quote:
consider the following not-unusual statements: "I floored the accelerator, and the telephone poles flew past in a blur...." "Hold your hands still" (advice to a skier). "Sit still!" (advice to a child squirming in the car seat). "Don't move, or I'll blow up the train." "Move your hips back." And so on.... What frames of reference are implied in these statements? Clearly in each of these, "still" is relative not to the surface of the earth, but to the "accelerated frame of reference" of the speaker or the person spoken to. When you tell a skier to "hold your head still," I certainly wouldn't expect that you mean to leave your head behind on the hill while the rest of your body schusses on down
.

"Hold your hands still." "Move your shoulders back." Expressions like these clearly and naturally imply the skier's accelerated frame of reference. It would be "messy," as you say, both mathematically and descriptively, to describe these simple body part movements from the inertial reference frame of the mountain. As I stated in that post, I believe that this is the point upon which we disagree. I do not at all concur that it is uncommon or unnatural to invoke the skier's accelerated frame of reference, and that it, in fact, can and does add great value and simplicity to descriptions of, basically, "how to ski."

Furthermore, I submit that it is quite natural to accept both frames of reference simultaneously. We can easily sense and recognize that we are turning and accelerating and moving in the mountain's inertial reference frame, even as we describe our body movements and sensations of force and balance from our accelerated frame of reference. Nothing wrong or unusual about that at all!

And in that accelerated frame of reference--whether we agree on how common and natural it is or not--centrifugal force is, for every practical and real purpose, a very real force. We feel it. We sense it. We can measure its magnitude and direction with standard scientific equipment (or a simple spring scale). In that frame of reference, it is both a physical reality and a mathematical necessity.

---

It's been a good discussion. No, none of this will make your turns better. Not everything is--or needs to be--about that. It is an intellectual exercise only--although as I've said previously, a deeply held misunderstanding here can certainly make your turns worse! An intuitive--not to mention scientific and mathematically accurate--understanding of frames of reference may go beyond what many are interested in spending the time or mental exertion to develop. That's fine, but if the discussion is not for you (anyone), please do not be critical of those who are fascinated by it and who seek to develop a better understanding. If you're looking for practical advice about how to make a turn, there are plenty of other threads where you'll find it.

But I will say this: if we conclude no more than that choosing the right frame of reference can make descriptions clearer and "less messy," as Chuck has described it, than others, then this discussion has served a useful and practical purpose. You want to keep it simple? Choose the right frame of reference!

Best regards,
Bob
Quote:
Of course not, there is of course a curvy motion.

Come on, Chuck--please, you must be getting tired of this, and I wouldn't blame you. There is a curvy motion only if you assume the right frame of reference. There is linear motion in another. And there is zero motion in yet another.

You either embrace the reality of varying frames of reference, or you do not. That should not be a matter of convenience or of which point you're trying to support at the moment.

Right?

Best regards,
Bob
Quote:
Get any bonafide physicist, sounds like you know a few, to confirm that I am wrong and I will write Epicski, or you, or any charity of your choice a check for \$100

Thank you for the offer, Chuck.

I have no desire to take your money. But more importantly, I have never said that you were wrong! I disagree only with your assertion that it is uncommon, unnatural, or categorically not useful to invoke the skier's accelerated frame of reference when describing ski technique. That is not a question of right and wrong, but merely a difference of opinion. Where it may seem that we disagree on "the facts"--namely regarding the "reality" of centrifugal force, I have stated numerous times that your analysis and math are dead on as far as I can tell, and that the apparent disagreement is simply a misalignment of the frames of reference we're using. (Is it a "fictitious disagreement"? )

Believe me, I fully respect your credentials as a physicist. And I truly appreciate the time you've spent in this thread.

But you have piqued my curiosity about your thinking about one more thing, and I'll ask one more question: At what point in one's education does he become a "bonafide physicist"?

Best regards,
Bob

Bob,

I think I said the ski deck skier is not moving back and forth in a straight line in the room. The operative phrase here is "the room". The curvy motion is relative to the room, like drawing a figure 8.. You are right that you can pick a frame of reference that make a motion appears to be any shape or line, and that where the business of inertial frame of reference comes in. You can only determine the net force from the motion of an object only if that motion is relative to an inertial frame of reference. Otherwise you have to also know the motion of the frame of reference itself (relative to some inertial frame of reference) to correctly determine the net force. The math is as I had described.

Regarding a "bonafide physicist", I would say anyone with a Ph. D. from an accredited program would qualified in this context since he/she most likely must have taken a formal advanced course in classical mechanic, a subject that is not generally considered exciting or new. A lot of people take a lot of physics courses but are not familiar with the real distinction and non-equivalence between inertial and accelerating frames of reference because the topic just didn't come up in their study. Any college physics professor would certainly be familiar with this stuff.

Best regards,

Chuck

@mdf,

No need to telegraph your punches; I'm just avoiding them without bothering to counter.  Maybe I'm being a little too restrictive in my pedagogy, but I just think that curvilinear space is too much of a leap for someone who believes a heliocentric reference frame is real and geocentric reference frame is unreal, or that the forces causing acceleration in some frame of reference that is accelerating with respect to the "real" frame of reference are fictitious.  I admit of course there is some merrit to building a bigger house of cards before having it all crash down (only to be instantly rebuilt as a very useful TOOL).

Ghost, Chuck,

Well Ghost, I made the leap to General Relativity for a reason.  I wanted to point out that Chuck's beloved inertial frames don't come with preprinted labels identifying them as such.  And the forces don't come with sticky notes either.

In GR, which is generally believed to be closer to "truth" than classical mechanics, you are going to have a hard time finding a truly inertial frame in this neck of the woods.  The astronauts are the closest you are going to find.

Once you realize the Earth-fixed "inertial frame" isn't inertial, it becomes silly to give it a special metaphysical status.

Chuck - you seem to have missed my point.  It is a "joke" because bringing GR into skiing is a bit over the top, not because it is wrong.  And in the GR framework, the astronaut's frame of reference is not accelerating - it is more nearly inertial (only those tidal and upper-atmosphere drag forces) than the frame of those of us on the ground.  And it is inconvenient for calculation because we would have to take the slow-motion, weak field approximation of GR to get numerical results, and that amounts to recovering the same classical  equations that your or Ghost would start with.

One more  point.  For complex, real world purposes (e.g. 6 degree of freedom inertial navigation, or robotics with articulated joints and actuators that are attached to other joints and actuators) the body fixed frame is often the only practical and efficient frame to do the calculations.  Or to get more basic yet more  esoteric, when you integrate up a Lie group generator to get a finite transformation, you are essentially working in the body-fixed frame.

When we're done here, anyone want to talk about something easy like information theory and thermodynamic entropy?

Sure thing, Chilehed. When we're done.....

Best regards,
Bob

PM me when it's time, I can expect to hear back what, around April maybe?

I thought I would add my two cents to the discussion.  After reading the primary dialog between Chuck and Bob I have concluded the following. It is not fruitful to argue nuances of physics with lay people such as Bob (no slight intended). Nor is it fruitful for Bob to try and teach a physicist about skiing using language that is not consistent with a physicists understanding of technical terminology. The language of physics is mathematics anyway and that is the only true way to argue or represent phenomena. Lay people have their own mental constructs for physical terms and without formal training or an understanding of the underlying mathematics they will not get beyond those constructs. For example the term fictitious force simple means that the force has no reality outside a certain reference frame. However people will argue that since they "experience them, they are real" and not fictitious in the sense of a vernacular definition of fictitious. It is also not true that centrifugal force is a real counteracting force to centripetal force.  It is analogous to the use of some words in the legal profession that have different meaning in a legal context than in the common vernacular. It is best if the terms fictitious, centrifugal, ect. are replaced with the term "apparent forces" that move the discussion into the lay realm of personal experience thus avoiding the confusion caused by the misinterpretation of technical definitions. It also avoids the inevitable digression into metaphysical and philosophical discussions.  In the case of skiing, the physics fits perfectly into the realm of Newtonian Physics and any analytical models whether derived from Newtonian equations of motion, Classical Mechanics, or Finite Element Analysis follow the linear mathematics of forces in an inertial reference frame, period. It makes perfect sense however  to describe a skier as experiencing an apparent force in certain directions or a person in a car experiencing an apparent sideways force during a turn. My masters racing coach often describes getting a ski up on edge to create a platform in the snow to push against. This is a perfectly valid mental construct for helping us to visualize and feel what we are trying to accomplish in our turns regardless of whether we are talking about about centripetal or centrifugal forces and  even if the physics is not entirely accurate.

By the way my credentials are as follows since someone asked for an opinion from someone in the engineering or physics profession:  I have 2 degrees in physics, I manage a group of 70 scientists and engineers who design and build space based optical remote sensing systems. I was part of the core team that fixed Hubble back in the early 1990s and was the lead optical engineer on the Hubble Cosmic Origins Spectrograph, Hubble Advanced Camera For Surveys, and the Ozone Mapping and Profiler Suite (OMPS) that was recently launched on a new weather satellite called NPP. At least one of the people I manage is a former physics professor and about 30% have PhDs in physics or optics and a number are avid skiers so I have discussions like this often. On another note, we have been hiring significant numbers of engineers in all disciplines this year so if you are a scientist or engineer who wants to work in Boulder CO look me up on Linkedin then go to our company website for job postings. I'm leaving my company name out of this post intentionally.

Quote:
Originally Posted by rcahill

The language of physics is mathematics anyway and that is the only true way to argue or represent phenomena. Lay people have their own mental constructs for physical terms and without formal training or an understanding of the underlying mathematics they will not get beyond those constructs. For example the term fictitious force simple means that the force has no reality outside a certain reference frame.

Seems to be Bob's interpretation of the term.  For some strange reason there appears to be at least one physicist who thinks the "no reality" extends to that certain frame of reference.  Perhaps that physicist has spent too much time studying physics and not enough time studying linguistics.

Cool ideas gentlemen, I've skied with Bob a number of times and while some of his details are slightly off at times, he is a pied piper who has helped more than a few skiers learn to learn skiing. I wonder though, does anyone else involved in this thread shares his same skiing credentials. Seems only fair to ask since Chuck brought up credentials.

Quote:
Originally Posted by Ghost

Seems to be Bob's interpretation of the term.  For some strange reason there appears to be at least one physicist who thinks the "no reality" extends to that certain frame of reference.  Perhaps that physicist has spent too much time studying physics and not enough time studying linguistics.

I may have wrapped myself around the axel a bit in trying to keep this semantically simple. Even though an apparent force like centrifugal force appears to exist in a rotating reference frame it still does not have a physical reality. For example, if the string is cut when swinging a ball around it is the removal of a real force (centripetal) that causes the ball to fly off tangentially. Centrifugal force if it were physically real would cause the ball to move in a different direction with a radial component. Since this does not happen the apparent centrifugal force does not physically exist and hence the term apparent. At risk of obfuscating matters further it is accurate to say that even though centrifugal force exists in a rotating reference frame it still has no physical reality. This is the point others were trying to make I believe.

Edited by rcahill - 12/23/11 at 7:09pm
Quote:
Originally Posted by jst4fun

Cool ideas gentlemen, I've skied with Bob a number of times and while some of his details are slightly off at times, he is a pied piper who has helped more than a few skiers learn to learn skiing. I wonder though, does anyone else involved in this thread shares his same skiing credentials. Seems only fair to ask since Chuck brought up credentials.

I only brought up physics credentials just in case someone would say I was full of it about my physics. I would never question Bob's skiing credentials. In fact, I have learned good stuff from Bob's writing. And Bob writes so well that reading his posts is always enjoyable even when I don't quite agree with him.

Quote:
Originally Posted by rcahill

it is accurate to say that even though centrifugal force exists in a rotating reference frame it still has no physical reality. This is the point others were trying to make I believe.

Yes, rcahill. And it seems the point is very counter intuitive and hard to accept for many people. Fortunately, this is all just for fun. We don't need to really understand it to ski.

Ok, now I am thinking that you two have never actually done a calculation in a rotating frame.

Your intuitions are tripping you up.

I invite you to actually write down the equations of motion, and see what the ball does in the rotating frame.  Take the time to actually do it -- don't assume you know the answer.

(Hint.. the ball does not move off tangentially -- that is what it does in the other frame.)

Quote:
Originally Posted by mdf
(Hint.. the ball does not move off tangentially -- that is what it does in the other frame.)

Bringing the the Coriolis force into the discussion serves no point.

Quote:
Originally Posted by skiatansky

Bringing the the Coriolis force into the discussion serves no point.

The ball moves off tangentially in a straight line in the room's frame, not in the rotating frame.  In the rotating frame, the ball starts off stationary and accelerates in a purely radial direction. The centrifugal force is what makes it accelerate away from the center.

I am not talking Coriolis -- that only comes into play later, after the ball has built up some radial velocity.

Quote:
Originally Posted by mdf
The centrifugal force is what makes it accelerate away from the center.

Oh, sorry, didn't realize you were back on the CF is not an imaginary force train.

Quote:
Originally Posted by skiatansky

Oh, sorry, didn't realize you were back on the CF is not an imaginary force train.

Well, I was done.  Sorry to be tedious.  But this

Quote:
Originally Posted by rcahill

... Centrifugal force if it were physically real would cause the ball to move in a different direction with a radial component. Since this does not happen ...

goes beyond linguistic issues to incorrect mathematics.

I think we have pretty much wrung all the fun out of this discussion.

It would be more interesting to look at the force balance and how it shows that angulation is a good idea.  (I know, its been done, but Chuck probably hasn't seen it.)

Hey math monsters, here a good question. During the transition from one turn to the next, the feet and the core move along separate but inter-related paths.  So which is flying off on a tangent and which is falling off the carousel . I know the cop out answer is it all depends on the frame but pick one and see how linking turns affects the clarity of expressing how to link turns.

mdf,

Nice animation. But perhaps you didn't read what I said earlier "...you can pick a frame of reference that make a motion appears to be any shape or line, and that ['s] where the business of inertial frame of reference comes in." I can select a FoR to make a skier or your ball to fly off tangent, radially outward, straight into the center, or even stationary in that FoR. It's trivial. Using an arbitrary frame of reference, you simply have to add an apparent force determined from the motion of this FoR (relative to an inertial FoR) to the object in question to describe the motion of the object. I had described the math. If the chosen FoR is moving linearly with a constant speed, the apparent force is zero. If it is rotating, you get the centrifugal monster.

So, there is really nothing fancy about the FoR once you get off the train that CF is real. Let me ask you one thing that hopefully will open the door for you to jump off that train (people who use Landau&Lifshitz as a text book, not just as a reference to snow the uninitiated shouldn't be passengers on that train). In your celebrated rotating FoR, it is rotating relative to WHAT?

I got the impression that you are proficient in the requisite math, here is another question: What is the equation of motion in the FoR that is rotating relative to another rotating FoR with different axes of rotation?

Frame of reference is just what we, humans who are so sure of ourselves, select to solve a problem, to show off our math, or to try to impress our friends. Mother nature doesn't give a hoot about our FoR. Forces are a completely different beast.  rcahill's "physical reality" is a nice phrase. Before homo sapien came up with the concept of FoR, rotating or not, did centrifugal force exist in the universe?

JASP, to make life simple I will pick the COM as the FoR. In this FoR, the core is not moving at all by definition, the skis swing back and forth. The exact motion depends of course whether the skier is you, smooth, or me, jerky motion. Not very useful to any skier, right? Talking about FoR is not a productive way to teach skiers to ski more like you and not like me. But then, I am not a ski instructor and can't presume to tell you how to teach skiing. Maybe you can tell me how to ski bumps better in the other thread.

Edited by ChuckT - 12/24/11 at 1:38am

I guess now is a good time  to get my feet wet on this forum.

mdf quotes that amused myself (and others) :

I assure you I understand the physics at least as well as you (Chuck T).  I was giving you the courtesy of assuming that you would recognize and understand the examples without a ton of background, and then use them to consider my points.  We can trade resumes by PM if that will make you happy.

I doubt that. Your "knowledge" of physics is almost laughable. Actually it is almost to a point where it seems you are just (what do young people call it?) trolling. Your credentials are not needed either. They are tattooed on your forehead. If you had an undergrad in physics, could you please divulge what school you attended so I and the good public viewing these forums can make sure that our kids don't end up there. Thank you.

Chuck T put down exactly how it is here:

#1 In my experience, it is very common to find people throwing smoke and mirror, especially at parties before they learn about the background of their new party mates, with fancy terminologies, a named equation or such devices when they don't really know what they are talking about.

That was a very polite way of saying you are full of it, which I believe to be true. All I have seen from you is the spouting off of cool physics terms as if you were name dropping celebrities you are "buddies" with to new party mates. Nobody likes "that" guy, and we all make fun of him after.

#2 I can't find my copy of Goldstein, but I am interested now to see what he says in the introductory paragraphs before we get generalized forces in generalized coordinates.  In a classical mechanics sense, force is whatever appears on the other side of "dp/dt =" (Chuck owned you on that!)

Why? You should know that generalized coord. are only a convenient mathematical masturbation form of Newtonian Mechanics. There is no new physics or assumptions past Newton where correction terms in non-inertial frames are considered "apparent" and non-physical. If you understood what you were doing past plug and chug, you easily see how these corrections from the non-inertial frames can be isolated. Still Newt holds; where were you in freshman physics? Wait, were you one of the kids memorizing equations and copying the solutions manual? Be honest. What else did Goldstien help you unlearn? Facepalm. Cmon buddy.

#3 Last night I dug out my copy of Misner, Thorne and Wheeler's "Gravitation" looking for a good quote to use.....  Obviously, you would describe the goal of the experiment quite differently, and you are free to do so.  Nonetheless, here is an example where "real physicists" find the most natural way to talk about Coriolis is as a real force on the same footing as any other.

Wow. Haha. You look for a quote in what is basically "GR for dummies" for proof that even though F=ma is only covariant in inertial frames, we should consider the correction terms of NIRFs as physical forces?

General covariance? Did you miss that part? Wait, did you miss all of GR? Or do you just like saying manifold to people? I know I do. It sounds pretty cool and it makes us sound smart.

#4 By the way, I recently read a note that pointed out that forces transform as Christoffel symbols.  I haven't had time to work it through, but it makes a lot of sense.

Oh really? It makes sense eh? Haha. I would love to hear why!

I am pretty sure google can help here. If it really made sense to you, you would see why there is and should be a noted difference between frame dependent apparent forces and physical forces.

#5 Gravity is the fictitious force felt by those of us on the ground in an accelerating reference frame.  The astronauts are not accelerating, and therefore do not experience the fictitious force of gravity.

Wait, so you are okay with calling gravity fictitious in its realm, but not corrections to Newton in NIRFs? I think that would be called wish washy? Can we have a criteria for determining when it is okay to call a force fictitious

#6 The ball moves off tangentially in a straight line in the room's frame, not in the rotating frame.  In the rotating frame, the ball starts off stationary and accelerates in a purely radial direction. The centrifugal force is what makes it accelerate away from the center.

Facepalm. No, he still meant the inertial frame of the room. I love the fact that you can engineer stuff without even understanding Newton's laws.

Those animations are cool though.

Ah Spooky - I think you must not have read the entire thread.  You don't seem to know what we are arguing about.

Once again, let me emphasize that we agree on the equations of motion; what we are disagreeing on is how to describe them.  In particular, I was addressing Chuck's claim that "no real physicist" would treat CF as real.  I claimed no real physicist would ever use the term "fictitious force" outside of  a freshman physics context.

For example, your point #2 - I wanted to find Goldstein to see what he would say about CF.  And since then, I dug it out -- yep, the closest he ever gets to the word "fictitious" is "apparent" or "terms" (in an equation).  Mostly, they are just called "forces."

The other point about #2 -- forces don't come with sticky notes on them.  Suppose I start with some fundamental theory and want to know what forces it predicts.  How do I know which terms in the equations to label forces?  I claim it is precisely whatever appears on the other side of the equation from
"d(momentum)/dt equals."  That is the definition of force.

Point #5 - no, that is a rhetorical shift.  My point was, if I do come over to the fictitious camp, what else can I do with it?  I admit, that was a bit convoluted for internet arguments sake.  But it is not something I invented.

#6 - you still don't get it.  You are arguing that because the centrifugal force does not appear in your favorite reference frame, it is not real.  Of course it doesn't cause radial acceleration in the frame where it doesnt appear!  It does cause radial acceleration in the frame where it does appear!  You guys are mixing up frames and drawing bogus conclusions, so much so that post #109 says something wrong rather than just misguided.  (And to fix it, you are have to resort to, "what the candidate meant to say was...")

#4 - it makes sense because "these corrections from the non-inertial frames [that] can be isolated" are precisely the terms that enter the equations of motion in arbitrary coordinates through Christoffel symbos.

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