Talk:Angular momentum

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Contents 1 Old, unsectioned comments 2 Tesla coil 3 Definition 4 diagrams 5 Cutting editorial comment from the article page here for discussion 6 relativistic angular momentum 7 kinetic energy 8 Angular momentum in relativistic mechanics 9 Units 10 Operator 11 Ice Skater, Big Bang, KE goes up! 12 The explanatory power of angular momentum 13 Smoke rings 14 Angular Momentum in layman's terms 15 L=Iw, vector or scalar 16 Conservation of Angular Momentum 17 Hamiltonian is not gauge invariant 18 O.K. Now give the people something they can read.... 19 Relevance 20 Picky suggestiong? remove the word massive 21 INTRODUCTION nit-picking

[edit] Old, unsectioned comments

The reason the proof of angular momentum was originally attached to Torque as a subpage, was because I considered the proof trivial, and not interesting to the majority of users interested in the article. In fact, I thought it would scare aware the math-phobic general public. I wrote it shortly after I rewrote Torque. The previous version of that article contained the misconception that the derivative of angular momentum is equal to torque only in special cases. I wrote Torque/Angular momentum proof to justify my alteration, to explain to whoever wrote the article why I'm right, and of course to increase the amount of information in Wikipedia by a tiny, trivial amount. I disagree with its inclusion in Angular momentum because the inclusion of this trivial, apparently random factoid is inelegant, confusing, and makes the article overly mathematical. -- Tim Starling 01:52 Apr 28, 2003 (UTC)

Only, it's non-trivial. To make it trivial requires certain quite reasonable assumptions - but a rigorous demonstration is far more awkward than (say) energy conservation. Essentially, in general you are dealing with an infinite number of particles. Then you have to assume that some terms in an infinite sum go to zero, which isn't obvious. PML.

That depends on your definition of trivial, doesn't it? There's trivial as in the maths is easy, and there's trivial as in List of songs which have the word Song in title or lyrics. I think it's both -- it's trivial mathematically for someone competent in the field, and also trivial in the sense that most people reading angular momentum or torque don't care about how to prove this identity. But I'm getting off the point. Even if it were non-trivial mathematically, it still shouldn't be in the article, due to the confusion factor. Since confusion factor increases with non-triviality, your statement seems to support my main point. -- Tim Starling 03:02 Apr 28, 2003 (UTC)

I would say it supports the reverse: since there is something to be said, it is better to note it than to slide past it. Your remarks, while accurate as far as they go, don't lead to us leaving it out but to us making the editing draw attention to the fact that there is more for interested people to follow up - without distracting casual browsers. The principle of a good encyclopaedia. Now, how to achieve both? If in doubt, I'd rather leave it in. PML.

How do we achieve both? Simple, by leaving it how it was when I wrote it, i.e. on its own page. That's the whole point -- I'm responding to Looxix suggesting merging Proof of angular momentum (which started out as Torque/Angular momentum proof) with Angular momentum, an act which I disagree with. Sorry if I didn't make that clear. -- Tim Starling 05:44 Apr 28, 2003 (UTC)

No problem for me, it was only an suggestion/question. In fact, until we have the possibility to link within a specific part of a page, I often prefer to have well linked small pages than one BIG page having all the sub-subject linked to the main article. -- Looxix 20:47 Apr 28, 2003 (UTC)

[edit] Tesla coil

I removed the following paragraph, which seems a bit dubious:

A good model of angular momentum is the inventor Nikola Tesla's Tesla coil, where due to angular momentum of the field, a energy force can be pulled off at 90 degrees to the spin of the field on the coil, called phase,see also polyphase coils.

This might be true, but it's not very clear. What is an 'energy force'? -- Heron 19:33, 4 Jul 2004 (UTC)

[edit] Definition

I'm not happy about the definition used at the beginning of this article. I think we ought to be able to improve on this. I'd like to suggest the following. Any comments / improvements, please? Ian Cairns 22:37, 2 Oct 2004 (UTC)

"Angular Momentum is the tendency of an object orbiting an origin to continue orbiting. This is the rotational analog(ue) of linear momentum, and reflects the moment of the linear momentum of the object orbiting the origin. A body rotating about an axis can be considered to be the sum of its individual particles. Likewise the body's angular momentum can be considered as the sum of the individual angular momenta of all the particles' The SI unit of angular momentum is the kilogram metre squared radian per sec (kg m² s^-1)."

seconded if no one speak against, i'll implement it next week. 12 Dec 2004

I do not think it is a good definition, since it conveys the idea of some kind of inertia that will keep a particle in orbit. This is not true, since a force is ´´´always´´´ required for the particle to follow the orbit (although a torque may not be necessary) . TomasG

the current def. is really poor, (the one above seems better, but do see a problem with orbit, AM is usually about rigid bodies, orbits usually considering LM); "In physics, the angular momentum of an object rotating about some reference point is the measure of the extent to which the object will continue to rotate about that point unless acted upon by an external torque." reasons; . "in physics", what else could it be? . "reference point" is a point from which something else is measured, not as used here, . a spinning object can move its center of rotation to another point, if that point is very close by, very easily, this is not whats written here . "external torque" understanding this term requires at least as much physics knowledge as the definition is trying to put accross, so does not help understanding. Asplace 14:29, 24 February 2007 (UTC)

[edit] diagrams

Diagrams!!! We need diagrams! Otherwise it is very hard for young students to understand what is being talk about in this article. For example the angles. Without diagrams the young students are merely guessing where the angle is measured from.

Post requests to Wikipedia:Requested pictures, if you will. —Josh Lee 02:39, May 6, 2005 (UTC)

[edit] Cutting editorial comment from the article page here for discussion

I cut the editorial comment below for someone to integrate as text in the article page.

• • • • Comment from somebody else: this only defines "torque" as being the time derivative of angular momentum - when is the torque zero? Torque does not appear in any of Newton's laws, and should therefore not be used to explain under which circumstances angular momentum is conserved. The time derivative of the angular momentum is not a law in analogy to Newton's second law, but a consequence of Newton's law: simply take the time derivative of the angular momentum as defined above, and plug in Newton's laws. It then follows that a particle in a central force field has its angular momentum conserved. This was shown explicitly in a previous entry on angular momentum, which has been removed. *******

The above editorial comment was added in this edit. ---Rednblu | Talk 20:58, 6 Jan 2005 (UTC)

[edit] relativistic angular momentum

Does anyone know if there is a symmetry under spacetime rotations in quantum field theory?

[edit] kinetic energy

I think it would be useful to show the relatationship between kinetic energy (I*omega^2) and angular momentum. What do you think?

I added the link rotational energy.--Patrick 22:31, 1 November 2005 (UTC)

Kinetic energy in terms of angular momentum is (L*omega/2). Kenny56 02:02, 2 November 2005 (UTC)

[edit] Angular momentum in relativistic mechanics

Although this section is very short (and very interresting), I think that it is VERY advanced! Quite frankly, I am not sure that the average reader of this page would find it very usefull!

There should be a way to separate the basic introduction of the subject to the more advanced material.

Alain Michaud 04:19, 19 February 2006 (UTC)

[edit] Units

This page needs to mention the units of angular momentum.

[edit] Operator

As far as im aware, the L² operator is missing a factor of minus h-bar squared in the front there.

[edit] Ice Skater, Big Bang, KE goes up!

I was once asked, Where do stars get their energy from? Where does the energy for the spinning earths core come from? Nuclear fusion for the first case, but what started out the process? My answer was "Conservation of Angular momentum". As a spinning rotating body contracts due to gravitation, Work is done: W=FxD. Ice skaters expend energy to bring their arms and legs to the center. In a primordial dust cloud this energy is converted to heat. Rotating contracting dust clouds get hotter until plants form and fusion is initiated in the center. All thanks to "Conservation of Angular momentum" and realizing that the original source of the energy comes from resigual potential / kinetick energy left over from the big bang.

Is this a fair answer and is it worthy of including as an interesting discussion for the general public.

--Tbmorgan74 18:59, 6 June 2006 (UTC)

[edit] The explanatory power of angular momentum

In the article it is stated:

The conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs close to the vertical axis of rotation. By bringing part of mass of her body closer to the axis she decreases her body's moment of inertia. As angular momentum is constant in the absence of external torques, the angular velocity (rotational speed) of the skater has to increase.

In my judgement, the logic of this statement is flawed. My intention is to replace the flawed statement with a correct one. In an article that I wrote for my own website, you can read what in my judgement the correct presentation is. Conservation of angular momentum (the sections 'a centripetal force doing work' and 'causality') --Cleonis | Talk 09:11, 14 July 2006 (UTC)

[edit] Smoke rings

Angular Momentum is a cross product, it is not a vector. Consider the Angular Momentum of a smoke ring.

• That's a question of definitions. OK it doesn't "transform like a vector", but the only author I've read who used that definition is Einstein. One modern definition of a vector is as an element of a vector space. The other main one is of an element of a three-dimensional vector space with extra operations (dot product, cross product). According to both definitions angular momentum is a perfectly reasonable vector. If you want to define vector differently and change every entry in the wikipedia to reflect that then go ahead. If I had my way angular momentum would be a skew-adjoint linear transformation, but I tried that on Angular velocity once and I admitted defeat fairly quickly. Buster79 15:26, 8 October 2006 (UTC)

What is the Angular Momentum of the Universe? Is it a zero tensor? Cave Draco 01:14, 7 October 2006 (UTC)

• What's your point? Buster79 15:26, 8 October 2006 (UTC)

[edit] Angular Momentum in layman's terms

"In layman's terms, it describes the "fasterness" of moving an object after changing its "closerness" to its "centerness" of rotation. A person in a spinning chair, who moves his legs and head inward toward the "centerness" of rotationality, will therefore, spin with more fasterness."

This doesn't make sense, rotationality isn't even a word. Someone might like to have another go at adding a layman's definition in there, though personally I don't see what's not to understand :) -TeeEmCee 21:23, 21 November 2006 (UTC)

We could use a better one, but that does make the most sense for a layman than anything else i've read. Something a bit easier to visualize than the anonymous "particle" would help. -RikiTikiTavi

[edit] L=Iw, vector or scalar

In the equation L=Iw, L is bold and I ad w are italic. Bold means vector and italic means scalar. This should be fixed so that both sides of the equation have the same types. --Alanic 23:08, 8 January 2007 (UTC)

[edit] Conservation of Angular Momentum

In the section on the conservation of angular momentum, this article states that if the external torques add to zero, then the angular momentum is constant. However, this fact is NOT obvious because we have not considered internal torques. In fact, Newton's laws do NOT allow us to assume that internal torques always add to zero. The Kleppner and Kolenkow textbook on mechanics has a long discussion on this, where it concludes that it is not possible to prove mathematically that angular momentum is conserved and is an empirical fact. Does anyone with more expertise on this topic care to comment and maybe even change the article? -maxx

Now I'm wondering if MY question is the same as yours Maxx, excepting that I'm asking it from the point of view of a non-specialist. But it has to do with how the "preservation of angular momentum in the Earth / Moon system works. I have posted a 10 point question at the talk page on Moon, and it's basically asking whether the Moon would still recess in order "to preserve combined angular momentum" if the tidal effects were insignificant. I should think not. I am not going to reprint the whole thing here, but here's the link Talk:Moon. And go to Point 11 on the list. I would certainly appreciate any answer either here or there--Myles325a 14:30, 11 April 2007 (UTC)

I've not read Kleppner and Kolenkow, and perhaps their discussion goes deeper than most, including relativistic considerations, etc. However, what I do know is that it's a fairly simple matter to show in the context of Newtonian mechanics that if the total external torque acting on a system is zero, then the total angular momentum of that system is conserved (see Corben and Stehle "Classical Mechanics", pp. 36-38, Dover, 2nd Ed.). Another way of stating this fact is that total angular momentum is conserved if the Hamiltonian (or energy function) describing the system is rotationally invariant. This is a special case of Noether's theorem, which says that, for every symmetry of a system, there corresponds a conserved quantity (and her theorem yields a prescription for computing these quantities as well).Milez (talk) 00:18, 14 April 2008 (UTC)

[edit] Hamiltonian is not gauge invariant

The Hamiltonian given in the article is invariant only under gauge transformations that do not depend on time. Xxanthippe 03:14, 5 April 2007 (UTC)

[edit] O.K. Now give the people something they can read....

This is not an encyclopedia article really. It is of almost no use to anyone who would be reading Wikipedia. Try to keep the context in mind. The person who reads this is not doing Physics at Uni. No, they have come upon some term and would like to knnw a little about it, just the JIST of the matter. Consider that they are disinclined to go to a reference library, and are too cheap to shell out for a sub to Britannica. No, what do you think a punter like that would make of the hieroglyphs you have got there? Absolutely nothing.

And yet, there is a fair bit the average mortal COULD know about angular momentum without dedicating themselves to a life of being a physicist. After all, there are academic treatises on anthropological issues which the lay reader could never understand, and does not want to understand. But in these fields, there are quite a few reference sources which will enlighten average Joe Blow as to what is happening in the Moggabogga tribe without weighing them down with a great deal of jargon, and material which is of interest primarily to the specialist. August and widely respected intermediary publications like New Scientist and Scientific American (and I read both) manage to bridge the gap between cocooned boffins and an interested and reasonably well-educated LAY audience. If they can do it, why is it that a bunch of amateurs, working for free, and writing for a lot of school students who can't / won't get to a library, feel impelled to dump this stuff on them. What, is it a "Look at me, I'm way, way, way ahead of you lot? Watch the master at work" syndrome"?

I suppose that before I started looking up stuff in WP, I had the idea that an Encyclopedia written BY the masses FOR the masses, would of course be far more accessible than one written by experts. Then I realised that that was not the case. At first, it seemed counter-intuitive. But then I began to see score upon score of articles, many on subjects far less forbidding than this one, but with a common problem. They were not accessible to the great unwashed, many were deliberately obscurantist, many had talk pages in which authors made open avowals that they would never compromise on their "work" by trying to "oversimplify" their material, that the Joe Blow who had stumbled on their pronouncements just had to realize the wonderful, incredible complexity of this material. Or otherwise, they should just take up macrame, or something.

I then came to an understanding. You see, in my working life, I spent a fair bit of time compiling manuals and tutorials for novices in computing areas. Most of my time was not spent in demonstrating the august splendour of which I had such mastery. In fact, most of my time and effort was spent in doing the very opposite. The real skill in my job was telling people something in as sweet, plain and simple a language as I could. I never burdened them with some aspect of computing that they did not need to know to do their jobs. I never used a technical term that had a plain English parallel that would do. I spent a fair bit of time grading the material, so that those who did not NEED to know the more complex stuff did not have to wade thru it to get to what they did need. But it was only until I came upon the phenomena of Wikipedia, and thought about it some, that I began to understand that the PRIMARY skill in any kind of explanatory writing lies in COMMUNICATION. In Communication, NOT in expertise in the subject. It takes a good communicator to make the difficult simple, it takes a COMMUNICATOR to assess from first principles - BEFORE they begin to write - WHAT people they are writing for, WHY these people are liable to be reading this stuff, WHAT they intend to do with it, HOW MUCH they know already, WHAT can I spare them, HOW can I grade the material so that it does not become dispiriting? HOW can I provide safety nets so that if they do lose the way, they can find the path again before they lose hope?

And then, while I was thinking of these matters, I would also have to think about how I could make a bridge BETWEEN what the trainee had experienced, what he/she had seen, was familiar with and even liked, to the more abstruse, foreign world I was trying to introduce them to. I spent a lot of time thinking about how I might do these things, a lot of time talking to the people who would be reading and learning from these manuals. I spent about 90% of my writing time on doing that and 10% of it on doing the research.

Now I didn't think that much of it back then. I guess I sort of keep my light under a bushel a bit. But it was only when I started becoming familiar with the Wikipedia world, that I bagan to realise just how good I was. I was a TEACHER, I was a COMMUNICATOR. I was not primarily an expert. And just as well, because many experts are rotten communicators. Of course, I had to be at least a second tier expert, and I guess that's why I was being paid. I had to have a useful mix of two skills not often found living happily together - the communicator who facilitates the education of people with the minimum of tears and the maximum of wonder and enjoyment, and the expert, who knows enough to at least give a reasonably accurate and useful account of the matter in question.

Now, a while back, I came upon an article in WP which purported to be NOT an article on SPECIAL RELATIVITY, but an Introduction to that subject. In other words, an introduction to an introduction to special relativity. And what did I find? Within 3 PARS of the start, we are into the kind of mathematical scribbling we see in YOUR article. Here is the VERY FIRST sentence of that "introduction". 'Everything started with the Michelson-Morley experiment to determine the absolute speed of the Earth through the theorised "luminiferous aether."' Why, I wondered, was it necessary to broach the concept of "luminiferous aether" in the first sentence of a introduction to an introduction to a brief entry on Special Relativity designed for people who won't shell out for a Britannica? And why mention "luminiferous aether" at all, considering that is not only a forbidding technical term, but an antiquated one to boot? Why indeed?

Eventually, I came up with the idea that the author did not know - or simply did not care - if people understood him or not. Rather like you. After all, neither he nor you, nor about a thousand others out there, are being PAID to write comprehensible English. I guess that's the difference. I WAS heing paid to write same, and I would have been out of a job had I not made every effort to get as MANY PEOPLE AS POSSIBLE to understand what it was I was saying, and so become proficient and happy workers. As it is, my work was widely regarded, by people who had a real vested interest in getting their staff to understand new technology, understand it well, and even - hey why not! - actually enjoy it. Now I imagine that if you were being paid a couple of dollars for every poor uneducated sod who read your material and came away a little wiser, then you would, I am sure, place a greater premium on clear and intelligible writing for a lay audience. And further, were you ACTUALLY BEING PAID a reasonable return, and you were menaced with dismissal if those depending on your tuition did NOT learn what they needed to know, then I feel sure that this would concentrate your mind wonderfully, and you would go to great lengths to write articles of the most lucid and transparent simplicity and beauty. But as it is, you are not, and you will be damned if you are going to make concessions for the stupid plebs.

Now, where was I? As yes, ANGULAR MOMENTUM. Well it's not the Bemuda Triangle, sure. It's not Paris Hilton. But it does have potential. Want to know the first thing I noticed when I opened the page. First off, all I saw were all those equations which would require college level maths to understand, and which therefore are a completely closed world to me and all but the most minute fraction of the human race. The second was the "ice skater". I always look for her when anybody tries to explain "angular momentum". And there she was, but instead of being in the first par, as the sort of illustration of angular momentum in action that everyone has seen, everyone enjoys, and thus is a PERFECT lead in to explaining what is going on as she spins faster by pulling in her arms, she is well into the body of the text, and the attendant description does not use HER to explain angular momentum, but utilizes the image replete with all the jargon.

Now, how did I get to the ANGULAR MOMENTUM article, anyway? You probably don't care by now, and I don't blame you. Once again, in my erstwhile job of making difficult things easy to understand rather than the reverse, I made sure I knew WHY people needed to know the stuff I was about to teach them. If our positions were reversed and it was me writing on "angular momentum" I might, for example, be interested in how people arrived at the article in the first place. You know, "Did you hear about the WP angular momentum article from your friends, your colleagues, or did you read about it in magazine, or did you simply lose a bet?" Well, this kind of information is of the UTMOST importance to any writer with a claim to being a purveyor of knowledge. Why do people read - or at least had that intention at the start - an article on angular momentum? Well, in my case, I had been reading, and proofreading the WP article on the Moon, and noticed that the material there on the Moon's recession from the Earth, due to angular momentum concepts, was less than perfectly clear. I had pondered in the past as to how the Moon might "sense" Earth's rotation across the space that separates them - and slow down accordingly. The whole question of the rate of the Moon's recession - whether it would stop, or go on forever, or stablize - was one which interested me. There was a link from there to angular momentum, so I took it, and I did not profit thereby.

Now I am not underestimating the difficulty of this subject. But, I would suggest it incumbent on the writer in such cases to make a concerted effort to take what IS EXPLICABLE concerning the subject and ISOLATE it. Then, using all the good educator's techniques of moving from the particular to the general, moving from the reader's everyday experience to experiences less familiar and so on, make an effort so that a diligent reader will have an "AHA" moment. Then a bit more slog, and then another AHA, and by the end, there will be a bit of light in that reader's head. They will know next to nothing about "angular momentum" when you figure how very much more YOU know about it. But they don't HAVE to know much about it, and if they did, they wouldn't be studying it there in WP. As it is, I'm not a deadhead, and I can tell you, I most certainly did not get a AHA moment out of your article. No, there was no glimpse of the Promised Land. I came in confused and left even more confused. Everything was and remains complete darkness. And I can tell you that I am not champing at the bit to get a eyeful of your "Torque" article. No sir, I've had enough for one day. But I can tell you, that if you working for me, then you wouldn't be working for me.

I guess that's part of the lesson of Wikipedia. It's an old one, and many would say, a cynical one, but true nonetheless. You get what you pay for. Still, even so, it is astonishing at times just how good a lot of the stuff is. I've noticed that with many articles, the Discussion page throws just as much light - if not more - on the subject, than does the main entry. And it has the sort of anarchic, to-and-froing, disputational flavour that is actually a lot closer to how knowledge is won from the mud of apathy than does the calf-bound, hide-bound, letter perfect productions of the big publishing houses.

But not here. Turning to the Discussion Page, I found the meditations of a very-like minded coterie of physicists. All of them are genuinely interested in the subject, and at a pretty advanced level, which is to be admired. But not one of them had the slightest interest in the issues I have raised. It was as if they were hermetically sealed off from all the readers who had appraoched the topic because THEY KNEW NOTHING ABOUT IT. WP is not designed as a common room in an ivy-league university. It is meant to be a repository of accessible knowledge for a PEOPLE'S ENCYCLOPEDIA.

And this is not an article which falls within that ambit. So, how can you do better? Well, I won't repeat myself. Hey, you probably disagree with everything I wrote here. You probably hate it. But you READ it. And I'll bet you understood every word.

Myles325a 19:36, 8 April 2007 (UTC)

Actually, while I appreciate what you say (at length), I'm a fourth year undergrad who's brain isn't working and was looking for alternative angular momentum definitions (for an accretion disk problem where packets of mass are falling onto a central star), and I suspect that Angular momentum is an article that is only ever going to looked at by people studying it, albeit quite probably at a school level. I agree the article looks a bit busy. GBM 23:18, 10 April 2007 (UTC)

Well, that was kinda my point. Wikipedia is not really here to cater to fourth year undergraduates. I would imagine that there would be any number of academic sites you could have googled, not to mention the material in your university library, where there is probably a whole floor of stuff for you to look at. This site’s first priority should be to serve the non-specialist, the general public in other words. I thought I had dealt with that in my piece. And no, lots of people run into the concept of angular momentum, often, as in my case, coming from such relatively non-technical topics like the Earth-Moon interaction. I also dealt with this in my piece. I would have suggested in these cases at aiming for people who are reasonably well-educated, have an amateur interest in physics, cosmology, astronomy and so on, but only rudimentary maths. The task is to provide a non-technical background explanation to these topics for a lay readership, only moving to the technical stuff at the end. If Scientific American and New Scientist can do it, then THIS organisation can. I also dealt with that, as you point out, at length. While I wrote at length, I can’t say your perusal was any more than cursory. --Myles325a 01:05, 11 April 2007 (UTC)

If Scientific American and New Scientist can do it

As a former reader of those magazines as a teenager and later a Physics student I can absolutely tell you. They Can't.

The article is not complicated, learning takes effort and unless you have some concrete suggestions to the article you should just stop rambling.

89.181.97.102 (talk) —Preceding comment was added at 01:25, 12 December 2007 (UTC)

[edit] Relevance

Hoaglang, Richard C. and Bara, Mike, Dark Mission: The Secret History of NASA, (2007), Feral House ISBN 978-1-932595-26-0. What has this book got to do with angular momentum? Xxanthippe (talk) 21:52, 8 February 2008 (UTC).

That appears to be some possibly weak justification for what sounds an awful lot like nonsense inserted below AM in ED. --Altered7th (talk) 11:05, 9 February 2008 (UTC)

Thanks. I have deleted it. Xxanthippe (talk) 11:41, 9 February 2008 (UTC).

[edit] Picky suggestiong? remove the word massive

2nd to the last sentence in the 2nd paragraph - "... the kinetic energy stored in a massive rotating object such as a flywheel is proportional to the square of the angular momentum." I think that the adjective 'massive' is mis-leading as this will be the case with any rotating object, even one that is of, relatively, low mass. Not being a subject matter expert, I hesitate to directly edit, but I do suggest this for your consideration.

Also, the discussion on the usefulness of this page to the layman is quite interesting in itself. I agree that the page takes some effort to read. Looking around the web, I don't find anything easy that also provides meaningful content. 75.35.217.119 (talk) 16:08, 10 February 2008 (UTC)

With regards to "massive": perhaps in this context 'massive' is being used to indicate the property of simply having mass - not necessarily having a relatively large amount of mass. Nevertheless it isn't the pinnacle of clarity and I agree with 75.35.217.119 that revision would be helpful. The lay reader would benefit more by the removal of the word - anyone predisposed to wonder whether the statement can be extended to the massless will likely already know the answer. --67.160.66.72 (talk) 13:56, 11 February 2008 (UTC)

[edit] INTRODUCTION nit-picking

In both paragraphs of the introduction, the author states that the angular momentum of a closed system can't be altered unless acted upon by an external TORQUE. Now, I know this isn't wrong since any force applied to the rotating mass at any given distance from the axis of rotation is equivalent to a TORQUE, but the wording just bothers me. In any classical Newtonian physics text relating to momentum, they will stress that an object will not change its momentum unless acted upon by an external FORCE.

Another issue I have is with the use of a "point" instead of an axis to define the rotation of a body. Using a point as a reference may have some relevance in advanced topics, however for an introduction, it seems counter-intuitive. With an axis (IE: a line), a lay person can visualize an object rotating with a given direction (which experts in the field go on to define with the right hand rule) without even realizing it. However, by saying "a point" instead, I personally first picture a sphere rotating in an given direction whithout rhyme or reason.

In the intent of keeping at least the introduction of this subject as simple as possible, wouldn't it be better to state:

"In physics, the angular momentum of an object rotating about some reference AXIS is the measure of the extent to which the object will continue to rotate about that AXIS unless acted upon by an external FORCE. In particular, if a point mass rotates about an axis, then the angular momentum with respect to the axis is related to the mass, the velocity and the distance of the mass to the axis.

Angular momentum is important in physics because it is a conserved quantity: a system's angular momentum stays constant unless an external FORCE acts on it. When that FORCE is acted upon the object at a given distance from the axis of rotation, the result is a TORQUE. Torque can also be described as the rate at which angular momentum is transferred in or out of the system.

When a rigid body rotates, its resistance to a change in its rotational motion is quantified by something called the Moment of Inertia. This Moment of Inertia is a concept that has alot to do with the shape of the object. In essence, it accounts for all the mass of the object and its distance from the axis of rotation. Follow the link to the Moment of Inertia page for more information.

Angular momentum is an important concept in both physics and engineering, with numerous applications. For example, the kinetic energy stored in a rotating object with a given mass, such as a flywheel, is proportional to the square of the angular momentum. Knowing how much kinetic energy something like a flywheel has, allows engineers to use that knowledge to design systems that can change the orientation of a sattelite in space, or store electrical power to be used later, or smooth out the rotation of a crankshaft in a traditional combustion engine.

Conservation of angular momentum also explains many phenomena in sports and nature."

To me, that has a better flow with fewer confusing "jumps" in knowledge. Please feel free to revise if I got some of the concepts wrong. 141.119.184.10 (talk) 18:24, 22 February 2008 (UTC)

I think the first sentence should remain as it is. First, it is incorrect to state that angular momentum remains constant unless acted on by a force. There are a lot of ways to apply a force that will not result in a change in angular momentum. It is a net torque that is necessary to change the angular momentum of an object, not just a force. But thanks for thinking about it and trying to make improvements to the article. PhySusie (talk) 18:37, 22 February 2008 (UTC)

Adding that clarification "...by an external FORCE resulting in a net TORQUE.", would still convey my point, and clarify the issue.141.119.184.10 (talk) 17:57, 25 February 2008 (UTC)