Talk:Newton-metre

newtre
Would anyone care to provide some evidence to back up the claim that "Some people, as a matter of convenience, have opted to use a gramatical contraction of these units that is outside of the traditional SI vernacular. Instead of saying newton-metre, these people will, in casual conversation, refer to torque in units of the "newtre"."?

If there is no significant use of this sort, I will delete it. Gene Nygaard 03:21, 21 Feb 2005 (UTC)


 * Never heard of it, and Google evidently hasn't either &mdash; Egil 07:31, 21 Feb 2005 (UTC)


 * I'll remove it now. —Michael Z. 2005-10-13 18:29 Z 

Newton metre or newton-metre?
The latter looks right to me. Which is it? —Michael Z. 2005-10-13 18:29 Z 


 * Either. I like the hyphenated version better, too, that is to say newton-meter rather than newton meter, both of which are also correct.  Gene Nygaard 20:14, 13 October 2005 (UTC)


 * The official SI website uses the form newton metre. See: http://www.bipm.org/en/si/si_brochure/chapter2/2-2/2-2-2.html


 * The US NIST prefers a space character rather than a hyphen. It says that is also the preference of American National Standard for Metric Practice ANSI/IEEE Std 268-1992. See: http://physics.nist.gov/Pubs/SP811/sec09.html Bobblewik 23:03, 13 October 2005 (UTC)

newton metre vs. joule
While the article is correct (as far as I know, anyway), I feel the "joule" paragraph is confusing and makes it almost seem as if there is some relationship between a newton metre and a joule, other than the dimension. Specifically, the sentence about the "normal" vs. "colinear" arm sounds like maybe a newton metre is a joule except measured in a different direction. It seems to me that the article should just state something like "although a joule can also be (or maybe "is often"?) expressed in units of newton metres, it is an unrelated unit of measure". Kwh033 04:12, 11 November 2006 (UTC)

I absolutely agreed. So I've made changes along those lines. I thought the key thing missing was the differentiation between what the meter term represents in the calculation for joules and torque. Its very different, for joules it represents a distant moved or displacement but for torque it represents a distance from the fulcrum. —Preceding unsigned comment added by 124.169.184.25 (talk) 05:44, 5 February 2011 (UTC)

Propose merge into Joule
As http://www.bipm.org/en/si/si_brochure/chapter2/2-2/2-2-2.html makes clear, a Joule, like any unit, can be correctly algebraically expressed in many different ways (one of which is newton-meter) and you should express it in the way that makes it clearest what you're talking about. Even if you're only talking about torque, says this source, in some contexts you want to say joule (or joule per radian), and other times you want to say newton-meter. This would make a nice little section in the joule article: You say that there's lots of ways to write a joule, and in the context of torque it's often written newton-meter, and in the context of circuits sometimes you would write it as coulomb-volt, and for gravitational potential energy it might be clearest to talk about kg m^2/s^2, and when you're running an appliance maybe watt-second is best. Having a separate article for each of these endless synonyms is silly. (Some of the synonyms, like this article, should be turned into redirects to joule.)

What do other people think? :-) --Steve (talk) 01:09, 31 August 2008 (UTC)


 * Strongly disagree - The Nm is commonly used as the unit for torque (i.e. moment of a force), I've never seen Joule used in this context. The change you propose would make the whole thing much less clear for non-expert readers.  Djr32 (talk) 11:05, 12 October 2008 (UTC)


 * If you haven't seen Joule/radian used as a unit of torque, you should read the link I posted. Or, this recent book about SI units, or this 2004 book on machine design, or this physics article, or many many others --Steve (talk) 15:51, 12 October 2008 (UTC)


 * I did read the link you posted - in my view, the critical sentence was "This, however, is an algebraic freedom to be governed by common sense physical considerations; in a given situation some forms may be more helpful than others." In the situation I had in mind (levers, balancing beams - all the sort of things that kids study in secondary school physics), the Nm form is both the most helpful, and the one commonly used.  (Table 4 linked from your link specifically lists the unit for "moment of force" as Nm.)


 * Looking at the new links, I realised that there is a context where the J/rad form makes sense, e.g. a motor which is doing (rotational) work against a (constant) torque. I think your first two links are dealing with this situation.  (Maybe it would be worth writing something about this in the article?)  While I can see where they're coming from here, it seems much like talking about doing work against a linear force, and hence expressing that force in J/m.


 * Incidentally, the "per radian" part is not an optional extra, as your second link makes clear!


 * Summary: I still think that there is a need for an article about Nm. —Preceding unsigned comment added by Djr32 (talk • contribs) 17:07, 12 October 2008 (UTC)


 * Strongly disagree. Even though they're algebraically equivalent, torque and energy are two extremely different concepts.  —Preceding unsigned comment added by Twin Bird (talk • contribs) 17:35, 19 October 2008 (UTC)


 * This isn't a proposed merger of torque and energy. It's a proposed merger of Joule and Newton metre. As a different example, absorptivity and wavevectors are extremely different concepts, but I've never seen anyone object to measuring both in inverse metres. :-) --Steve (talk) 18:33, 19 October 2008 (UTC)


 * True - however, if there were a particular name for inverse meters in one or the other, there's no doubt that there would be an objection to using it in regard to the unrelated concept. The joule is, specifically, a unit of energy that just happens to be equal to a newton times a meter.  What you're suggesting is like merging the hertz into the becquerel, or the sievert into the gray.  Twin Bird (talk) 21:06, 29 October 2008 (UTC)


 * OK, ok, point well taken. (Another example is gauss (unit) versus Oersted.) I retract my merger proposal. --Steve (talk) 21:22, 29 October 2008 (UTC)

J/rad is commonly widely used .Voproshatel (talk) 14:04, 5 May 2023 (UTC)

meter Newton
Shouldn't this be mN, meter x Newton because of how you take the cross product of the radius of the wrench or whatever and the force applied to it? Banaticus (talk) 19:04, 13 October 2008 (UTC)


 * Mathematically the two would be identical, but Nm is the conventional choice. (Possibly because mN would be ambiguous with milliNewtons.) Djr32 (talk) 20:11, 13 October 2008 (UTC)


 * In cross products, A X B is not identical to B X A -- doesn't the cross product of torque require that it be mxN, or mN? It's been a while since I've done cross products, so I could be wrong, but I think it has to be in that order.  Whatever we do, it's going to be ambiguous with something, so it might as well list the correct order. Banaticus (talk) 18:55, 29 October 2008 (UTC)
 * The difference is the sign; it's not worth worrying about. "Newton-meter" rolls off the tongue better anyway.  Twin Bird (talk) 21:08, 29 October 2008 (UTC)


 * That's not right, there's no sign difference. You have R X F. "Newton" is a scalar factor within F, and "meter" is a scalar factor within R. The scalar factors commute, even though the underlying vectors do not. Example:
 * (2, 0, 0) X (0, 3, 0) = (0, 0, 2*3) = (0, 0, 3*2)
 * Likewise,
 * (1 m,0,0) X (0,1N, 0) = (0,0,1 m*N) = (0,0,1 N*m)
 * --Steve (talk) 21:46, 29 October 2008 (UTC)

Some errors
Article states:


 * "While a newton metre is dimensionally equivalent to a joule, the SI unit of energy and work, in a newton metre, the force and the distance arm are normal to each other, while in the joule, force and distance are co-linear. Another fundamental difference between the two is the fact that work is a scalar quantity, expressed as dU=F•dr, whereas the moment of a force or torque is defined as a cross product and as such is a vector quantity."

This is written as if "newton metre" were a synonym of "torque", and "joule" a synonym of "energy". They're not. They're units. The fact that work is a scalar while torque is a vector is a difference between work and torque, not a difference between a newton metre and a joule. It's entirely possible to have a scalar with units of newton metres, for example the magnitude of the torque vector. Also, the first sentence is a faulty comparison; for work, the so-called "distance" is the displacement of the point to which you're applying force, and for torque, it's a vector between the axis about which you're measuring torque and the point to which you're applying force, and anyway they're usually neither co-linear nor normal to the force. If no one objects, I plan to delete and rewrite this. --Steve (talk) 18:52, 19 October 2008 (UTC)


 * For simple cases, we assume that the force involved with a torque is tangential to a circular object, must like the basic movement equations (v=vi+at) generally ignore friction. In any case, we could decompose a torque which was not tangential to a 2D circular object into two vectors, one that is tangential and one that is perpendicular to that vector.  Then we could proceed to ignore the perpendicular vector while calculating pure torque.  So, let's keep the "colinear" and "normal" terms, even though I'd much rather see "pependicular" rather than "normal" -- no matter what the history of the word "normal" is, its general every day meaning isn't the same as "perpendicular", which is much better generally understood. Banaticus (talk) 18:51, 29 October 2008 (UTC)


 * I feel like you missed my point. This is a paragraph describing the difference between calculating a torque and calculating work. In my view, it's describing the it very poorly, but never mind. The point is that the unit of torque is not the same thing as torque, and the unit of work is not the same thing as work. The paragraph says it's describing the difference between Nm and J, but really it's describing the difference between how one calculates torque and how one calculates work. I'm going to go ahead and rewrite it, and we can discuss whether it's an improvement. --Steve (talk) 21:38, 29 October 2008 (UTC)


 * Steve - I generally like your changes. Two issues:
 * "Newton metre is the unit of moment (torque) in the SI system." became "Newton metre is a unit in the SI system often used as the unit of moment (torque)." I see what you're trying to do here, but it leaves the first sentence seeming very vague.  How about "Newton metre is a unit of moment (torque) in the SI system."?  (On an unrelated point, I'll fix the link to Moment (physics) to avoid going to what is effectively a disambiguation page.)
 * "However, expressing a torque in Joules is discouraged" - I don't think this is going far enough! The Joule really is the unit of energy, not the unit of energy and things which are dimensionally equivalent to energy.  J/rad would be OK, as your first reference makes clear (though see my previous comments).  Djr32 (talk) 22:30, 1 November 2008 (UTC)
 * I agree with both of those. I made some changes, but you're welcome to further edit. I changed "discouraged" to "strongly discouraged"...I don't think it would be correct to go further and say "forbidden", based on what I've seen on the BIPM website anyway. --Steve (talk) 23:43, 1 November 2008 (UTC)

Conversion to kilos
obviously newtons are weight (well force but in this context weight) and kilograms are mass. These only apply at nominal standard for gravity at the earth's surface-- hence essentially G (9.801...) in the equations. Should this somehow be added (without being too wordy)? I would suggest somehow without precocity referring to G (9.80665...) and then using it in the equations. This is only a mean value for G (but usually good enough). SimonTrew (talk) 00:35, 23 March 2009 (UTC)

Newton-Meters is both Torque and Energy/Work and must be dissambiguated
I would like to ask the question: So if I push a box with an applied force of one Newton, for a distance of one meter, what do you call it? I call it a Newton-Meter, and it is indeed an amount of Energy/Work (force x distance) and not a torque (force applied at a distance). To say Newton-Meter is a unit of torque is only true if it is indeed referring to torque. I suggest you change the first line to read the Newton-Meter can be either a unit of torque or a unit of work/energy. Then point out this article discusses torque and dissambiguate to an article that discusses energy. Same goes for foot-pound.

By the way, elsewhere in WikiP, you will find a conversion from Newton-meters to Joules, and this is referring to energy, not torque. —Preceding unsigned comment added by Jefffisch (talk • contribs) 14:43, 9 September 2009 (UTC)


 * If you push a box with an applied force of one Newton, for a distance of one meter, the amount of energy/work is 1 joule. You wouldn't call it 1 newton-meter. --Steve (talk) 16:19, 9 September 2009 (UTC)


 * Eshbach's handbook of engineering fundamentals - 10.4 Engineering Thermodynamics and Heat Transfer "In SI units the basic unit of energy is Newton-Meter". I am sure there will be varying opinions on this, but your average Physics book uses both foot-lbs and Ergs and NM and J when doing such a calculation.  If you look in WikiP under foot-lbs you find it says "The foot-pound force, or simply foot-pound (symbol: ft·lbf or ft·lb) is a unit of work or energy (a scalar) and also a unit of torque (a vector)." Since there is no God of units dictating that Newton-M must be written as Joules, or that Kg-m/s^2 be written as Newtons, for that matter, and since you don't get to dictate common practice, I suggest you do the same to Newton-meters.  Otherwise you will confuse those who are not in your sphere of practice.  —Preceding unsigned comment added by 71.243.13.245 (talk) 20:24, 11 September 2009 (UTC)


 * By the way, as a practicing engineer for 30 years in electromechanical systems, I use Joules only when referring to electrical energy, and I use either foot-lbs or N-m when referring to mechanical energy. Otherwise, in mixed systems, you can lose track of where the energy is coming from or going (i.e. mechanically or electrically derived).  —Preceding unsigned comment added by 71.243.13.245 (talk) 20:38, 11 September 2009 (UTC)
 * Also, as per the comment above by Banaticus, in AP Physics courses in many schools, students are taught to use m-N for torque and N-m for work, since torque is indeed a vector calculation. They are only invertable if, as you point out, you are have a scalar problem. In real life situations, for example, piezoelectric wave transmission, you do not have scalar quantities.  —Preceding unsigned comment added by 71.243.13.245 (talk) 21:03, 11 September 2009 (UTC)


 * OK, I didn't know of that usage. I added a small paragraph to the article, using your reference.


 * I agree that there's no right and wrong for how to express units like these; but there is the BIPM recommendations and we might as well put them in. Are you OK with how I phrased that paragraph?


 * I'm surprised that anyone is taught to observe a difference between m-N and N-m. I wasn't, and I would personally find that quite confusing. After all, torque=r×F and torque=-F×r are both true vector equations, and would give opposite order for the units. That said, if there are textbooks or handbooks that do this, we may as well put it into the article. --Steve (talk) 23:30, 11 September 2009 (UTC)


 * That is certainly better and more accurate. Thanks. Yet, it still seems a little confusing to read from my point of view.  I think that when you go to a WikiP article in the first place, the first paragraph is a quick reference to set the stage for further reading. I think it is always better to lay out there that there is more than one skin on this cat. Otherwise many readers will backout of the discussion (and not get to the paragraph about energy).  For example, look at the WikiP article about Torque.  It is quick to point out that there is Torque and there is Moment, and then later explains that while these are not differentiated in the academic field of Physics, in the field of Mechanical Engineering, they are not the same.  So if you start out with a question about how Torque and Moment relate, you will see this and read further for the details.  (IMHO)  —Preceding unsigned comment added by 71.243.21.169 (talk) 16:58, 12 September 2009 (UTC)


 * I'm flattered you picked the torque article as an example...I put in all the terminology discussion a few months ago! Anyway, I tried to do what you suggested, since it's a good point. :-) --Steve (talk) 05:46, 27 September 2009 (UTC)

Newton half-meters?
Lets say I want to tighten a bolt with 20N. That is roughly the same as applying a force of 20N and the end of my wrench, which is one meter long. Let's say now, that my wrench is only 0.5 meters long. How much pressure should then be applied at the end of it. 40N? 80.162.194.33 (talk) 21:14, 2 August 2011 (UTC)


 * Pressure would depend on the area of the spanner's handle which you're pushing (and actually vary over different parts of the handle. As for force, you're right: 20 N × 1 m = 20 N·m = 40 N × 0.5 m. J IM ptalk·cont 00:27, 15 March 2012 (UTC)

Torque vs work
I have just removed a paragraph about the relationship between torque and work (again). In my view, it does not belong here. It is important to draw attention to the fact that torque and energy are different physical quantities even though the unit "newton meter" is sometimes used for each. That does not mean it's appropriate in a stub-length article to describe ways in which one might crop up in the calculation of the other. It's as if, in a short article on the unit of length "foot", there was a paragraph explaining how you could describe a human foot using this unit: the width of the ball of the foot and the heel, the length from heel to toe, etc. It's a completely random and unnecessary example, which is only there because the name happens to be the same. Rracecarr (talk) 20:26, 5 March 2012 (UTC)


 * I think it's relevant, both to further emphasize the distinction (and actual relationship) between torque and work, which is obviously independent of the precise units used for each, but also because it specifically expresses the calculations in terms of the relevant SI units, and hence explains why "joules per radian" is a reasonable reading of the newton-metre as a unit of torque, whereas a naive dimensional analysis would just identify J and N·m.
 * Yes, this is all explained in much greater detail at Torque, but giving just the key formulas here seems reasonable, and plausibly useful to someone who just wants to understand how the torque of an engine is related to its power. In any case, how is the article ever going to grow beyond a stub if we proactively remove all arguably non-essential material? If the revised paragraph is still confusing, it should of course be fixed further, and maybe even trimmed (we can probably lose the integral in the footnote), but I don't see a strong case for outright removal. Hqb (talk) 21:13, 5 March 2012 (UTC)


 * I copy here for reference the text I most recently removed (minus the footnote):


 * The relationship between torque and work is that the torque (in N·m) can be used to calculate the energy expended (in Joules) by multiplying it by the angle of rotation (in radians) through which it acts. Or it can be used to calculate power output (in watts) by multiplying it by the speed of rotation (in radians per second).


 * I sort of buy your argument that if things always get removed from short articles when they appear to be given undue weight, the article will never grow. I'm less convinced that it's the best way to emphasize the distinction between the two usages--I imagine for some people the idea that you can "convert between" torque and energy might just make it more confusing.  Although it's pretty abstract, it might be more appropriate to add something similar to the sentence at Foot-pound (energy): The newton meter is a compound unit, a multiplicative combination of a force unit (newton) with a displacement unit (meter).  Since force and displacement are each vector quantities, they can be multiplied together using a scalar product, yielding an energy, or a vector product, yielding a torque. Rracecarr (talk) 21:59, 5 March 2012 (UTC)

I'm pretty much responsibly for both the second major paragraph and the 3rd one you don't like. It is indeed intended to be there to improve the clarity of distinction between torque and energy by showing how one is just a component of the other. Your proposed alternative significantly complicates the matter for a layman reader. Its the fact most people don't really know what a scalar or vector product is that led to all the confusion in the first place. I agree the article needs to flow better but its addition or restructuring of material that needs to happen, not outright removal. — Preceding unsigned comment added by 124.168.246.110 (talk) 03:53, 6 March 2012 (UTC)


 * I'm willing to be outvoted. But when I imagine coming to this page without a clear idea of what energy or torque is, it seems to me that including a description of how to calculate energy from torque would probably not be helpful.  There are many different types of energy.  Most of them do not intuitively correspond to a torque and an angular displacement.  This can all be explained, and it is, in other articles.  Not sure this one is the place for it.


 * Also, see the German version of this article for an example of other ways of distinguishing between the two meanings:  Rracecarr (talk) 21:22, 6 March 2012 (UTC)


 * I tend to agree with Rracecarr. This is a relationship between torque and energy.  It belongs in articles dealing with torque and/or energy.  This article is about a unit used to measure torque.  Should this said relationship be repeated on every article about units of torque? J IM ptalk·cont 00:37, 15 March 2012 (UTC)

Conversion Table
The various items in the conversion table were inconsistent with each other, expressed to different numbers of decimal places, and not consistently linked. I cleaned up the table by ensuring the proper use of "≈" as opposed to "=", calcing all factors to 8 digits, using the same syntax for and equivalents for the english units, adding the definitions of a couple of constants to help show how the conversion factors were derived, and added more links to the appropriate wiki articles. Compare version 2015-09-27T19:54:16‎ with previous to see changes. Gcronau (talk) 16:39, 27 September 2015 (UTC)

SI Authority discourages newton-metre usage for Joule?
This article contains the statement:

With "this usage" referring to newton-metre being used as a synonym for Work/Energy/Joules. The article for "Work (Physics)" contains a nearly verbatim copy of the above statement. And while I can find about 1500 hits on Google for claims that the SI authority "discourages" this usage, they mostly appear to be just cut and pastes from these 2 Wiki articles. All I was able to find on the main SI website at http://www.bipm.org was the document "si_brochure_8_en.pdf", which contains the following text:

The above is the only reference to "torque" in the entire document and a combined search of the terms: "newton-metre", "joule", and "torque" on the BIPM website only turned up references to the above document. Now, I see torque being used as an "example"(the above quoted section carried on and cited a few more "examples"). I also see the phrases "may be thought of" and "suggesting", but what I don't see are things like "must be used", and more pointedly, the use of the word "discouraged". Or any text implying that they discourage said use. I have attached a "Citation Needed" tag to the above statement. Does anyone have access to any (other)text from SI/BIPM that actually states that the newton-metre usage for Joules/Work is discouraged? If so, please chime in. I am going to add this same block of text to the talk page for "Work (Physics)" to get more eyes on the issue.Gcronau (talk) 19:54, 27 September 2015 (UTC)
 * Interesting question. I can think of several publications that discourage use of products like "1 N m" to mean "1 J", but none of them BIPM publications, and they might not use this particular example (I'd need to check).  In fact they seem more along the lines of criticism of BIPM for not discouraging them. Dondervogel 2 (talk) 20:50, 27 September 2015 (UTC)


 * That's the right statement. The person who wrote it knows very well that kg m^2 / s^2 can be referred to as "joule", it's the elephant in the room. The fact that they don't suggest using "joule" for torque strongly suggests that they don't think it's a good idea to do so. Also the context strongly suggests that they are worried about distinguishing torque from energy---again energy is the elephant in the room when you're thinking about "quantities with units kg m^2 / s^2". So I think the word "discouraged" is justified.


 * But nevertheless I edited the wording a bit to make the reference more clear and shift the references so that "generally discouraged" cites an explicit statement in a textbook and BIPM is cited more for explaining why it's a bad idea. --Steve (talk) 22:16, 27 September 2015 (UTC)


 * You stated: '...knows very well that kg m^2 / s^2 can be referred to as "joule"...', but see, that's part of my issue. My stance is that ((kg m^2)/s^2) isn't just something that can maybe sorta sometimes be referred to as a joule, ((kg m^2)/s^2) is a joule. Period. It's the very definition of a joule. (Also, in dimensional analysis terms, Work is ((M L^2)/T^2). This too is the very definition of work.) Also, you stated: "The fact that they don't suggest using "joule" for torque strongly suggests that they don't think it's a good idea to do so." In this, we agree. And I think you misunderstood me, or I didn't explain myself clearly enough. I was never suggesting that torque be described in joules, quite the contrary, I not only don't think it should be described in joules, I also don't think it should be described in newton-metres(or "newton metres", or "newton meters", or "N&middot;m", or whatever) either. On the other hand, I think newton-meters is an appropriate alternate expression for joules.
 * Torque IMO is a force, and should be described as a force. Maybe using some completely new units, because torque simply is not ((kg m^2)/s^2). In the simple case of W = F L, it is assumed that the vectors of F and L are aligned to produce W=((M L^2)/T^2). However, with torque, the vector of the second L is at 90 degrees to the force vector, the component of that vector that is in line with the force vector is always 0, so W is always 0.(When I'm holding a torque wrench at 80ft-lbs, it's not moving. The work being done is 0, there is only force against the handle.(And I know torque is also measured for rotating engines, but such engines aren't measured by torque alone, they're always measured by a combination of torque and horsepower. Torque is the force measurement, and work can be derived from HP-seconds.)) To my mind, the radius/length of the handle/moment arm length should lend no units to the equation, it should be considered a dimensionless quantity.
 * Look at it this way: Imagine a too-heavy-to-move weight. You try to lift it, but can't. You've applied force, but have done no work. You now put a fulcrum next to the weight with a lever sitting on it and jammed under the weight. You push down on the lever, but still can't move the weight. Work still has not been accomplished. The length of the lever has multiplied the force, but it hasn't added another dimension to the equation, since only upward movement of the weight is the second L of the work formula and not the length of the lever. And since that upward movement is 0, work is also 0, regardless of the length of the lever. So too, I think the length of the moment arm in torque is equivalent to the length of the lever. It's a force multiplier, but not it's own dimension.
 * But re-addressing a part of the original quote from BIPM, and getting(finally) to my basic point: "In practice, with certain quantities, preference is given to the use of certain special unit names, or combinations of unit names, to facilitate the distinction between different quantities having the same dimension. When using this freedom, one may recall the process by which the quantity is defined." I strongly think that it's important that standards organizations, and SI/BIPM in particular, bring a certain level of rigor, and, well, standardization to their standards. That terms like "freedom", "special cases", and sanctioning things done "in practice", should be anathema to such an organization. I think that the above quote is just plain weasel-wording. It's another way of saying: "We know that the units used for torque fly in the face of the methodology used to construct most(all?) other units, but torque has been expressed in units of newton-metres(and in the US, especially foot-pounds) for so long, we just decided not to fight that battle."
 * Most(All?) other units(SI or otherwise) that are expressed in the format of "Unit Unit", or "Unit-Unit", or "UnitUnit", or "U&middot;U" imply simple multiplication of the 2 units with a 0 vector angle. Watt-hour, Watt-second, amp-hour, foot-pound, inch-ounce, foot-lambert, lumen-second, lux-second, pascal-second, newton-meter, and others, all imply a straight multiplication between the 2 units. And if you multiply newtons((kg m)/s^2) by metres(m), you get ((kg m^2)/s^2) which is joules which are the units of work, and torque is just not work.
 * Ok, I was actually in the process of editing a whole new section for this talk page which detailed all my issues with this subject, when I saw your message. I had intended to just make a couple of quick points addressing a few items from your message, and damn, you got me monologuing... I'll have to decide whether to finish that new section, or just expand what I wrote here. Gcronau (talk) 03:48, 28 September 2015 (UTC)
 * (1) Your view--that it's fundamentally wrong to use newton-metres as the unit of torque, and people keep doing it only out of tradition--is so far from mainstream physics and engineering that discussing it doesn't even belong on a wikipedia talk page. Unless you find a textbook echoing your opinion, it's original research and will never be part of the wikipedia article, so there's no point in discussing them. See WP:TALK. Try physicsforums maybe?
 * (2) A quantity is not the same as its unit. Newton-metres is a unit for torque, not a synonym of torque. Just like "meter" is not a synonym for "distance". Therefore it means nothing for two different quantities to have the same unit. Wavenumber is often measured in units of inverse meters, and absorption coefficient is often measured in inverse meters, and 1D number density is often measured in inverse meters, but these are three quantities that have nothing whatsoever to do with each other. (Or at least, they are not more related than any two randomly-chosen physical quantities.) So it is possible to say "Both torque and work have units of kg m^2/s^2", and also say "Torque is just not work". There is no contradiction between those two statements.
 * (3) When calculating the area of a rectangle, you multiple the length and the width, which are perpendicular dimensions. Do you think it's wrong to measure area in square meters?
 * (4) I think it's best to say that ((kg m^2)/s^2) and joule and newton-metre are three different names for the same unit. Just like "Steve" and "Steven" are two different names for the same person, me. You can say "Steve is Steven. Period." And in a certain sense it's true: I am me. But in another sense, Steve and Steven are not the same name, and not interchangeable. On my tax forms, it would be inappropriate to use "Steve", but appropriate to use "Steven". So when you say "((kg m^2)/s^2) is a joule. Period.", you're not exactly wrong, but you're misunderstanding the issue. They are different names for the same thing, and in different contexts one name may be more appropriate to use than the other name. --Steve (talk) 14:15, 28 September 2015 (UTC)

Does unit use Unicode middle dot (·) or dot operator (⋅)?
As above. 210.162.143.223 (talk) 06:23, 26 June 2023 (UTC)
 * Like for all units expressed with a multiplication, the is generally preferred to, if easily available. However, the middle dot is part of the basic Latin-1 character set, so it may be more convenient to type, and will probably look the same in most contexts. Hqb (talk) 07:06, 26 June 2023 (UTC)

Unit of torque is Joule/rad
In the context of circles, angles and rotation, units of length are either tangential or\rm radial. Let there be two new units that replace good old $$ \rm m $$ (meters): $$ \rm m_{tan} $$ (tangential meters) and $$ \rm m_{rad} $$ (radial meters). The unit of a $$ \rm rad $$ is the conversion or ratio between these two units.

$$\rm rad = \frac{\rm m_{tan}}{\rm m_{rad}} = \frac{\rm m}{\rm m_{rad}} $$

Angular frequency in this context should be $$\rm rad/s $$, not $$ 1/ \rm s $$. Formulation of the relationship of $$ L $$ and $$ \tau $$ is a little more clear if you add $$ \Delta $$s or $$ d $$s like this: $$ \tau \cdot dt = dL $$. Doesn't really matter for this question use $$ s $$ instead of $$ ds $$ or $$ \Delta s $$.

So the units are $$ [\tau] = \rm N\cdot m_{rad} = \frac{\rm N\cdot m}{\rm rad} = \frac{\rm J}{\rm rad} $$. Notice the use of radial meters.

Additional related information is. Voproshatel (talk) 08:37, 2 July 2023 (UTC)