Newton-metre unit symbol

[Danijel Gorupec]

I have problem understanding Newton-metre unit (or should it be written in all-lowercase style: newton-metre? Or newton-meter perhaps?).

 

I don't have the problem with the unit itself, but with the way the unit is written: N m (or even with a small central dot in between: N*m). According to Wikipedia, the newton-metre unit has a space between 'N' and 'm'. But this would indicate the 'dot product', wouldn't it?

 

It seems to me that it would be better to write the Newton-meter unit all compact: Nm. This way 'Nm' is clearly a unique symbol, and not a compound unit. If you insist, I might accept: N x m (indicates vector product).

 

Now, in my software (Math-o-mir) I implemented the newton-metre as a compound unit only because Wikipedia says so. But I am bothered with this and I am about to discard Wikipedia teaching. First I would like to hear what you can say about it. Thanks.

[imatfaal]

According to BIPM (which I think is authoritative on these matters)

 

http://www.bipm.org/en/publications/si-brochure/section2-2.html

 

newton metre or N m

 

I guess \cdot is acceptable too

 

In forming products and quotients of unit symbols the normal rules of algebraic multiplication or division apply. Multiplication must be indicated by a space or a half-high (centred) dot (·), since otherwise some prefixes could be misinterpreted as a unit symbol. Division is indicated by a horizontal line, by a solidus (oblique stroke, /) or by negative exponents. When several unit symbols are combined, care should be taken to avoid ambiguities, for example by using brackets or negative exponents.

 

 

http://www.bipm.org/en/publications/si-brochure/section5-1.html

[mp][/mp]

 

And on a more questioning note - do we really want to make the unit look like a vector? It is true that force and displacement are vectors as are the various resulting moments of force / torques - but when we quantify one are we not giving a scalar magnitude and a direction via unit vector; thus the units appended should be scalar products not vector products

[John Cuthber]

Also, It's a capital N because it's from Newton's name and a lower case m because the metre isn't named after someone.

(Conveniently, that stops it getting muddled up with the nanometre, though the space is also a hint.)

[imatfaal]

...

newton metre or N m

 

Also, It's a capital N because it's from Newton's name and a lower case m because the metre isn't named after someone.

(Conveniently, that stops it getting muddled up with the nanometre, though the space is also a hint.)

 

I presume that is addressed to me - and your comment is not wholly correct. The unit symbol is capitalised if it comes from a proper name - you will note that both Daniel and I did that. However the unit name is not capitalised - the BIPM give it as newton metre - with the exception of degree Celsius - where degree is the unit and Celsius remains a name.

 

 

Unit symbols

Unit symbols are printed in roman (upright) type regardless of the type used in the surrounding text. They are printed in lower-case letters unless they are derived from a proper name, in which case the first letter is a capital letter.

 

BUT

 

In English, the names of units start with a lower-case letter (even when the symbol for the unit begins with a capital letter), except at the beginning of a

sentence or in capitalized material such as a title.

 

from

SI Brochure: The International System of Units (SI) [8th edition, 2006; updated in 2014]

[studiot]

Hello Daniel did you understand that stuff about vectors, dot and cross products?

 

I ask this because there are two units that are the product of force (Newtons) and distance (metres)

 

Force and distance are always vectors in this context so when we multiply them two products can be formed.

 

Most folks use the Newton-metre to refer to the vector product or moment. This is still a vector. Distance in this case is taken at right angles to the line of the force.

 

So far as I know we haven't graced anyone with this unit and the unit of moment is only the Newton-metre.

Perhaps we should call them the Archimedes?

 

The alternative multiplication is the cross product and the result is a scalar we call work. Work has the same dimensions and unit as energy - the Joule.

People seem to use both lower and upper case j's for this unit indiscriminately. Also the Newton metre is not often used for this unit.

[Danijel Gorupec]

Thanks for referencing BIPM... a much more relevant source than Wikipedia. BIPM mentions newton meter and claims specifically it to be a compound unit: N m = kg m^2 / s^2.

 

It is not easy for me to accept this, because if so then there is no difference between newton meter and joule: N m = J. In my mind, however, these are completely different things (For example, in vague terms... Joule is somehow 'integrative' - it does not exist in an infinitesimal small time scope, it is not a momentary value. Newton meter is somehow 'derivative', it is a momentary value.)... This brings me to your observation...

 

 

And on a more questioning note - do we really want to make the unit look like a vector? It is true that force and displacement are vectors as are the various resulting moments of force / torques - but when we quantify one are we not giving a scalar magnitude and a direction via unit vector; thus the units appended should be scalar products not vector products

 

I pondered on this... I can accept that if I write torque like T = 10 N m, I actually meant |T| = 10 N m. Thus, I can accept that units are always scalars. But this does not mean that newton meter, even if scalar, is equal to joule (for sure a scalar).... But notation, as suggested by BIPM, does not show this difference. I am not sure if BIPM claims 'N m' and 'J' are the same thing, or they just claim that we don't need to care about it while writing these units down (bacause it is a common understanding or something).

 

Consider example: I make a value called 'specific toruqe'. This value tells what is the torque on each infinitesimally small portion across a hinged beam. The unit is Nm/m (newton meter per meter). Do you think this 'Nm/m' is the same as 'N'? I do not. But if one accepts BIPM notation, then it is confusing why we cannot shorten this m/m factor.

Hello Daniel did you understand that stuff about vectors, dot and cross products?

 

I ask this because there are two units that are the product of force (Newtons) and distance (metres)

 

Force and distance are always vectors in this context so when we multiply them two products can be formed.

 

Most folks use the Newton-metre to refer to the vector product or moment. This is still a vector. Distance in this case is taken at right angles to the line of the force.

 

So far as I know we haven't graced anyone with this unit and the unit of moment is only the Newton-metre.

Perhaps we should call them the Archimedes?

 

The alternative multiplication is the cross product and the result is a scalar we call work. Work has the same dimensions and unit as energy - the Joule.

People seem to use both lower and upper case j's for this unit indiscriminately. Also the Newton metre is not often used for this unit.

 

Yes studiot, I understand this... and the question is why is this difference not reflected in BIPM notation (one newton meter is written as 'N m' or 'N*m' that suggests a dot product.)

 

Yes, I would like Archimedes (although 'A' is already taken)

[John Cuthber]

 

 

I presume that is addressed to me - and your comment is not wholly correct. The unit symbol is capitalised if it comes from a proper name - you will note that both Daniel and I did that. However the unit name is not capitalised - the BIPM give it as newton metre - with the exception of degree Celsius - where degree is the unit and Celsius remains a name.

 

 

The explanation of the fact that the unit has a capital and minuscule letter wasn't aimed at anyone in particular.

And, as far as I know, it is correct; it's N m rather than n m or N M because there was a Mr Newton, but there wasn't a Mr Metre.

[studiot]

 

Yes studiot, I understand this... and the question is why is this difference not reflected in BIPM notation (one newton meter is written as 'N m' or 'N*m' that suggests a dot product.)

 

Sorry I wouldn't have t' foggiest.

 

Us grunts just get on with it.

 

Rules and regs we leave to the lawyers who like that sort of thing.

 

Edited February 8, 2015 by studiot

[swansont]

Thanks for referencing BIPM... a much more relevant source than Wikipedia. BIPM mentions newton meter and claims specifically it to be a compound unit: N m = kg m^2 / s^2.

 

It is not easy for me to accept this, because if so then there is no difference between newton meter and joule: N m = J. In my mind, however, these are completely different things (For example, in vague terms... Joule is somehow 'integrative' - it does not exist in an infinitesimal small time scope, it is not a momentary value. Newton meter is somehow 'derivative', it is a momentary value.)... This brings me to your observation...

 

 

Torque and energy have the same units, but it's not correct to use units of energy with torque. But neither is a fundamental unit.