A couple of days ago, I noticed that the torque unit used by my teachers is $mN$, and while reading on the internet it came to my notice that in all textbooks the official unit is $Nm$.
I asked one teacher about it and he insisted that I'm wrong, and while I told him that I read it on Wikipedia, he said that the sources or references used by Wikipedia aren't necessarily correct and I think I agree with him on that.
I checked my book and the only time it's mentioned is while discussing string torsion (I explained how it appears at the end of the post) but while solving problems, all our physics teachers us $mN$.
All of my teachers convince us using the idea that torque should be distinguished from energy since their units have the same dimensions and they represent different quantities (and I agree on this one) and that torque is the cross product between position vector and force to further support their point that it must be $mN$ and not $Nm$ even though the second point doesn't make any sense.
I kept looking online and eventually found the SI units official brochure published by the International Bureau of Weights and Measures and it clearly states that the unit must be $Nm$ and it couldn't be wrong (since it's the official units reference by definition).
My problem is that my school textbooks, while not in English, write its equations in English letters and notation (also left to right) so it couldn't be a matter of translation.
I'm not even trying to argue with him (because that's impossible, even if I had proof, he's too stubborn)
and in fact, he told me to look into more trustable references (he suggest old French textbooks/literature since he thought they were more dependable on than others even though I couldn't find any and they're probably outdated by now).
So is this choice of units purely conventional, or does matter mathematically, or are both units correct?
Best Answer
Just like $2\times3=3\times2$, There is no difference between newton-meters and meter-newtons. They're two different ways of saying the same thing.
Probably your book is trying to avoid confusion when you learn about energy, which is also measured in newton-meters, although we normally rename the unit, when referring to energy, as joules.
You should go ahead and call the unit of torque "meter newtons" in your class, because that's what your instructor expects. But be prepared to see other people call it "newton meters". I'd even strongly recommend using newton-meters anywhere except in your class, since the unit ${\rm m\cdot N}$ (meter-newtons) is much too easily confused with $\rm mN$ (millinewtons).