# What do we mean, concretely, by the unit $\rm N\:m$ (newton $\cdot$ meter)? [duplicate]

What do we mean, concretely, by the unit $$\rm N\:m$$ (newton $$\cdot$$ meter)?

For example, $$1 \:\rm m/s$$ mean that each second, we make one meter. Also, $$1\:\rm m/s^2$$ mean that each second the speed is $$1 \:\rm m/s$$ faster. Also, $$1\:\rm N/m$$ mean that each meter, the force is $$1\:\rm N$$ more powerful.

Now, I don't understand when instead of division we have a multiplication. For example, what mean $$1 \:\rm N\:m$$? How can I interpret this? (instead the fact that $$\:\rm N\:m=J$$). What is the phenomena behind?

## marked as duplicate by AccidentalFourierTransform, user191954, stafusa, Kyle Kanos, John RennieOct 9 '18 at 16:13

When we say that the torque $$\tau$$ exerted by a force $$F$$ applied at a distance $$L$$ from the fulcrum is given by $$\tau = FL,$$ the core of the statement is the fact that the "turning power" of a force $$F_1=1\:\rm N$$ exerted at a distance $$L_1=2\:\rm m$$ from the fulcrum is exactly the same as that of a force $$F_2=2\:\rm N$$ exerted at a distance $$L_1=1\:\rm m$$ from the fulcrum, i.e. that as far as "turning" is concerned, the two situations are identical, and, moreover, that there is a numerical measure of their turning power, $$\tau = FL = 2\:\rm N\:m,$$ which is the same for both.
Thus, when we say that a given situation produces a torque of, say, $$\tau = 8 \:\rm N\:m$$ about a given point, we're saying that it's the same effect as if you had a force $$F=8\:\rm N$$ exerted at a distance $$L=1\:\rm m$$, or a force $$F=1\:\rm N$$ exerted at a distance $$L=8\:\rm m$$, or a force $$F=4\:\rm N$$ exerted at a distance $$L=2\:\rm m$$, or a force $$F=2\:\rm N$$ exerted at a distance $$L=4\:\rm m$$, and so on.
• Thank you for this answer. It really make sense (when we talk about momentum). But $Nm$ is also equivalent to Joule. Since Joule is related to "Energie", how can we connect the "Energie" and the $Nm$ ? Also the Work of a force is in $Nm$. What does it mean that the work of $F$ is $3Nm$ ? – idm Oct 8 '18 at 16:10
• Just to be sure (I'm always confuse with energy, so it's good that you point on this), if the work of a force $F$ on an object $M$ is 3J it mean that if $F=3N$ it can displace the object of 1 meter only ? – idm Oct 8 '18 at 18:37