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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 Rennie Oct 9 '18 at 16:13

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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.

  • $\begingroup$ 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 $3Nm$ ? $\endgroup$ – idm Oct 8 '18 at 16:10
  • $\begingroup$ For one, it is important to keep the units for torque and energy separate. But that said, the same principle applies: 3 J is the work produced by a 3N force acting over a 1m displacement parallel to that force, or by a 1N force over 3m, or any other equivalent combination. $\endgroup$ – Emilio Pisanty Oct 8 '18 at 16:17
  • $\begingroup$ 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 ? $\endgroup$ – idm Oct 8 '18 at 18:37
  • $\begingroup$ No. It means that it's the work performed by a 3N force over one meter. It can also be the work expended, say, over three kilometers, by a 1 mN force. And so on. $\endgroup$ – Emilio Pisanty Oct 8 '18 at 18:39

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