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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?