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I am having a hard time to understand the meaning of measurements that involve a product of physical units, like $10\, \rm N\cdot m$ ($10$ Newton-meters), $3.33\, \rm J\cdot s$ ($3.33$ Joules-second), and so on.

When I have a quocient of physical units, everything is simple: $10\, \rm m/s$ (meters per second) means that in every one second, I travel a distance of $10$ meters. $25\, \rm N/m^2$ (Newtons per square meter) means that in every square with side equal to $1\, \rm m$ in a surface, I have a force of $25\, \rm N$.

But what does the product $10\, \rm m\, s$ ($10$ meters-second), $25\, \rm N\, m$ (Newton-meters) mean? I just can't figure out the meaning of this even after many online searches.

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  • $\begingroup$ What is the context of ms and Nm? The units by themselves don’t have any definite meaning. They must be considered in the context of the equation that generated them. Please add the context to your question $\endgroup$
    – Dale
    Feb 21, 2021 at 3:11
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    $\begingroup$ The compound units are context specific. You need to read through a physics book to understand the context first ... then you will understand the compound units that match that context. $\endgroup$ Feb 21, 2021 at 3:54
  • $\begingroup$ This has been asked and answered on this site multiple times. A good place to start is What exactly is a kilogram-meter? and the questions Linked to it shown in the sidebar on the right-hand side. $\endgroup$ Feb 21, 2021 at 11:28

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$J/s$ represents the rate of change of a process as you seen to understand. On the other hand $J\cdot s$ can be thought in the following ways:

  • Imagine you have a simple graph (simple because it would be easier to imagine) like a constant function $K$ where $y-$axis is labeled to be joule and $x-$axis is defined to be second. Consider that you want to know the difference (consumption) between $t_1$ and $t_2$, this area under the curve will be given by $K(t_2-t_1)$ and this will be in the units of $J\cdot s$.

  • You can write $J\cdot s$ as $\frac{J}{1/s}$ where this stands for the rate of change in $J$ per $1/s$ (so rate of change of Joule per frequency).

You can always use this above explanation for other units as well independent of what the units are unless there's something alarming like when you want to determine the area between two periods of time but the function is not continous in between and etc.

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