My textbook's equation for work done is:
work done = force * distance
So this means that the unit should be Nm. However, when I researched on Google, a lot of people were saying that the unit is J.
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$\begingroup$ Joule is a derived unit for energy (or work done). $1 J = 1 Nm = 1 kgm^2s^{-2}$ $\endgroup$– PolaroidDreamsCommented Jun 9, 2018 at 6:21
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$\begingroup$ Oh, I didn't know that. Text books have all the complex stuff, but they miss out small stuff like this ._. $\endgroup$– MythicalCode_Commented Jun 9, 2018 at 6:23
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$\begingroup$ @JustCurious What is 1kgm2s-2 (don't know how to use superscript yet) $\endgroup$– MythicalCode_Commented Jun 9, 2018 at 6:28
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$\begingroup$ Newton is the unit of force. $F = ma$. Expressing $1N$ in terms of basic SI units, we have $1kgms^{-2}$. Hence, $1Nm = 1kgm^2s^{-2}$. $\endgroup$– PolaroidDreamsCommented Jun 9, 2018 at 6:31
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$\begingroup$ @JustCurious Can you answer this question so I can accept it? $\endgroup$– MythicalCode_Commented Jun 9, 2018 at 6:38
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3 Answers
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The unit you should use for work done and energy is the joule (J) which is indeed the same as the newton metre (N m).
There is another physical quantity which is the product of force and distance and that is torque or moment of a force.
The unit you should use for torque is the newton metre (Nm) and not the joule.
Naming the units of work done and torque differently helps to emphasis the fact that work done and torque refer to two different physical quantities although the definitions of both quantities have the product of force and distance in them.
$\text{work done}= \vec{\rm force} \,\cdot\, \vec{\rm displacement} $ and $\vec {\rm torque}= \vec{\rm force} \,\times\, \vec{\rm displacement} $
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J (joule) is a derived unit for energy (or work done) named after the physicist James Joule. Since $W = F.d$, we have 1 J=1 Nm. We can also express in terms of basic SI units, yielding us
1 J = 1 kg m$^2$s$^{-2}$.
answered Jun 9, 2018 at 7:31
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J (joule) is the SI unit of $work$ which is equal to N m. It's a derived unit of work and the name is chosen in honor of James Joule who is pretty well known for his work in Thermodynamics.
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1$\begingroup$ Typographical conventions… Use italics for algebraic quantities, but upright (roman) for units. If you type the name of the unit in full, it starts with a small letter, even if it's named after someone. When you abbreviate the unit, the first letter of the abbreviation goes to a capital. Examples: joule abbreviated to J, hertz abbreviated to Hz. $\endgroup$ Commented Jun 9, 2018 at 9:59