Torque and energy

I've always been confused about why the units of torque, which are force × distance (in SI base units N×m) are the same as those for work: why, in SI units, is torque measured in joules?

But it's obvious, because torque really is work: if you turn something through 1 radian exerting a torque of 1Nm, then you do 1J of work on whatever it is you are turning. The units of torque are really joules per radian, but radians, of course, are dimensionless.

I don't know why it took me so long to understand this.


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