# Nm into Joules

Maybe this is a stupid question but...

If I have a torque value of, let's say, 100 Nm, am I right in saying that it takes 100 Joules of energy to generate that torque since 1 Nm = 1 Joule.

Doc Al
Mentor
If I have a torque value of, let's say, 100 Nm, am I right in saying that it takes 100 Joules of energy to generate that torque since 1 Nm = 1 Joule.
No, that's not right. Even though torque is measured in Nm, and a Nm is dimensionally equivalent to a Joule, that does not mean that torque and energy are the same thing or that it is correct to measure torque in Joules. (Joules are reserved for energy--never used for torque.)

And generating a torque doesn't necessarily require any energy at all, just as generating a force doesn't.

Dale
Mentor
2020 Award
The difference is that energy is a scalar quantity and torque is a vector quantity. A vector cannot be equal to a scalar even if the units are the same.

Got it. Thanks

jtbell
Mentor
Note that the work done by a torque equals the torque (in N.m) times the angle (in radians) through which the object rotates during the process. But radians don't "count" as far as dimensional analysis is concerned (they're a dimensionless ratio), so the work comes out with units of N.m = J as expected.

So, am I right in saying that if I have 100N in 1 meter and I turn my meter long handle 0.2rad that I do 100N * 0.2rad = 20Joules of work?

Doc Al
Mentor
So, am I right in saying that if I have 100N in 1 meter and I turn my meter long handle 0.2rad that I do 100N * 0.2rad = 20Joules of work?
Sure.

Note that work = torque*angle is the rotational equivalent to work = force*distance.

ZapperZ
Staff Emeritus
So, am I right in saying that if I have 100N in 1 meter and I turn my meter long handle 0.2rad that I do 100N * 0.2rad = 20Joules of work?

Pay attention to the post regarding "scalar" versus "vector". For example, what happened if you've moved for the whole 2pi radians when the force is conservative? How much work have you done?

Zz.

Doc Al
Mentor
I think electerr is just asking about applying an external torque through an angle, not conservative forces.

You are right Doc Al I wasn't asking about conservative force but I believe the answer to the question posed by ZapperZ is 0 Joules since the distance between the starting point and the ending point is 0, then 0 * 100Nm = 0 Joules, or...?

Doc Al
Mentor
You are right Doc Al I wasn't asking about conservative force but I believe the answer to the question posed by ZapperZ is 0 Joules since the distance between the starting point and the ending point is 0, then 0 * 100Nm = 0 Joules, or...?
No. If you apply a torque of 100 Nm continuously through an angle of 2π radians, then the work you do is 100*2π = 200π Joules.

Edit: Since ZapperZ specified a conservative force, the answer to ZapperZ's question is zero. But that's not your question. And the reason that the answer to his question is zero (for a conservative force) is not that torque*Δθ = torque*0 = 0, but that ∫torque dθ = 0. (The torque is not constant.)

Last edited:
Dale
Mentor
2020 Award
The work done by a conservative force around a closed path is 0 so I think that a conservative force cannot apply a continuous torque through an angle of 2pi radians. If we look at the torque on a wheel due to the conservative force of gravity we see that the net torque is 0 (otherwise it would spontaneously spin faster and faster).

Last edited:
Hi There

I don't know for sure, but, if we know the circumference of the circle and apply a 10 N.m torque * 2randians (and 2rads = 2 meters of circumference travel)

Then 10n.m * 2m = 20N.m of work? And I presume that also = 20 joules?

Willy

Last edited:
Doc Al
Mentor
I don't know for sure, but, if we know the circumference of the circle and apply a 10 N.m torque * 2randians (and 2rads = 2 meters of circumference travel)

Then 10n.m * 2m = 20N.m of work?
No. The work done is torque*angle, not torque*distance. (Check the units!)

(Realize that this thread is several years old.)