Is 100 Nm Equal to 100 Joules of Energy?

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Discussion Overview

The discussion revolves around the relationship between torque and energy, specifically whether a torque value of 100 Nm is equivalent to 100 Joules of energy. Participants explore the definitions and dimensional analysis of torque and energy, as well as the conditions under which work is done in rotational systems.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that while torque is measured in Nm, which is dimensionally equivalent to Joules, this does not imply that torque and energy are the same or that torque can be measured in Joules.
  • Others argue that generating torque does not necessarily require energy, similar to how generating force does not require energy.
  • A participant notes the distinction between scalar and vector quantities, stating that energy is scalar while torque is vector, thus they cannot be equal.
  • One participant explains that work done by a torque is calculated as torque times the angle through which an object rotates, emphasizing that radians are dimensionless.
  • Another participant questions the calculation of work done when applying a torque through a specific angle, leading to discussions about the implications of conservative forces and closed paths.
  • Some participants clarify that the work done is dependent on the angle through which the torque is applied, and not merely on the torque value itself.
  • There is a discussion about the work done by conservative forces and how it relates to torque and angular displacement.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between torque and energy, with no consensus reached. Some agree on the mathematical relationships involved, while others challenge the interpretations and implications of those relationships.

Contextual Notes

There are unresolved assumptions regarding the definitions of work, torque, and energy, as well as the conditions under which these quantities interact. The discussion includes various interpretations of the effects of conservative forces on work done.

electerr
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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.
 
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electerr said:
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.
 
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
 
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?
 
electerr said:
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.
 
electerr said:
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.
 
I think electerr is just asking about applying an external torque through an angle, not conservative forces.
 
  • #10
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...?
 
  • #11
electerr said:
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.)
 
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  • #12
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).
 
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  • #13
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
 
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  • #14
willyadventur said:
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.)
 

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