[hamdani yusuf (OP)]

The law of conservation of energy can also be used to understand torque. If a force is allowed to act through a distance, it is doing mechanical work. Similarly, if torque is allowed to act through an angular displacement, it is doing work. Mathematically, for rotation about a fixed axis through the center of mass, the work W can be expressed as

The equation clearly implies that SI unit of torque is Joule per radian.
When unit of torque is stated as Newton meter, it's important to note that the meter here is for perpendicular distance with the direction of force.
But when Newton meter is used to express work, the meter here is for parallel distance with the direction of force.

If a quantity is expressed in Newton meter, more information is needed to determine whether it's a quantity of work or torque, because the distance in meter doesn't tell if it's parallel or perpendicular with the force in Newton (tangential or radial to the circular trajectory, respectively).
On the other hand, the unit Joule already tells that it's a dot product of Newton and meter, which means the distance in meter here is always parallel to the force in Newton. Expression of torque requires the conversion from parallel to perpendicular distance, which can be done by dividing it by angle of rotation.
IMO, expression of torque as Joule/radian is better for eliminating ambiguity. It's just an unfortunate path of history which lead us to this confusion, that the concept of energy wasn't explicitly quantified in a standard unit when the concept of torque was introduced.

 

[hamdani yusuf (OP)]

Thus, we can avoid confusion by...

Thus far, the list of people who are confused by this only seems to have one entry, and that's you.

I've shown that even Gemini gets confused.

Do you  know that Gemini isn't a person?
Its a prototype undergoing testing.

It's trained using commonly used data in various fields. When it makes mistakes, the cause can usually be attributed to the errors in the training data.

[Bored chemist]

When it makes mistakes, the cause can usually be attributed to the errors in the training data.

And once again, all together now...
The lies we tell to children.

[hamdani yusuf (OP)]

When it makes mistakes, the cause can usually be attributed to the errors in the training data.

And once again, all together now...
The lies we tell to children.

The children eventually grow up. They will have to face the reality.
A lie requires discrepancy between what we say and what we think. It's hard to prove. IMO, it's more likely an honest mistake.

[hamdani yusuf (OP)]

I sense another epic study of confusion is beginning.

Most people don't feel confused because they never think deeply enough about this, which made them fail to recognize the inconsistency.

[paul cotter]

Nonsense. Torque is a force that may or may not produce a rotation. If rotation occurs work is done and then the displacement angle is of significance. In the absence of rotation there is no angle involved and obviously no work.

[Bored chemist]

A lie requires discrepancy between what we say and what we think. It's hard to prove. IMO, it's more likely an honest mistake.

You think parents telling kids about the tooth fairy are honestly mistaken?

[alancalverd]

Many people, myself included, have noted that the dimensions of torque are the same as the dimensions of energy, but I doubt whether anyone has confused the two quantities, particularly since the invention of the clock spring.

Indeed the torque applied to a clock spring exactly determines the amount of energy you can get out of it.

[paul cotter]

Hi Alan, as you know I am a committed pedant and I disagree with your last statement, re the clock spring. The energy stored in the spring is determined by the torque applied multiplied by the number of rotations, not just the torque. Since this thread is another exercise in confusion I will forgive your error, this time. PS: to be totally utterly pedantic I think one would have to do an integration of the torque over the full winding cycle as the torque will not be constant.

[hamdani yusuf (OP)]

Nonsense. Torque is a force that may or may not produce a rotation. If rotation occurs work is done and then the displacement angle is of significance. In the absence of rotation there is no angle involved and obviously no work.

When a torque produces no angular acceleration, then there must be another torque working in equal magnitude but on opposite direction. It's similar to force and linear acceleration.

We must have learned about it in school.

[hamdani yusuf (OP)]

A lie requires discrepancy between what we say and what we think. It's hard to prove. IMO, it's more likely an honest mistake.

You think parents telling kids about the tooth fairy are honestly mistaken?

No, afaik.
But there are illiterate groups of people who tell similar fairytale stories to children not knowing that they are false.
The difference lies in whether what they say is the same as what they think to be true.

[hamdani yusuf (OP)]

One of the first lessons introduced in process safety training is that we can't manage the risk from a hazard that we can't identify. Likewise, to reliably solve a problem, we need to identify it first, and then look for potential solutions, and select and do the most effective and efficient one.

[alancalverd]

I think one would have to do an integration of the torque over the full winding cycle as the torque will not be constant.

As the tightening torque increases with each turn of the key, I think the final torque equals the stored energy, same as when you stretch a bolt by tightening it. The difference is the much smaller hysteresis and energy loss of a spring.

[hamdani yusuf (OP)]

Hi Alan, as you know I am a committed pedant and I disagree with your last statement, re the clock spring. The energy stored in the spring is determined by the torque applied multiplied by the number of rotations, not just the torque. Since this thread is another exercise in confusion I will forgive your error, this time. PS: to be totally utterly pedantic I think one would have to do an integration of the torque over the full winding cycle as the torque will not be constant.

You seem to understand the formula.
But somehow you are missing its implication to the unit of torque.

[hamdani yusuf (OP)]

I think one would have to do an integration of the torque over the full winding cycle as the torque will not be constant.

As the tightening torque increases with each turn of the key, I think the final torque equals the stored energy, same as when you stretch a bolt by tightening it. The difference is the much smaller hysteresis and energy loss of a spring.

I think you should relearn about the formula I quoted above. It seems like you are being confused.
The final torque might be proportional to the stored energy, but clearly not equal.

[hamdani yusuf (OP)]

Thus, we can avoid confusion by...

Thus far, the list of people who are confused by this only seems to have one entry, and that's you.

Which part of my statement made you think that I'm the one who is being confused?

[paul cotter]

In reply to #32, I think you may be right, Alan. In which case I have to proffer my humble abject apology for sanctioning you. I have had a long hard day and I don't wish to analyse the spring winding but I believe you are correct.

[vhfpmr]

If you have a spring that follows Hooke's law, the displacement, s is proportional to the force, f, and the area under the graph is the energy stored: E=fs/2, or E=TΘ/2 (ie the area of a triangle).

[hamdani yusuf (OP)]

Many people, myself included, have noted that the dimensions of torque are the same as the dimensions of energy, but I doubt whether anyone has confused the two quantities, particularly since the invention of the clock spring.

Indeed the torque applied to a clock spring exactly determines the amount of energy you can get out of it.

I see you're ignoring the energy lost to friction, which can be a significant portion in real life applications.

[Bored chemist]

Thus, we can avoid confusion by...

Thus far, the list of people who are confused by this only seems to have one entry, and that's you.

Which part of my statement made you think that I'm the one who is being confused?

The fact that you think there is confusion.