# Difference Between Torque and Moment

1. May 30, 2010

### Red_CCF

I understand that the two terms are not synonyms in the engineering context, but I never really understood the difference. My prof last year did a demonstration where he spun a meter stick to represent moment but twisted it to represent torque but I didn't really understand what he was getting at.

Clarification is appreciated.

Thanks.

2. May 30, 2010

### Phrak

Unfortunately the context varies. Are you in the US or Europe. Are you talking about engineering terms or physics terms?

3. May 30, 2010

### Dickfore

"Moment" of any physical quantity is associated with the distribution of that quantity around some axis. It is usually some power (1 or 2) of the distance of a point from the axis times the value of the physical quantity itself at that point and summed over all points. If the system is continuous, the summation is an integration over volume (area, length), but the multiplication is with the volume (area, linear) density of the quantity.

In this way, we have moment of inertia (mass), moment of force (torque), moment of impulse (angular momentum) and so on.

4. May 30, 2010

### alxm

Well, in https://www.physicsforums.com/showthread.php?t=399791" thread I just argued that 'moment' more or less means 'torque', since 'moment' or 'drehmoment' is the word for torque in German (and in many other languages).

jason12345 answered that it's from Latin, which is true. It's derived from Latin in all these languages. But Etymonline doesn't really address the specific physics term (and different usages have different etymologies), so it's hard to say which route this usage took. The reason I suspect it's from German (or French), is that it's the usual word for 'torque' there (e.g. torque-wrench is momentschlüssel), whereas English has 'torque' and 'moment'. And from the 'torque' sense, it got generalized to any axial force.

Ultimately I suppose that 'moment' could historically be applied to anything that had anything to do with motion or force (since that's what the Latin term meant), and there was no rigorous distinction between these things until after Newton.

But I tend to read the word the way Dickfore does, I.e. more or less as 'something around an axis; something involving a cross-product'.

Last edited by a moderator: Apr 25, 2017
5. May 30, 2010

### jack action

Last edited by a moderator: May 4, 2017
6. May 30, 2010

### Red_CCF

I'm in Canada and unfortunately I have to look at it from both an engineering perspective (in an structures course) and a physics perspective (in a classical mechanics course).

The moment I'm thinking about is the Nm one (the force causing rotation), not the mass moment of inertia (resistance to rotation).

I actually have an additinal question now after reading the link jack action provided. The wiki page says a couple is a system of forces that causes moment but no resultant force, but if something is rotationally accelerating (due to moment), then shouldn't there be a force be acting on it? Or does resultant force apply only in terms of causing translational motion but not rotational?

7. May 30, 2010

### jack action

From the http://en.wikipedia.org/wiki/Couple_(mechanics)" [Broken]:

Furthermore the difference between a moment and a torque (which is the result of a moment obtained from a couple) is this:

Last edited by a moderator: May 4, 2017
8. May 30, 2010

### Studiot

Red,
The difference comes when we consider 3 Dimensions.

Both a couple and a moment can only act in a plane.

A torque has an effect in the third dimension perpendicular to that plane.

This is why mechancical engineers talk about shaft torque. If a moment or couple is applied at one section (perpendicular to its axis) of the shaft, the twist is transmitted down the length of the shaft as a torque. A moment or couple may be recovered at another section. Depending upon the characteristics of the shaft material the twist may be described by a helix which is a 3 D object.

9. Jun 3, 2010

### jason12345

Looking into it further, Archimedes is credited with discovering the operating principle of the lever:

"movement, moving power" = force * distance from pivot.

Since moment is Latin for "movement, moving power", then it seems to me almost certain now that The Romans translated the work of Archimedes on the lever from Greek to Latin.

Last edited by a moderator: Apr 25, 2017
10. Jun 3, 2010

### Dickfore

Newton's most famous work was "Philosophiae Natrualis Principia Mathematica" and it was in Latin. Therefore, he was a Roman. Also, we write in English, therefore we are all English.

11. Jun 4, 2010

### jason12345

Using Wikipedia, I think it's generally true that:

The principle and laws of the lever are explained in two volumes by Archimedes: On the Equilibrium of Planes.
This was written in Doric Greek and translated into Arabic by Thābit ibn Qurra (836–901 AD), and Latin by Gerard of Cremona (c. 1114–1187 AD) from Arabic scientific works found in the Arab libraries of Toledo, Spain. Hence, these works were now available for the first time to people in Western Europe before the Rennaisance.

12. Jun 4, 2010

### Red_CCF

Oh so it's because the direction of the torque is perpendicular to both the radius and force vector (along the axle, perpendicular to the plane of the radius and force vector) while the direction of the moment is on the same plane as the force and radius vector? So the difference is due to their defined direction vectors?

13. Jun 4, 2010

### PhanthomJay

Oh, no, the direction of a torque or moment are both perpendicular to the plane of the position and force vectors. From a Civil Engineering perspective, I go back to your very first post and agree with your professor.... 'torques' are moments which tend to twist or rotate a body about its longitudinal axis, whereas 'moments' are moments which tend to bend or rotate a body about an axis perpendicular to its longitudinal axis. For the former case, the direction of the torque is along the longitudinal axis of the body, perpendicular to the plane of the force and position vectors; for the latter case, the direction of the moment is along the axis perpendicular to the longitudinal axis of the body, pependicular to the plane of the force and position vectors. I hope that's clearer than mud.

14. Jun 4, 2010

### Red_CCF

But doesn't that apply to moment (just one force) as well? For example, if I spin a wheel, the resultant force is not zero yet there is no acceleration of the center of mass and causes rotation only. It might be just me but the wiki page seems to imply that this effect can define/indentify a couple but doesn't a moment have the same effect as a couple in this case?

Last edited by a moderator: May 4, 2017
15. Jun 4, 2010

### Red_CCF

So the only difference is along which axis this rotation occurs? What is the longitudinal axis of a body? Is it like the axis perpendicular to a plane/surface of, for example, a CD disk and how do we identify this axis?

16. Jun 4, 2010

### Studiot

These sketches may help. Sorry about the quality.

The first figure is a straight prismatic bar, with no forces applied.
The longitudinat axis is aligned along the X axis.
Every cross section of the bar is a rectangle in a plane parallel to the ZY plane as shown at the side.

The second sketch shows a couple applied at the ends about the Y axis, bending the bar in the ZX plane, but leaving it undisturbed in the Y direction.
Every cross section is still a plane rectangle, but rotated in the Z direction.

The third sketch shows a torque applied about X axis, twisting the bar along its length.
Cross sections are now rotated relative to each other.
You may note that a torque can only be applied like this by two opposing couples. A single couple would merely cause the bar to rotate, not twist.

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17. Jun 4, 2010

### Red_CCF

Wow thanks for the diagrams, they cleared some things up for me. I just need a few clarifications.

So the wikipedia explanation of a couple/torque is not complete correct (http://en.wikipedia.org/wiki/Couple_(mechanics))? [Broken] Two couples are needed to produce a torque but one applied couple would actually produce a moment (just spinning)?

For case 2, the direction of the moment would be in the y direction and for case 3, the direction of the torque would be in the x direction?

Also, in case two, I didn't really quite get why the bar is undisturbed in the Y direction (no force in that direction?) and how each cross section is rotated in the Z direction? Is the cross section cut in the direction of the ZY plane?

Last edited by a moderator: May 4, 2017
18. Jun 4, 2010

### Studiot

Sorry if I gave the impression you have to have two couples for a torque. What I meant to say was that to cause the twist in the bar you have to twist one end with a couple and either twist the other way or apply a restraining couple at the other end. If you don't do this the bar will spin round, like the output shaft from a motor. The motor will develop more or less torque depending upon the restraint.

Both remarks about the sections are meant to show the three dimensional nature of torque and its ability to transfer a couple from one plane to another.

Please note I said couple each time because a couple is composed of two forces in linear equilibrium. A moment is a single force, which cannot be in linear equilibrium by itself.

To get back to the geometry.

In sketch 2, imagine a centre above the bent bar, so that the bar forms an arc of the circumference of a circle, with the centre above it.
All the sections are rotated along radii of this circle, so only the one in the very middle is still 'upright'. All the rest lean over, left or right.
However this is a 2 dimensional effect as all the action takes place in the X and Z directions.

Imagine a grid painted on the side and top of the bar.

In sketch 1 it is just a rectangular grid, showing the X, Y and Z coordinates of any point.

In sketch 2 The grid on the top surface is still rectangular, the Y values have not altered, but (nearly) all the X and Z values have altered on both the top and sides.

In sketch 3 you can picture (or draw) how the grids will be twisted. All three coordinates will change.

19. Jun 4, 2010

### Red_CCF

I don't really get how torque can transfer couple from one plane to another? What if there is a couple, but it just causes a spin (no twist), would it still be called a torque even though there is no twist? However, if there is a counter-couple against the applied couple, it would be called a torque? Where does the transfer occur?

And for the second part, basically it's the fact that the bar is not bending (no force applying in) the y direction such that an individual point on the bar only shifts along the x and z due to the applied force?

20. Jun 4, 2010

### jack action

To spin a wheel, it requires a couple and the resultant force is zero. There is the force you apply on the outside of the wheel and there is the opposite and equal reaction at the center of the wheel.

Even if it spins, it is still going to twist. Imagine the previous example of the spinning wheel, imagine the wheel is made of a soft rubber, it will deform (twist) as you turn it.

If you push on a solid bar it will deform (compress), because everything can be model as a spring. The softer the material, the more evident it will be, but no matter what, the force will transmit through bar to reach the other end. In rotation, it is the same thing: when you apply a torque (the equivalent of a force for rotation), there will be a twist but the torque will still be transmitted to other end of the shaft. You can model every shaft as a rotational spring like you can model every bar as a linear spring.