Difference Between Torque and Moment

[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.

 

[Phrak]

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

 

[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.

 

[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'.

 

[jack action]

http://en.wikipedia.org/wiki/Couple_(mechanics)"

http://en.wikipedia.org/wiki/Torque#Terminology"

 

[Red_CCF]

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

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?

 

[jack action]

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?

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

Its effect is to create rotation without translation, or more generally without any acceleration of the centre of mass.

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

The moment of a force is only defined with respect to a certain point P (it is said to be the "moment about P"), and in general when P is changed, the moment changes. However, the moment (torque) of a couple is independent of the reference point P: Any point will give the same moment.

 

[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.

 

[jason12345]

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'.

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.

 

[Dickfore]

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.

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.

 

[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.

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.

 

[Red_CCF]

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.

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?

 

[PhanthomJay]

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?

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.

 

[Red_CCF]

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



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

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?

 

[Red_CCF]

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.

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?

 

[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.

 

[Red_CCF]

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.

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))? 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?

 

[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.

 

[Red_CCF]

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.

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?

 

[jack action]

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?

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.

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?

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.

 

[Red_CCF]

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.

Okay now I'm more confused . What would be examples of moment then because by Newton's 3rd law everything action has a equal and opposite reaction?

So the transmitted torque is basically a couple that turns the other way from the applied couple?

 

[jack action]

Going back to basic, based on these 3 wikipedia pages:

http://en.wikipedia.org/wiki/Moment_(physics)"

http://en.wikipedia.org/wiki/Couple_(mechanics)"

http://en.wikipedia.org/wiki/Torque"

Moment: It is the tendency of a system of force to twist or rotate an object.

In physics, moment and torque are synonyms.

In mechanics, a torque is a special case of a moment which creates rotation about the center of mass without translation of that center of mass.

In mechanics, the system of force that produces a torque has a special name: it is called a couple.

In mechanics, how can you prove a moment is a torque?

A moment is only defined with respect to a certain point P (it is said to be the "moment about P"), and in general when P is changed, the moment changes. However, the moment of a couple (torque) is independent of the reference point P: Any point will give the same moment.

 

[Red_CCF]

Going back to basic, based on these 3 wikipedia pages:

http://en.wikipedia.org/wiki/Moment_(physics)"

http://en.wikipedia.org/wiki/Couple_(mechanics)"

http://en.wikipedia.org/wiki/Torque"

Moment: It is the tendency of a system of force to twist or rotate an object.

In physics, moment and torque are synonyms.

In mechanics, a torque is a special case of a moment which creates rotation about the center of mass without translation of that center of mass.

In mechanics, the system of force that produces a torque has a special name: it is called a couple.

In mechanics, how can you prove a moment is a torque?

A moment is only defined with respect to a certain point P (it is said to be the "moment about P"), and in general when P is changed, the moment changes. However, the moment of a couple (torque) is independent of the reference point P: Any point will give the same moment.

Yes that's more clear to me now. Just one thing, in the torque wiki page, terminology section, it mentions that bending moment is not a torque because there is a net force, but this would mean that a beam is moving which is not the case so I think it's wrong, do you agree?

 

[jack action]

Yes that's more clear to me now. Just one thing, in the torque wiki page, terminology section, it mentions that bending moment is not a torque because there is a net force, but this would mean that a beam is moving which is not the case so I think it's wrong, do you agree?

Let me give you another example. Imagine a rocket in space. If the astronauts want to rotate the rocket, they will turn on two opposite reaction control thrusters with a distance d between them (image e in the following figure).

If one thruster is stronger than the other, then the resultant force is not zero, so there will be a rotation about the CG, but there will also be a translation of the CG as well. No matter where the thrusters are wrt the CG, the acceleration (in translation) will be the same, but the angular acceleration about the CG will depend on the position of the thrusters wrt the CG. This is a moment.

If the two thrusters have the same force, the resultant force is zero with a moment F X d setting the rocket in pure rotation, no matter where they are wrt the CG. This moment, we refer to it as torque.

Now imagine that rocket back on Earth, held rigidly by a shaft passing through its CG and this shaft held rigidly by a vertical pole aligned with the CG, such that nothing can move. Assume the thrusters are aligned with the vertical pole. Let's apply the same forces.

In the first case (one thruster stronger than the other), there will be a compression (or tension) force in the vertical pole due to the resultant force of the thrusters. There will also be a bending moment applied to that pole. The moment strength will depend on the position of the thrusters wrt the pole.

In the second case, there will be no vertical force in the pole, since the resultant force of the thrusters is zero. There will also be no bending moment either. There will only be a torque applied to the shaft, with magnitude F X d, no matter where the thrusters are wrt the shaft.

 

[koolraj09]

Hi
I agree with Studiot, Torque(in engineering terms) always acts parallel to a surface or axis,while moment acts perpendicular to the axis.