# Coupleand Torque

Please explain the difference between couple, torque and moment of the force?

Stonebridge
On the left: a couple.
two equal forces, in opposite directions (antiparallel) with their lines of action separated by a distance x
The couple has a moment equal to F times x

On the right: the force F has a moment about the axis O which is equal to F times r
r is the perpendicular distance of the line of action of the force from O.
This is also referred to as the torque of the force about O.
Torque and moment mean the same thing.
(I have a feeling there may be a slight difference in terminology on different sides of the atlantic on this one. Is this true? Mine is how it is defined in the UK)

Thanks Stonebridge can you please also explain differences in their properties?

Homework Helper
(I have a feeling there may be a slight difference in terminology on different sides of the atlantic on this one. Is this true? Mine is how it is defined in the UK)

Hi Stonebridge!

I don't think it's a country thing, it's just a general lack of consistency.

"torque" can mean moment

"a torque" can mean a couple

"a pure moment" can mean a couple

… it just depends which book you're reading, or who your professor is

(oh, and I suspect engineers like to talk about applying a torque instead of a couple, as in torque-wrench )

Stonebridge
Thanks Tiny-tim
Yes there has always been a bit of inconsistency on this.
I also think this may be what is causing the problem for the original poster.

To Ali
I'm not sure what you are asking for. There isn't really any more to say about these terms. It's easier to talk about actual examples where you have to use them to solve a problem.
Do you have a specific problem we can look at?

Studiot
Firstly there is no ambiguity or inconsistency about these terms. Nor is there any difference bewtween UK and US practice.

All three terms describe a turning effect.

The first two, couples and moments look at things from the viewpoint of the external force needed to generate the turning effect.

A couple requires two parallel, equal and opposite forces. It is always a vector (at right angles to the plane of the forces) and has the same effect on any point in its plane. It is non localised.
There is no single force which can be statically equivalent to a couple.

A moment requires one force and is localised. A moment about a straight line is a scalar. A moment about a point is a vector.

Edit however that one force can be the resultant of as many as you like acting in combination.

Torque is the actual turning effect itself, regardless of source. It is used for instance to describe the turning effect available at the ouput shaft of a machine - how hard can it turn something? This can obviously be converted to a specific force at a specific distance or a specific pair of forces but there are many solutions.

Torque also appears internally within bodies when we consider torsion. It appears in the angular deformation equivalent of Hookes law

Contrast the following for a circular shaft

$$\delta = \frac{{FL}}{{AE}}$$

gives the linear deformation, $$\delta$$, for an applied force F with youngs modulus E, lenght L and cross section area A

$$\theta = \frac{{TL}}{{JG}}$$

gives the angular deformation $$\theta$$, in radians for an applied torque T, moment of inertia, J and shear modulus G.

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Homework Helper
Firstly there is no ambiguity or inconsistency about these terms.

Torque is the actual turning effect itself, regardless of source.

Sorry, but I completely disagree.

There is inconsistency in practice.

An additional example: torque is perhaps best know in the phrase "torque equals I alpha", where it means the same as "moment (of force)".

(and i suspect that the reason for using the "wrong" word in this case is that using "moment" would cause confusion with I, which of course is "moment of inertia")

Stonebridge
Firstly there is no ambiguity or inconsistency about these terms.
I don't think the claim was that the terms are ambiguous or inconsistent. It's occasionally the usage, that is.
Nor is there any difference bewtween UK and US practice.

I'm glad we all agree on this.

Homework Helper
I'm glad we all agree on this.

Nooo … I love it when there's a difference bewtween UK and US practice …

I particularly like spelling words like "centre" the English way.

Studiot
What fun, I hope you noticed we have a new physical dimension in Somerset after a few ciders

lenght

Studiot
An additional example: torque is perhaps best know in the phrase "torque equals I alpha", where it means the same as "moment (of force)".

Personally I think the best know examples are in either the 'torque wrench' or the output torque v engine speed of say a Ford engine.

Of course torque and moment refer to the same turning effect.

Consider the following.

I have a socket set.

If I attach my 9inch crank bar to the driver I get a certain torque on the nut.
If I attach my 15inch crank bar to the driver I get a different torque on the nut.
Using my torque wrench I can apply only the appropriate torque as specified by the manufacturer.

Again if I now attach and extension shaft between the crank and the socket to reach down into the engine to access a nut, I can define (or measure) the force and the lever arm of the crank to calculate the moment I am applying at my end of the extension.
But what of the socket end? I am applying a torque to the nut but what forces are acting?

Then again If I remove the socket form the nut and rotate it in free air by the crank bar, I am definitely applying a force (and therefore moment) to the crank end.
Equally the socket end rotates because it is still subject to a torque, but what forces are now acting?

sganesh88
Equally the socket end rotates because it is still subject to a torque, but what forces are now acting?
Intermolecular forces. If there's no direct connection, it won't rotate.