# What are the proper definitions of moment, couple, torque, 'moment of force'?

When I read some scientific articles I am getting confused with the interchange being used between Torque, Couple, Moment, 'Moment Of Force'.

Have I got this correct?

Moment is supposed to be some action of a quantity at a distance from some point.

Couple are two equal and opposite forces acting on an object , but with a distance between them.

Torque is a twisting effect where a force is applied at a distance from some point on a physical object (I am assuming there must be some physical medium connecting that force to that point on a physical object).

Moment Of Force = Torque

Moment of Couple = Torque effect (cannot be a Torque because it's not a single force about a point)

Why do some say a Couple is a Torque?

Why do some say Torque is a free vector when they actually mean Couple?

Isn't there a need for the science community to provide better clarity on these definitions?

• There is often a distinction between torque, which is applied along a fixed axis (like a shaft) and moment (moment of force) which is applied along an arbitrary axis. So if you know the direction use torque, otherwise use moment. – John Alexiou Aug 24 '20 at 11:17

Torque, moment and moment of force are often used interchangeably to mean the twisting effect of a single force about a given axis.

However, torque can also be used to mean the twisting effect of a pair of equal forces acting in opposite directions at different points i.e. a couple. With this meaning, the magnitude and direction of the couple’s torque is independent of where it is measured, hence it can be referred to as a “free” vector.

The Wikipedia article on torque explains these different usages clearly.

• But the word 'Torque' is being used to mean 2 different things and that can cause confusion. For example, I read an article today and after looking through all the equations the author said the net torque was a free vector (he really meant couple). – Dubious Aug 23 '20 at 15:00

As @Gandalf61 pointed out you can find a definition of torque on Wikipedia.

Although the terms moment and torque are often used interchangeably, since they are mathematically the same, a moment differs since it is used in connection with requirements for static equilibrium so that a moment does not actually cause rotation. It is only a measure of the tendency to cause rotation that must be counteracted by other moments so that rotation does not occur for equilibrium. In short, the term moment is used in statics whereas the term torque is used in dynamics.

Your understanding of a couple is basically correct but it is different from moment and torque because it involves two equal and opposite parallel forces that can cause rotation without translation. Note that the two forces must be parallel.

Hope this helps

• I thought 'moment' was a general term that can used to describe the action of a physical quantity at a distance from some point. Like the 'moment of momentum ' or 'moment of inertia' , etc . The equations normally use the distance ( or the distance with an exponent value) to describe the action done by that quantity. So are you saying that 'Moment Of Force' does not cause rotation? One can apply a 'Torque' in both static and dynamic scenarios. You can apply a torque with a spanner and not move the bolt , or it can move the bolt. – Dubious Aug 23 '20 at 15:13
• @Dubious Regarding moment vs torque, they are mathematically the same. This post discusses moment vs torque, not the general term moment. It's really a matter of how the terms are applied (where they are used). While there is nothing wrong with using the term torque in statics, I've only seen the term moment used, i.e., the sum of the moments must equal zero (so that there is no rotation). I've never seen "sum of the torques equals zero). The term torque may or may not be used in connection with actual rotation. But I believe it is in dynamics. – Bob D Aug 23 '20 at 15:33
• A 'moment of force' vs Torque are mathematically the same. I've seen moment of force used in articles describing dynamics and I've also seen articles and graphs stating the 'Net Torque' = 0 . Just google 'Net Torque'= 0 and you will see lots of examples. – Dubious Aug 23 '20 at 17:17
• Wikipedia: In physics, a moment is an expression involving the product of a distance and physical quantity, and in this way it accounts for how the physical quantity is located or arranged. Moments are usually defined with respect to a fixed reference point; they deal with physical quantities located at some distance relative to that reference point. For example, the moment of force, often called torque, is the product of a force on an object and the distance from the reference point to the object. In principle, any physical quantity can be multiplied by a distance to produce a moment. – Dubious Aug 23 '20 at 17:27
• Check out the confusion on this physics forum website and you can find the same in other forums too. :physicsforums.com/threads/… – Dubious Aug 23 '20 at 17:37

I like to define torque (or moment of force) as the work per unit angle of rotation that can be done by a force (or a combination of forces) acting in a manner that tends to cause a rotation. This helps remind you that there is a distance involved (proportional to the radius) and that you need the component of force in the direction of motion. (And it's consistent with the relation: work = torque x angle.)

• Do you mean the potential to do work because an applied Torque doesn't necessarily mean rotation? – Dubious Aug 23 '20 at 22:30
• Yes, that is what I mean. – R.W. Bird Aug 24 '20 at 13:28

The term moment of X implies that X happens at a distance as you mentioned. Additionally, there is a commonality in how they are calculated which involves the cross product of position and X. The cross product is used to extract the moment arm distance to that X.

• Moment of rotation (aka velocity) => $$\boldsymbol{v} = \boldsymbol{r} \times \boldsymbol{\omega}$$
• Moment of momentum (aka angular momentum) => $$\boldsymbol{L} = \boldsymbol{r} \times \boldsymbol{p}$$
• Moment of force (aka just moment) => $$\boldsymbol{M} = \boldsymbol{r} \times \boldsymbol{F}$$

So if you want to be technically correct, use the moment of X terms, and not the colloquial ones such as velocity, angular momentum and moment. I know crazy!

But you cannot do that, because you can have velocity without rotation, or moment without a force. The velocity of a purely translating rigid body is not generated from rotation, but it is the same for all parts of the body. It is a free vector because it is not associated with particular location, like the moment of rotation.

Similarly, a pure torque is not generated from a force at a distance (and hence the term moment is avoided) but something felt equally by all parts of the body. It is also a free vector because it is not associated with a particular location, like the moment of force.

A common way to generate a pure torque is by a force couple (aka just couple) which means two equal and opposite forces offset from each other arranged in such a way to generate the specific torque vector needed. This is mostly a result of the fact the mechanics primarily deals with contacts between bodies which only forces at the contact points, and there is no good way to apply a pure torque to a body without applied some kind of force combination also.

In practice, torque is meant to be used when the result is known (a moment along a specified axis) but the means of generating this torque aren't important. But a moment is used when the details of how it is generated are important.

Consider the following example

A rotating shaft with an asymmetric mass attached to it is cantilevered off one end of the shaft with a bearing, and a torque is applied on the shaft. Find the reaction forces and moments on the bearing.

Here there is a distinction between the shaft torque whose details are unimportant to the problem other than the moment is along the shaft axis and the reaction moments of the bearing whose details are important and act along an unknown arbitrary direction.

• When you say "pure torque " do you mean "moment of a couple " which is also known as a "pure moment" or a "force couple" ? See what I mean about the ambiguity of all these terms? You have your own ideas, while others have theirs and there shouldn't be this 'confusion' in physics. Look at Wikipedia's definition of a couple and it sounds cryptic. – Dubious Aug 24 '20 at 12:48
• Wikipedia: A better term is force couple or pure moment. Its effect is to create rotation without translation or, more generally, without any acceleration of the centre of mass. In rigid body mechanics, force couples are free vectors, meaning their effects on a body are independent of torque. This is not to be confused with the term torque as it is used in physics, where it is merely a synonym of moment.[1] Instead, torque is a special case of moment. Torque has special properties that moment does not have, in particular the property of being independent of reference point, as described below. – Dubious Aug 24 '20 at 12:49
• A pure torque is when you have a moment without a net force. It could be a force couple or a magnetic effect that causes it, but the end result is just a (free) moment vector with zero force vector. – John Alexiou Aug 24 '20 at 23:01
• Many thanks but then you have to define a 'moment' as a 'moment of something' . So what it is a 'pure torque' a 'moment' of ? Look at the definition of moment in my next comment. So the confusion still remains because there is no fixed reference point for a couple. Yet the definition causes ambiguity by saying 'Moments are usually defined' . – Dubious Aug 25 '20 at 2:21
• Wikipedia:In physics, a moment is an expression involving the product of a distance and another physical quantity, and in this way it accounts for how the physical quantity is located or arranged. Moments are usually defined with respect to a fixed reference point; they deal with physical quantities as measured at some distance from that reference point. – Dubious Aug 25 '20 at 2:21