The Differences Between Torque, Moment, and Couple

Out of these three terms, most people are probably more familiar with torque. Torque is casually defined as the rotating force about a given axis – such as a turning screw driver or steering wheel. The standard SI unit for torque is the newton meter, denoted as N·m or just N m. A newton meter is defined as a force of one newton applied perpendicularly to a moment arm that is one meter long.

I will get into the more technical definitions of terms below, but just remember that although the information in this article is considered more or less standard, terminology varies to some degree depending on country and region.

For example, torque is often widely and loosely used to mean any rotating force regardless of any external factors, and this is not necessarily wrong, per se. But when describing more detailed components of objects in rotation and related forces, this requires more specific terminology. Besides the more common torque, moment and couple are also closely related to rotation, so let’s explore the relationship and differences.

Moment Vs. Torque

In physics, the two are used synonymously, whereas in mechanical engineering, they are slightly different. Understanding the seeming contradiction or discrepancy may help you in deciphering their meanings in various contexts. Since physics treats these two the same, let’s find out how mechanical engineering defines them.

In mechanical engineering, moment is the more general term for the tendency or effect of one or more forces which are applied to an object to cause a rotation about an axis. A torque on the other hand, is the moment of what’s called a couple, or a pure moment, and requires a net-force of zero. A couple is the mechanical system we see in action when turning a screw with a screw driver.

As per the name, a couple is a pair of forces, equal but opposite, running parallel to each other such that their lines of action don’t coincide or intersect. The net-force of these two parallel and opposing forces equal zero as one is positive and the other negative, “canceling” each other out. There is a rotation but no translation or acceleration of its center of mass.

“Sorry, but I still don’t get what a couple is.”

To illustrate the concept of a couple better, consider the turning of a flathead screw with a driver. As you position the driver tip into the screw-head and begin applying torque, you should be able to visualize the two opposing forces working to turn the screw in perpendicular directions to the “minus” slot on the screw-head. This is a simple couple at work.

In other words, a couple can be described as the combination of two equal and opposite forces that rotate an object about an axis, with torque being its “moment”. Once again, moment and torque are interchangeable in physics, but not in engineering. In this context, torque can be thought of as the force that is produced by a “twist”, as opposed to one that is produced by a lever arm attached to a fulcrum.

Other Differences between Moment and Torque

Other commonly accepted differences include moment being used for statics-related situations such as non-rotational analysis of beams, and torque being used for cases where an object is turned about an axle or pivot, such as the above example of a screw driver. In such cases, torque can also be used when a lever arm is present as in, “the longer the lever arm, the more ‘torque’ you get”.

As you can see, there are generally accepted definitions which delineate the two terms, but there is also some inconsistency as well, depending on context and region. It’s best not to get too hung up on the exact “definition” of each, but to simply have a basic knowledge of how these terms are generally treated so you can find your bearings. In most cases you can correctly assume the meaning for the term in question by the context.

Denotations for Moment and Torque

In engineering, a moment is the effect equal to the applied force multiplied by the perpendicular distance from the pivot point – τ = r×F, where τ (tau) is the moment, r is the distance, and F is the force applied.

This is in contrast to the definition of torque in this context, which is equal to the applied force multiplied by the perpendicular distance between the two opposing forces of a couple – τ = F×d, where τ is the torque, F is the applied force, and d is the perpendicular distance between the parallel forces.

Note the difference in denotations where r is used for moment, and d is used for torque. The symbol “r” is usually used to denote radius, which is exactly what it’s being used for here. The lever arm extends from the fulcrum and its length equals the radius of an imaginary circle it would make if it were to complete a revolution. The “d” on the other hand, can be seen as used to distinguish the couple from the moment, and as such, describes the distance between the two opposing force vectors which make up a couple.