Of these three terms, most people are probably most familiar with torque. Torque is casually defined as rotational force about a given axis, such as a rotating screwdriver or flywheel. The standard SI unit for torque is the newton meter, denoted Nm or simply Nm. One newton meter is defined as a force of one newton applied perpendicular to a moment arm one meter long.

I’ll get into the more technical definitions of terms below, but remember that while the information in this article is considered more or less standard, terminology varies to some degree by country and region.

For example, torque is often used broadly and loosely to refer to any rotational force, regardless of external factors, and this is not necessarily incorrect per se. But when more detailed components of rotating objects and related forces are described, this requires more specific terminology. In addition to the most common torque, moment and torque are also closely related to rotation, so let’s explore the relationship and differences.

Moment versus pair

In physics, the two are used equally, while in mechanical engineering they are slightly different. Understanding the apparent contradiction or discrepancy can help you decipher their meanings in various contexts. Since physics treats these two in the same way, let’s find out how mechanical engineering defines them.

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

According to its name, a couple is a pair of forces, equal but opposite, that run parallel to each other so that their lines of action do not coincide or intersect. The net force of these two parallel and opposite forces is equal to zero, since one is positive and the other is negative, “cancelling” each other. There is a rotation but not a translation or acceleration of its center of mass.

“I’m sorry, but I still don’t understand what a couple is.”

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

In other words, a torque can be described as the combination of two equal and opposite forces that rotate an object about an axis, the 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 produces a “turn”, as opposed to that produced by a lever arm attached to a fulcrum.

Other differences between moment and couple

Other commonly accepted differences include the use of moment for situations involving statics, such as non-rotational analysis of beams, and the use of torque for cases where an object rotates about an axis or pivot, such as the above example of a screwdriver. In such cases, torque can also be used when there is a lever arm as in “the longer the lever arm, the more ‘torque’ you get”.

As you can see, there are generally accepted definitions that delimit the two terms, but there are also some inconsistencies, depending on the context and region. It’s best not to get too hung up on the exact “definition” of each, but simply have a basic understanding of how these terms are treated in general so you can get your bearings. In most cases, you can correctly assume the meaning of the term in question from 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 applied force.

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 for torque. The symbol “r” is usually used to indicate radius, which is exactly what it is used for here. The lever arm extends from the fulcrum and its length is equal to the radius of an imaginary circle it would make if it were to complete one revolution. The “d”, on the other hand, can be seen as being used to distinguish torque from moment, and as such describes the distance between the two opposing force vectors that form a torque.