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## Convert kilonewton meter [kN·m] to pound-force foot [lbf·ft]

1 kilonewton meter [kN·m] = 737.5610331755 pound-force foot [lbf·ft]

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I-beams in construction

Overview

Terminology Use in English

Examples of the Moment of Force

Conclusion

## Overview

The moment of force is a physical property of objects that is similar to and often confused with torque. The moment of force is the measure of the ability of the force to produce turning or twisting movement of a body about an axis. Its magnitude is equal to the vector product of a vector of force applied to an object and a perpendicular distance from the axis to the line of action of the force, which causes rotation. **Torque** is a related concept and is measured the same way as the moment of force, but it is defined as the tendency of an object **to rotate** when a force is applied to it. It is also measured as a product of the force and the distance between the point of application and the axis of rotation.

Two forces that the hand applies to the screwdriver, and which the screwdriver applies to the screw head create torque

In this article, we discuss at length the difference between the moment of force and torque but we should note that in most cases both torque and moment of force in English refer to the same concept and are used interchangeably. There are very slight nuances in the usage of these words and this often causes confusion. Besides, English is one of the few languages that use two separate terms. In many other languages, only one term is used. Here we discuss the nuances in detail to help clear the confusion in the usage of these two terms.

## Terminology Use in English

As we already mentioned above, both moments of force and torque are used to describe the same phenomenon but are sometimes used in different contexts. In this section, we examine the contexts in which “moment of force” is used more commonly than “torque”. Torque is often defined as the phenomenon that causes a change in the angular momentum. The moment of force, on the other hand, does not have to cause this change. This is to say that torque is a specific instance of the moment of force. We can also say that torque is the moment of force, but the moment of force is not necessarily torque.

Below we will consider some examples of this. We should again reiterate, however, that this difference between the moment of force and torque is distinguished in some contexts, but in other situations, torque and moment of force are used interchangeably.

Two hands act upon a tap wrench generate two forces, and this creates a torque

To understand what the moment of force is we need to understand what a moment in physics is in general. A **moment** indicates the magnitude with which a given force acts on the object from a given distance. This magnitude depends both on the magnitude of the actual force that is acting upon the object and also on the distance from the point of application of the force to a certain point on the object. As we saw in the definition above, for the moment of force this point is on the axis of rotation.

The moment of force is proportional to the force and to the radius. This means that if a given force is applied to the object at a given distance from the axis of rotation, then the magnitude of this force is magnified by the radius, and the effect of the force on the object is greater than the actual magnitude of the force itself. This principle is used when generating mechanical advantage by using systems of levers, gears, and pulleys. When we look at the moment of force in this context, we often look at the application of force on the arm of a lever, for example. You can see examples of how levers work in the article on torque.

Bending moment. In this structure, there is no rotation and thus no torque, and only the moment of force is present

Torque and moment of force are also sometimes distinguished in another way. Torque sometimes refers to a moment of a “couple”. Here a **couple** is two forces of the same magnitude that are acting in opposing directions and that cause the object to rotate. The sum of these vectors is zero. Moment of force is, therefore, a more general term, and torque is a specific instance.

In some contexts, torque is used when the object moves or rotates, while the moment of force is used when the movement does not occur, for example in systems such as support beams and other structural elements. In these systems, the edges of the beam or structure can either be fixed or can rotate. In the latter case, the beams are said to be simply supported. When a force is acting upon the beam, for example in a direction perpendicular to its surface, it generates a moment of force. If the movement of the beam is not restricted, it will rotate freely, but if it is restrained, then an internal moment will be generated to counteract the moment of force. As a result, the body will be deformed. This internal moment, which counteracts the moment of force, is known as the **bending moment**. As you see in this example the moment of force is not the same as torque because it does not cause a change in the angular momentum. This lack of change in momentum is due to the internal counteraction of the body to these external forces.

## Examples of the Moment of Force

Here the moment of force equals the weight that each child applies to the seesaw times the distance to the fulcrum. The girl is closer to the fulcrum but applies more force than the boy, and this helps keep the seesaw nearly at equilibrium.

The moment of force coupled with the bending moment that we discussed above is one example of a moment of force in real life. Moment of force is a useful concept in construction and structural engineering because knowing the moment of a force that acts upon a structural element allows us to determine the amount of stress that the system has to withstand. This stress includes the strain caused by the structure upon itself, for example, the strain caused by its weight, as well as the stress caused by the external elements such as the wind, the snow, the rain, the items stored in the building such as furniture, and the people that enter the building. In structural engineering, the load that includes people and items stored in the building is called a **live load**, while the load caused by the weight of the structure is called a **dead load**.

I-beams were extensively used during the construction of Royal Alexandra Bridge across Ottawa River in 1900

When a force is applied to a beam or another structural element, a bending moment acts upon it and compresses some parts of the beam, while stretching the other parts. For example, imagine a beam that has a force acting downwards on it, and is applied around the middle of this beam. Because of this force, the beam assumes a “smiley” shape. The top portion of it is being compressed, especially around the middle where the force is applied. The bottom portion, especially around the center, is being stretched apart. If the moment is too great for the material to sustain, then the beam breaks.

The maximum stress is on the very top and the very bottom layer, therefore it is common in structural engineering to reinforce these areas. A good example is an **I****-beam**. Its cross-section is shaped as the uppercase letter “**I**” with top and bottom serifs. Sometimes it looks more like the uppercase “H”. This is a very efficient design because the areas that experience the greatest stress are reinforced, but the material use is minimal. Often I-beams are made of steel, but it is possible to use other materials to make strong beams that withstand great forces. On YouTube, you can find examples of experiments that test the strength of I-beams made of materials that are less durable than steel, such as plywood and styrofoam.

I-beams are a popular choice when the bending moment is affecting the structure. They are also useful when dealing with **shear stress**, which is the stress that acts in parallel to the surface of the structure. The body section known as the “web” is responsible for withstanding shear stress. I-beams are not designed to resist torsional stress, however. **Torsional stress** is generated by the twisting motion. To minimize it, the structures are made circular, hollow, and with a larger diameter, which can reduce their weight. Their surfaces are polished to ensure that there are no areas with concentrated stress.

Engine torque creates torsional stress on the fuselage of this turboprop aircraft

## Conclusion

In this article, we considered the difference between torque and the moment of force in English terminology and looked at some examples of the moment of force. Here we mainly looked at the hindrance that the moment of force causes but there are many situations when the moment of force is useful. The article on torque discusses these examples in detail. The distinction in the terminology that we discussed is mainly relevant in the US and the UK mechanical engineering, but in the US and the UK physics, the terms torque and moment of force are generally used interchangeably.

References

This article was written by Kateryna Yuri

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### Mechanics

**Mechanics** is the branch of physics, which studies the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.

### Moment of Force Converter

**Moment of force** (also called torque or just moment) is the tendency of a force to twist or rotate an object. A moment is the product of the force and the moment arm. The moment arm is the perpendicular distance from the point of rotation, to the line of action of the force. The moment may be thought of as a measure of the tendency of the force to cause rotation about an imaginary axis through a point.

In SI, the moment of force is measured in **newton-meter** (N·m). One newton meter is equal to the torque resulting from a one-newton force applied perpendicularly to a one-meter long moment arm. In CGS, the moment of force is measured in **gram-force centimeter** (gf·cm).

### Using the Moment of Force Converter Converter

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