## Main Difference – Moment vs. Couple

In physics, the terms **moment** and **couple** are related to forces that cause turning effects on bodies. The **main difference** between moment and couple is that, **in a moment, there may or may not be a resultant force** as a consequence of the forces causing the turning effect whereas, **in a couple, there is no resultant force**.

## What is Moment

Technically, a **moment** is a combination of a physical quantity and a distance. However, in this article we use the term “moment” to mean the “torque” that an object experiences due to a force. The torque about any point due to a force is given by the cross product between and the vector drawn from the point we are interested in, to the point where force is applied:

The **magnitude** of torque could be given by the product of force and perpendicular distance to the line of action of force:

So in this case,

## What is Couple

A **couple** describes a system where there is a resultant *torque* by a system of forces, without there being a resultant *force*. Let us look at a system where a pair of forces, each with a magnitude , separated by a perpendicular distance form a couple.

Since the net force must be 0, it follows that the forces must be acting in opposite directions and also that they have the same magnitudes. We calculate the torque due to these forces below.

Let us consider the torque at . This is the midpoint between the two forces. Each force contributes to a clockwise turning effect about this point. So, the total (clockwise) moment about O is:

Note that for a couple, the resultant torque is always the same regardless of about which point the moments are taken. In the above example, we can confirm this by taking the moment about point . In this case, the torque by the *force at * is 0 (because the distance to the force is 0). Then, the net torque is only due to the force at the other end of the object. This force is at a perpendicular distance away, so the torque is:

Examples of couples involve forces applied by hands on a steering wheel, forces on the head of a screwdriver and forces acting on pedals of a bicycle.

## Difference Between Moment and Couple

### Resultant Force:

A **moment** may or may not accompany a resultant force.

A **couple** does not accompany a resultant force.

### Effect of Force:

A **moment** can occur with only one force.

But, a **couple** cannot be produced by a single force.

Image Courtesy:

“Hands on a steering wheel.” by Vernon Chan [CC BY 2.0], via Wikimedia Commons