MOMENT OF COUPLE IN MECHANICS

We have started a new topic in our previous post i.e. engineering mechanics. We have seen there the basics of engineering mechanics such as concept of force system, principle of transmissibility of forces and its limitations, classification of force system, body force and surface force, moment of a force and Varignon’s theorem in mechanics.

Now, we will be interested to understand here the concept of moment of a couple with the help of this post.

Moment of a couple

The force system consisting of two equal and parallel but non-collinear forces with opposite sense will be termed as couple.

Let us consider the following figure where two equal and parallel forces are acting on a body in opposite direction. We will now understand here the moment of a couple for the given force system.

Let us consider an arbitrary point P and position vectors for these two forces are r₁ and r₂ as displayed here in above figure.

Moment of these two forces about arbitrary point P could be determined with the help of following equation as mentioned below

Where, a is the difference between position vectors r₁ and r₂_.

From above equation, we can conclude that there will be net moment M as mentioned above due to these two forces those are equal, parallel, non-collinear and with opposite sense.

Where, d will be the perpendicular distance between the line of action of these two forces as shown in the above figure.

There is one very important observation from above equation. The value of moment of a couple will not be dependent over the location of point of interest. Moment of a couple will be a free vector.

Let us recall the concept of moment of a force, moment of a force will be dependent over the point of interest.

Two couples will have the same sense to cause the rotation in same direction and it could be understood with the help of following figure.

Therefore, we have seen here the concept of moment of a couple with the help of this post. Further we will find out the difference between the moment of a force and moment of a couple.

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Further we will find out, in our next post, difference between moment of a force and moment of a couple in engineering mechanics.