Engineering Mechanics
November 16, 2019

## DIFFERENCE BETWEEN MOMENT OF FORCE AND MOMENT OF COUPLE

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 in mechanics.

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Now, we will see the concept of moment of a couple here.

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Now, we will be interested to understand here the difference between moment of force and moment of couple in engineering mechanics with the help of this post. first we will see here the basics of moment of force and after that we will find out the moment of couple in engineering mechanics.

Further we will secure the basic difference between the moment of force and moment of couple with the help of this post.

Further we will secure the basic difference between the moment of force and moment of couple with the help of this post.

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**Moment of a force in mechanics **

As we have studied earlier that the effect of a force on a body or object will be the combination of translation motion i.e. linear motion and rotational motion. Only translation or only rotational motion will be in exceptional cases.

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**Moment of force **

Moment of force is basically defined as the measure of the tendency of the force to rotate the body about the point of interest.

Let us consider the following figure where a force F is acting at a point on the body. Let us think that we need to find out the moment of this force F about a point P which is an arbitrary point on the body as displayed here in following figure.

Let us assume that r is the positional vector of the force F with respect to the arbitrary point P.

Therefore, we can write down the equation to find out the rotary or rotational effect of force F about the arbitrary point P as mentioned here.

Above equation is representing the moment of force in vector form. Let us now find out the magnitude of the moment of force.

Moment of force = Force x Perpendicular distance from the pivot point to the line of action of the force

Unit of moment of force = Unit of force x unit of distance

Unit of moment of force = N x m

Unit of moment of force will be N-m in SI system.

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**Sign convention for moment of force **

We need to consider and visualize physically how the force is trying to rotate the object. In order to find out the sign of moment or moment of force i.e. positive or negative moment, we use the concept of right-hand thumb rule.

If force is trying to rotate the object in anti-clock wise direction, moment of force will be taken as positive.

Let us see here the following figure, when we will close the finger in anti-clock wise direction, thumb will be in upward direction and it will be the indication for positive moment of force in our sign-convention for moment of force.

Similarly, if force is trying to rotate the object in clock wise direction, moment of force will be taken as negative.

Therefore, we need to take care the sign conventions for moment of force and we must note it here that moment of force will be always expressed with its magnitude, unit of measurement and sense of rotation i.e. positive or negative sign.

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**Important notes **

There are few very important points that we need to keep in our mind while dealing with the moment of force.

- Like force, Moment of force is also a vector quantity.
- Moment of force and force are sliding vectors.
- Anti-clock wise rotation or counter clock wise rotation about the pivot will be taken as positive.
- Clock wise rotation about the pivot will be taken as negative.
- Moment of force will be considered as the function of magnitude of the force and the moment arm.
- Unit of moment of force will be N-m in SI system.

Now, we will see the concept of moment of a couple here.

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**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

**r**and_{1}**r**as displayed here in above figure._{2}
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**r**and_{1}**r**_{2}_{. }
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.

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**Difference between moment of force and moment of couple **

There is one very basic and important difference between two above.

Let us think, what is the difference???

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 think, what is the difference???

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.

While in case of moment of force, moment of a force will be dependent over the point of interest.

Therefore, we have seen here the basics of moment of force, moment of couple and also the difference between these two with the help of this post.

Therefore, we have seen here the basics of moment of force, moment of couple and also the difference between these two with the help of this post.

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Further we will find out, in our next post, varignon's theorem in engineering mechanics.

### Reference:

Engineering Mechanics, By Prof K. Ramesh

Image courtesy: Google