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.
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.
Reference:
Engineering Mechanics, By Prof K. Ramesh
Image courtesy: Google
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