The document defines moment as the turning effect of a force about a point, and provides the mathematical formula for moment as M = P x l, where P is the force and l is the perpendicular distance to the point. It then explains Varignon's Principle of Moments, which states that the algebraic sum of moments of all forces about any point equals the moment of the resultant force about the same point. The document goes on to discuss parallel forces and couples, defining a couple as two equal and parallel forces acting in opposite directions, and provides examples of couples in real life. It compares torque and moment to a couple. Finally, it provides example problems calculating resultants and moments.

1. MOMENT & COUPLE
APPLIED MECHANICS

2. MOMENT
It is the turning effect produced by a force, on the body, on which it acts.The moment of a force is
equal to the product of the force and the perpendicular distance of the point, about which the
moment is required and the line of action of the force.
Mathematically, moment,
M = P × l
where P = Force acting on the body, and
l = Perpendicular distance between the point, about which the moment is
required and the line of action of the force.
Consider a force P represented, in magnitude and direction, by the lineAB. Let O be a point, about
which the moment of this force is required to be found out, as shown in Fig.1. From O, draw OC
perpendicular to AB. JoinOA and OB.
Now moment of the force P about O = P × OC =AB × OC
But AB × OC is equal to twice the area of triangleABO.
Thus the moment of a force, about any point, is equal
to twice the area of the triangle, whose base is the line
to some scale representing the force and whose vertex
is the point about which the moment is taken.

4. VARIGNON’S PRINCIPLE OF MOMENTS (OR LAW OF
MOMENTS)
It states, “If a number of coplanar forces are acting simultaneously on a particle, the algebraic
sum of the moments of all the forces about any point is equal to the moment of their resultant force
about the same point.”

5. PRACTICAL PROBLEMS

8. PARALLEL FORCES
We have studied forces acting at one point. But, sometimes, the given forces have their lines of
action parallel to each other. A little consideration will show, that such forces do not meet at any
point, though they do have some effect on the body on which they act. The forces, whose lines of
action are parallel to each other, are known as parallel forces.
The parallel forces may be, broadly, classified into the following two categories, depending upon
their directions :
1. Like parallel forces.
2. Unlike parallel forces.

9. PARALLEL FORCES

10. PARALLEL FORCES

11. PARALLEL FORCES

12. PARALLEL FORCES

13. COUPLE
Couple, as per the physics language, appears when two equal and parallel forces act
opposite to one another.To add more,Torque is a vector quantity as well, while the
moment of a couple is free vector.
The following are some of the applications of couple in real-life:
i. The steering of a car used by a driver.
ii. The movement involved in opening and closing a normal facet.
iii. Screwdriver.
iv. Rotating the cap of a jug.
v. The movement involved in a key.
It is was defined earlier, a couple is generally a blend of two equal and parallel forces
that act opposite to each other. It comes with an identical magnitude, but in an opposite
direction, influenced by a perpendicular distance.
MC = r * F,

14. Comparison b/w torque(moment) & couple

15. COUPLE

16. COUPLE

17. • Q.1 A student averaged 45 miles per hour on a trip. What was the student’s speed in feet
per second?
•
•
• Q.2 A push of 180 N and pull of 350 N act simultaneously at a point. Find the resultant of the
forces, if the angle between them be 135°.
• Q.3 Find the magnitude and direction of the resultant of the concurrent forces of 8 N, 12 N,
15N and 20 N making angles of 30°, 70°, 120°.25 and 155° respectively with a fixed line.
•
• Q.4 Find magnitude of the resultant force, if 30, 40, 50 and 60 N forces are acting along the
lines joining the center of a square to its vertices.