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MOMENT & COUPLE
APPLIED MECHANICS
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.
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.”
PRACTICAL PROBLEMS
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.
PARALLEL FORCES
PARALLEL FORCES
PARALLEL FORCES
PARALLEL FORCES
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,
Comparison b/w torque(moment) & couple
COUPLE
COUPLE
• 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.

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torque & couple.pptx

  • 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.
  • 3.
  • 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.”
  • 6.
  • 7.
  • 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.
  • 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,
  • 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.