Moments
It is the turning effect produced by a force, on the body, on which it acts. The moment 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 force.
i.e. M = F x l
In vector form,
It is the turning effect produced by a force, on the body, on which it acts. The moment 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 force.
i.e. M = F x l
In vector form,
While the moment M (vector) of a force about a point depends upon the magnitude, the line of action, and the sense of the force, it does not depend upon the actual position of the point of application of the force along its line of action.
Types: i. Clockwise moment "+ve"
ii. Anticlockwise moment "-ve"
Law of Moments
It states that "If a number of forces, all being in one plane, are acting at a point in equilibrium, the sum of clockwise moments must be equal to the sum of anticlockwise moments taken about any point in the plane of forces."
Couple
Types: i. Clockwise moment "+ve"
ii. Anticlockwise moment "-ve"
Law of Moments
It states that "If a number of forces, all being in one plane, are acting at a point in equilibrium, the sum of clockwise moments must be equal to the sum of anticlockwise moments taken about any point in the plane of forces."
Couple
- Couple is defined as combination of two equal and opposite forces separated by a certain distance.
- Couple is produced due to equal but unlike forces.
- Couple is unable to produce any translatory motion (i.e. motion in a straight line). It produces only rotation in a body.
- Couple Moment = M = P x a
- Two forces P (vector) and -P (vector) having same magnitude, parallel line of action and opposite senses are said to form a couple.
Characteristics of Couple
- The algebraic sum of the forces constituting the couple is zero.
- The algebraic sum of the moments of the forces, constituting the couple about any point is same.
- A couple cannot be balanced by a single force, but can be balanced only by a couple; but of opposite sense.
Resolution of a Force into Forces and a Couple
Consider a force F(vector) acting on a rigid body at a point A defined by the position vector r(vector).
To have the force act at point O, we can attach two forces at point O, one equal to F(vector) and the other equal to -F(vector), without modifying the action of the original force on the rigid body.
Thus, any force F(vector) acting on a rigid body may be moved to an arbitrary point O, provided that a couple is added, of moment equal to the moment of F(vector) about O.
The resultant of a system of forces can be obtained as below:
i. Simplest Resultant of a General Force System
Consider a force F(vector) acting on a rigid body at a point A defined by the position vector r(vector).
To have the force act at point O, we can attach two forces at point O, one equal to F(vector) and the other equal to -F(vector), without modifying the action of the original force on the rigid body.
Thus, any force F(vector) acting on a rigid body may be moved to an arbitrary point O, provided that a couple is added, of moment equal to the moment of F(vector) about O.
- Te reverse of the theorem is also true i.e. if we have a system consisting of a force and a couple, the force can be shifted to a new position such that the new couple generated by doing so is equal and opposite to the given couple.
The resultant of a system of forces can be obtained as below:
i. Simplest Resultant of a General Force System
ii. Simplest Resultant of a Coplanar Force System