Moments and Their Applications

INTRODUCTION

In the previous chapter, we have been discussing the effects of forces, acting on a body, through their lines of action or at the point of their  intersection. But in this chapter, we shall discuss

the effects of these forces, at some other point, away from the point of intersection or their lines of action.

MOMENT OF A FORCE

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.

GRAPHICAL REPRESENTATION OF MOMENT

Consider a force P represented, in magnitude and direction, by the line AB. Let O be a point, about which the moment of this force is required to be found out, as shown in

Fig. 3.1. From O, draw OC perpendicular to AB. Join OA and  OB.

Now moment of the force P about O = P × OC = AB × OC

But AB × OC is equal to twice the area of triangle ABO. 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.

UNITS OF MOMENT

Since the moment of a force is the product of force and distance, therefore the units of the moment will depend upon the units of force and distance. Thus, if the force is in Newton and the

distance is in meters, then the units of moment will be Newton-meter (briefly written as N-m). Similarly, the units of moment may be kN-m (i.e. kN × m), N-mm (i.e. N × mm) etc.

TYPES OF MOMENTS

Broadly speaking, the moments are of the following two types:

1. Clockwise moments.

2. Anticlockwise moments.

CLOCKWISE MOMENT

It is the moment of a force, whose effect is to turn or rotate the body, about the point in the same direction in which hands of a clock move as shown in Fig. 3.2 (a).

ANTICLOCKWISE MOMENT

It is the moment of a force, whose effect is to turn or rotate the body, about the point in the opposite direction in which the hands of a clock move as shown in Fig. 3.2 (b).

Note. The general convention is to take clockwise moment as positive and anticlockwise moment as negative.

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.”