Moment of a Force

Moment 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.

Fig. 1

Mathematically, moment,

                        M = P × d

  Where,

           P = Force acting on the body

           d = Perpendicular distance between the point, about which the moment is required and the

                  line of action of the force.

Fig. 2

Let a force ‘P’ act on a body which is hinged at O. Then, moment of P about the point O in the body is

                                       Moment = F x ON

Where 

           ON = perpendicular distance of O from the line of action of the force F.

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

Fig. 3 Representation of Moment

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 (N-m). Similarly, the units of moment may be kN-m (i.e. kN × m), N-mm (i.e. N × mm) etc.

Types of Moment

The moments are of two types.

1) 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. 4 (a).

2) 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. 4 (b).

The general convention is to take clockwise moment as positive and anticlockwise moment as negative. But there is no hard and fast rule regarding sign convention of moments.

Fig. 4 Clockwise and Anticlockwise Moments