The product of a force and the perpendicular distance of the line of actions of the force from a point is known as moment of the force about that point.
Let F = A force acting on a body as shown in Fig.2.28
r = Perpendicular distance from the point.
O on the line of action of force F.
Then moment (M) of the force F about O is given by, M = F × r
The tendency of this moment is to rotate the body in the clockwise direction about O. Hence this moment is called cloakwise moment If the tendency of a moment is to rotate the body in anti-clockwise direction, then that moment is known as anti-cloakwise moment. If cloakwise moment is taken –ve then anti-cloakwise moment will be +ve.
In S.I.system, moment is expressed in N m (Newton meter).
Fig. 2.29 shows a body on which three forces F1, F2 and F3 are acting. Suppose it is required to find the resultant moments if these forces about point O.
Let r1 = Perpendicular distance from O on the line of action of force F1.
r2 and r3 = Perpendicular distance from O on the line of action of force F2 & F3 respectively.
Moment of F1 about O = F1 × r1 (cloakwise)(-)
Moment of F2 about O = F2 × r2 (cloakwise)(-)
Moment of F3 about O = F3 × r3 (anti-cloakwise)(+)
The resultant moment will be algebraic sum of all the moments.
(so) The resultant moment of F1, F2 andF3 about O = – F1 × r1 – F2 × r2 + F3 × r3
Problem 2.15. Four forces of magnitude 10 N, 20 N, 30 N and 40 N are acting respectively along the four sides of a square ABCD as shown in Fig.2.30. Determine the resultant moment about the point A. Each slide of the square is given 2 m.
Sol. Given :
Length AB = BC = CD
= DA = 2m
Force at B = 10 N
Force at C = 20 N
Force at D = 30 N
Force at A = 40 N
The resultant moment about A is to be determined. Perpendicular distance from A on the lines of action of these forces will be zero.
Hence their moments about A will be zero. The moment of the force at C about point A
= Force at C × distance from A on the line of action of force at C
= (20 N) × (Length AB)
= 20 × 2 N m = 40 N m (anti-cloakwise)
The moment of force at D about point A
= Force at D × distance from A on the line of action of force at D.
= (30 N) × (Length AD)
= 30 × 2 N m = 60 N m (anti-cloakwise)
Resultant moment of all forces about A
= 40 + 60 = 100 N m (anti-cloakwise). Ans.