MOMENTS 63 



Now the component of R along AM is a force of which the line 

 of action intersects L, and so can produce no tendency to turn a 

 body about L, while the component of R along the line through A 

 parallel to L can again produce no tendency to turn about L. Thus 

 R can be resolved into three components, of which only the first, 

 the component along AS, tends to set up rotation about L. We 

 have defined the moment of the whole force R in such a way that 

 it becomes identical with the moment of that one of its components 

 which tends to set up rotation. 



It will be noticed that a moment has sign as well as magnitude. 

 In moving along the line of action of a force ft, we may turn in 

 either one direction or the other about a line L. We agree that 

 when the turning is in one direction the moment of R about L is 

 to be regarded as positive; when the turning is in the other 

 direction the moment is taken to be negative. 



49. If a particle is in equilibrium under the action of any num- 

 ber of forces, the resultant of all these forces must be nil. The 

 sum of the moments of the separate forces, taken about any 

 line whatever, is equal to the moment of the resultant and is 

 therefore nil. 



Hence we have the result : 



When a particle is in equilibrium under the action of any forces, 

 the sum of the moments of these forces about any line whatever 

 must vanish. 



SYSTEM OF PARTICLES IN EQUILIBRIUM 



50. Consider a system of particles supposed to be in equilibrium 

 under the action of any number of forces. As we have seen, the 

 forces acting on any single particle will be of two kinds : 



(a) external forces, forces applied to the particle from outside, 

 as for instance the weight of the particle ; 



(b) internal forces, forces of interaction between the particle and 

 the remaining particles of the system. 



