36 



PROPERTIES AND RELATIONS OF FORCES. Art. 30 



Concurrent forces are those whose lines of action intersect 

 in one point. 



The moment of a force is a measure of its tendency to rotate 

 a body about an axis or a point, and is equal to the magnitude of 

 the force multiplied by the perpendicular distance of its line 

 of action from the axis or point (foot-pounds or inch-pounds). 



The center or origin of moments is the point about which 

 any force may have a tendency to turn a body. 



The lev er arm of a force is the perpendicular distance from 

 its line of action to the center of moments. 



In Fig. 17. the moment of R l about 

 e is R^Xae ; of P about e is PXde and 

 of R : about D is R^Xad or R^XAD. 



A couple consists of two equal and 

 parallel forces acting in opposite direc- 

 tions. The moment of a couple is the 

 same about any point in its plane, and is equal to one of the equal 

 forces multiplied by the perpendicular distance between their 

 lines of action. Fig. 18 shows two parallel 

 forces P acting in opposite directions, forming 

 a couple. Take any point whatever as a and 

 draw a line from it perpendicular to the lines 

 of P. The total moment about a is equal to 

 the algebraic sum of the moments of each force 

 taken separately. 



17 * 



Fig. 18. 



Taking any other point as c, the total moment is 



If either & or d be taken as the center of moments, the mo- 

 ment of one force becomes zero and the total moment is again 

 PXbd. This exhausts all the possible cases, and proves that the 

 moment of the couple is PXbd for any center of moments. 



Equivalent systems of forces are such as may be substituted 

 for each other without changing the effect. 



The resultant of a system of forces is the simplest system 

 that is equivalent to it. The resultant of any number of co-planar 

 forces is a single force or a couple. See Art. 34. 



The equilibrant of a system of forces is the simplest system 

 that will hold the given system (or its resultant) in equilibrium. 

 If the resultant is a single force, the equilibrant is in every re- 



