94 MECHANICS 



product of the magnitude of the force and the length of the 

 lever arm. This product is called the moment of the force 

 with respect to the point in question. Thus, in Fig. 1, the 

 moment of the force W with respect to the point a is the 

 product obtained by multiplying the magnitude, 10,000 lb., 

 by the perpendicular distance, 10 ft., from the point a to the 

 line of action of W. 



The point a, Fig. 1, that is assumed as the center around 

 which there is a tendency to rotate, is called the center, or 

 origin, of moments. 



The perpendicular distance from the center of moments 

 to the line along which the force acts, is the lever arm of the 

 force, or the leverage of the force. 



Since the unit of force is the pound, and the ordinary unit 

 of length is the foot, the unit of moment will be a derived 

 unit, the foot-pound (abbreviated to ft.-lb.), and moments 

 will usually be expressed in foot-pounds. In Fig. 1, for 

 example, the moment of the force W with respect to the 

 point a is 10,000X10 = 100,000 ft.-lb. 



The moment of a force may be expressed in inch-pounds 

 (in.-lb.), foot-pounds, or foot-tons (ft.-T.), depending on the 

 unit of measurement used to designate the magnitude of the 

 force and the length of its lever arm. For instance, if the 

 magnitude of a force is measured in pounds, and the lever 

 arm through which it acts in inches, the moment will be in 

 inch-pounds; again, if a force of 10 T. acts through a lever 

 arm of 20 ft., the moment of the force is 10X20 = 200 ft.-T. 



Positive and Negative Moments. In order to distinguish 

 between the directions in which there is a tendency to 

 produce rotation, the signs + and may be used. Thus 

 if a force tends to produce right-hand rotation, that is, rota- 

 tion in the same direction as the hands of a clock, it is called 

 positive, and its moment takes the sign + ; a force that tends 

 to produce rotation in the opposite direction is called neg- 

 ative, and its moment takes the sign . The selection of 

 one direction for positive and another for negative is merely 

 an arbitrary distinction to show that the directions are 

 opposite. It has, however, been adopted by engineers, and 

 should always be used as given. 



