SECTION II 



FIRST AND SECOND MOMENTS 



10. Static moment. If a force acts upon a body having a fixed 

 axis of rotation, it will in general tend to produce rotation of the 

 body about this axis. This tendency to rotate becomes greater as 

 the magnitude of the force increases, and also as its distance from 

 the axis of rotation increases. The numerical amount of this tend- 

 ency to rotate is thus measured by the product of the force by its 

 perpendicular distance from the given axis, or center of rotation. 

 This product is called the first moment, or static moment, of the 

 force with respect to the given axis, or point. 



Thus, let F denote any force, P the fixed axis of rotation, as- 

 sumed to be at right angles to the plane of the paper, and d the 

 perpendicular distance of F from P. Then d is called the lever arm 

 of the force, and its moment about P is defined as 



Moment = force X lever arm, 



or, if the moment is denoted by If, 



(9) 



M = Fd. 



P 



(Center or axis 

 of rotation) 



It is customary to call the 

 moment positive if it tends to 

 produce rotation in a clockwise 

 direction, and negative if its 

 direction is counter-clockwise 

 (Fig. 6). 



11. Fundamental theorem of 

 moments. When two concur- 

 rent forces act on a body simul- 

 taneously, their joint effect is 

 the same as that of a single force, given in magnitude and direction 

 by the diagonal of the parallelogram formed on the two given 



15 



FIG. 6 



