MECHANICS 93 



each other. Through O as a center draw an indefinite 

 line XX' in the required direction of one of the components, 

 and through the same center O draw the indefinite line YY' 

 in the direction of the other component. Then XX' and 

 YY' are at right angles to each other, since the components 

 to be found are to be at right angles to each other. The 

 line XX' is commonly called the XX' axis, or simply the 

 X axis, and the line YY', the YY' axis or the Y axis. From 

 A draw a line perpendicular to the X axis, as Aa', and also 

 a line perpendicular to the Y axis, as Aa". Then Oa' is the 

 component force in the direction of XX' and Oa" is the other 

 component in the direction of YY'. 



When the components Oa' and Oa" are horizontal and 

 vertical, as in the present case, they are called, respectively, 

 the horizontal component and the vertical component of the 

 force OA. 



MOMENTS OF FORCES 



DEFINITIONS AND MEASUREMENTS 



In Fig. 1, W is a weight that tends to fall that is, to act 

 downwards with a force of 10,000 Ib. It is well known 

 that if some fixed point, as a, not in the line along which 

 the weight W acts, is con- 

 nected with the line of action 

 of W by a rigid arm, so that 

 W pulls on one end of this 

 arm while the other end is 

 firmly held at a, the pull of 

 W will tend to turn, or rotate, 

 the arm about the point a. 



It is also known that the 

 tendency to rotate is directly 

 proportional to the magni- 

 tude of the force, provided the 



arm remains of the same length, and directly proportional 

 to the length of the arm, if the force remains constant. In 

 general, therefore, the rotative effect is proportional to the 



