94 



STATICS OF RIGID BODIES 



TRANSMISSIBILITY OF FORCE 



69. Consider a rigid body acted on by two forces W A) W B at 

 two points A, B, these forces being equal in magnitude but acting 

 in the opposite directions AB, BA. 



Either the rigid body will be in equilibrium under the action of 

 these two forces, or else it can be held at rest by three forces P A , 

 P B , P c at the points A y B, and any third point C not in the line 

 AB, these forces being in the directions already mentioned, namely 

 P c being perpendicular to ABC, and P B perpendicular to AB. 



FIG. 48 



Let these forces, if necessary, be put in so that the body is in 

 equilibrium under the action of the forces W A , W B , P A , P B , P c . 

 The body being in equilibrium, the sum of the moments of these 

 forces about any line, or of their components in any direction, must 

 vanish, by 50. 



Let us consider what is the sum of the moments about the line 

 AB. The forces W A> W B , P A , P B all meet this line, so that the 

 moment of each of these forces vanishes. Thus the sum of the 

 moments about the line AB consists of the moment of the single 

 force P c , and for the sum of these moments to vanish, the moment 

 of P c must vanish. Now P c is perpendicular to the line AB, and 

 does not intersect it, so that the moment of P c can vanish only if 

 the force P c is itself equal to zero. This means that no force is 

 required to keep the body from turning about AB as axis of 

 rotation. 



