CONDITIONS OF EQUILIBEIUM 93 



intersect in some line PQ passing through P. This line is called 

 the axis of rotation. The rotation can be imagined as a turning 

 about an imaginary pivot running along the axis of rotation. 



CONDITIONS OF EQUILIBRIUM FOR A EIGID BODY 



68. We have seen that a rigid body is fixed when three non- 

 collinear points in it are fixed. It follows that, whatever forces 

 act on a rigid body, we can always hold it at rest by applying 

 three suitably chosen forces at three points which are not in a 

 straight line. 



"We can, however, select these forces in a special way. 



Let us select any three points A, B, C, subject only to the con- 

 dition that they are not in a straight line. By a suitably chosen 

 force acting on the particle at A we shall always be able to keep 

 the point A at rest. 



When A is fixed B may or may not tend to move. If B tends 

 to move, the direction of motion of B must be perpendicular to 

 BA, since A cannot move. Hence after A is fixed it must be 

 possible to fix B by applying at B a force perpendicular to BA. 



When A and B are both fixed the only motion possible for the 

 third point C is one perpendicular to both AC and BC,Le. perpen- 

 dicular to the plane ABC. Thus C can be held at rest by a force 

 perpendicular to the plane ABC, and the whole body is now held 

 at rest. Thus it has been proved that a rigid body can be held at 

 rest, in opposition to the action of any system of forces, by the 

 application of the following forces at three arbitrarily chosen 

 points A, B, C not in a straight line: 



(a) a force at A, direction unknown ; 



(I) a force at B, direction perpendicular to the line AB ; 



(c) a force at C, direction perpendicular to the plane ABC. 



The condition that the original system of forces should hold 

 the body in equilibrium is of course that no additional forces are 

 required to fix" the body, and hence that the three forces introduced 

 at the points A } B, C should each vanish. 



