.92 STATICS. [152. 



(10) A homogeneous rod AB = 2 / of weight Crests with one end A 

 on the inside of a fixed hemispherical bowl of diameter 2 a and leans at 

 C on the horizontal rim of the bowl, so that the other end B is outside. 

 Determine the inclination to the horizon 9 in the position of equilibrium. 



2. STABILITY. 



152. The equilibrium of the forces acting on a rigid body may 

 subsist while the body is in motion. Thus, if the motion con- 

 sist in a mere translation with constant velocity, the equilibrium 

 will not be disturbed during the motion if the forces remain 

 equal and parallel to themselves. 



If, however, the body be subjected to a rotation, this will in 

 general not be the case. The present considerations are re- 

 stricted to the case of plane motion ; the forces are supposed 

 to lie in the plane of the motion and to remain equal and 

 parallel to themselves and applied at the same points of the 

 body. 



153. Let A^AZ (Figs. 42 and 43) be a rigid rod having two 

 equal and opposite forces F lt F 2 applied at its extremities in the 



*-* A? i K '' 



Fig. 43. 



direction of the line A^A^. Let this rod be turned by an angle 

 <f> about an axis at right angles to A^A^. In the new position 

 the forces F v F 2 , instead of being in equilibrium, form a couple 

 whose moment is F l ' A^A^ sin <f>. 



If in the original position of the rod the forces tend to increase 

 the distance A^ 2 (Fig. 42), the couple in the new position will 



