96 



MECHANICS 



of the body or bodies may be considered as concentrated. 

 If the body or system were suspended from any other point 

 than the center of gravity, and in such a manner as to be 

 free to turn about the point of suspension, it would rotate 

 until the center of gravity reached a position directly under 

 the point of suspension. 



Center of Gravity of Plane Figures. If the plane figure 

 has one axis of symmetry, this axis passes through its center 

 of gravity. If the figure has two axes of symmetry, its center 

 of gravity is at their point of intersection. 



The center of gravity of a triangle lies on a line drawn from 

 a vertex to the middle point of the opposite side, and at a 

 distance from that side equal to one-third the length of the 

 line; or it is at the intersection of lines drawn from the ver- 

 tex.es to the middle of the opposite sides. The perpendicular 

 distance of the center of gravity of a triangle from the base 

 is equal to one-third the altitude. 



The center of gravity of a parallelogram is at the inter- 

 section of its two diagonals; consequently, it is midway 

 between its sides. 



The center of gravity of an irregular four-sided figure may 

 be found as follows: First divide it, by a diagonal, into two 

 triangles and join the centers of gravity of the triangles by a 

 straight line; then, by means of 

 the other diagonal, divide the fig- 

 ure into two other triangles, and 

 join their centers of gravity by 

 another straight line; the center 

 of gravity of the figure is at the 

 intersection of the lines joining 

 the centers of gravity of the two 

 sets of triangles. 



Another method by which to 

 locate the center of gravity of an 

 irregular four-sided figure is illus- 

 trated in Fig. 3. Draw the diag- 

 onals ac and bd, and from their intersection e, measure the 

 distance to any vertex, as ae. From the opposite vertex, 

 lay off this distance, as at cf. Then from f, draw a line to 



FIG. 3 



