MECHANICS 265 



Center of Gravity of Solids. For a solid having three axes of 

 symmetry, all perpendicular to each other, like a sphere, cube, 

 right parallelepiped, etc., the point of intersection of these 

 axes is the center of gravity. 



For a cone or pyramid, draw a line from the apex to the 

 center of gravity of the base; the required center of gravity 

 is one-fourth the length of this line from the base, measured 

 on the line. 



For two bodies, the larger weighing W lb., and the smaller 

 P lb., the center of gravity will lie on the line joining the 

 centers of gravity of the two bodies and at a distance from the 



Pa 

 larger body equal to , where a is the distance between 



the centers of gravity of the two bodies. 



For any number of bodies, first find the center of gravity of 

 two of them, and consider them as one weight whose center of 

 gravity is at the point just found. Find the center of gravity 

 of this combined weight and a third body. So continue for 

 the rest of the bodies, and the last center of gravity will be the 

 center of gravity of the whole system of bodies. 



To find the center of gravity mechanically, suspend the 

 object from a point near its edge and mark on it the direction 

 of a plumb-line from that point ; then suspend it from another 

 point and again mark the direction of a plumb-line. The inter- 

 section of these two lines will be directly over the center of 

 gravity. 



MOMENT OF INERTIA 



The moment of inertia of a plane surface about a given axis is 

 the sum of the products obtained by multiplying each of the 

 elementary areas, in to which the surface may be conceived to be 

 divided, by the square of its distance from the axis. 



The moment of inertia is usually designated by the letter 7. 

 The value of the moment of inertia used in calculating the 

 strength of beams and columns is usually taken about the 

 neutral axis of the figure, which, with the exception of rein- 

 forced-concrete sections, is passing through the center of 

 gravity of the figure. 



