CENTER OF GRAVITY. 



47 



Fig. 13. 



Illustrate 

 first case. 



the 



the center of gravity of the cylinder will be at the point I, wiule its center 



of magnitude is at c. The cylinder 

 will tlien roll up the mclined plane to 

 the position a I, because the center 

 ic ] of gravity of the mass, Z, \viU endeavor 



to descend to its lowest point. 



91. A prop that supports 

 the center of gravity sup- 

 ports the whole hody. This support may be applied iu 

 T u . .V three different ways : 



In what three •' 



center"if Grat ^' "^^^ poiut of support may he applied di- 

 ity be support- rcctly to the center of gravity of the body. 



2. The point of support may have the cen- 

 ter of gravity immediately below it. 



3. The point of support may have the center of gravity 

 immediately above it. 



In the first case, where tlie point of support is applied di, 



rectly to the center of gravitj', the body will remain at rest u\ 



any position ; this is illustrated in the case of a common wheel, 



where the center of gravity is also the center of the figure, and this being 



Pig. 14, supported on the axle, the wheel rests 



indifferently in any position. In Fig, 



14, let a, the center of the wheel, which 



=■ is also its center of gravity, be supported 



by an axle; — the wheel rests, no matter 



-a- to what extent we turn it. 



In the second case, where the point 

 - C of support is above the center of gravity, 

 the body, if it is allowed freedom of mo- 

 tion, will not rest in perfect equilibrio 

 tmtil its center of gravity has descended to the lowest position, which in all 

 cases ■noU be immediately beneath the point of suspension. 

 •ewmd case. ° '^^^' ^ ^'g- I'*) ^^^ the wheel, the center of gravity of which 

 is at a, be suspended from the pomt b, by a thread, or hung 

 upon an axle, having freedom of motion on that point. However much wa 

 may move it, either right or left, toward m or n, as shown by the dotted lines, 

 am and an, it swings back again, and is only at rest when b and a are in the 

 same perpendicular line. 



In the third case, where the point of support has the cen- 

 third caTC. * '■°'' °^ gravity above it, a body will remain at rest only so long 

 as the center of gravity is in a vertical line, above the point 

 of stipport. In Fig. 14, suppose the wheel to be supported at the point c, sit- 

 uated iu a vertical line a c, immediately below the center of gravity, a; bo 



