The Principles of Mechanics Designed for the Use of Students in the University

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If a rotatory motion be communi- cated to a body, and it be then left to move freely, the axis of rotation will pass through the center of gravity. For the center of gravity itself, either remaining at rest or moving uniformly forward in a right line, has no rotation.
Prop. XL.
(185. ) If a body he placed upon an horizontal plane, and a line drawn from it's center of gravity perpendicular to that plane, the body will be sustained, or not, according as the perpendicular falls within or without i
...t's base.
Let ABDC represent the body, G it's center of gravity; draw G^ perpendicular to the horizon; join CG, and with the radius CG describe the circular arc HGF; then the body cannot fall over at C, unless the center of gravity describes the circular arc GF. Suppose the whole force of gravity applied at G (Art. 178. ), and take GE to represent it; draw Ex OF GRAVITY* 109 perpendicular to CG; then the force GE is equi- valent to the two Gx, xE, of which Gx cannot move the body either in the direction GF or GH; and when E falls within the base, xE acts at G in the direction GH; therefore the center of gravity cannot describe the arc GF, that is^ the body cannot fall over at C.


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