EQUILIBRIUM

in mechanics, fs: the state of rest of a body under the action | of two or more forces. The H. may be neutral, stable, or unstable. Neutral equilibrium.—If a body’ or a material system is’ balanced by the forces which act: upon it in any position in which it may be placed, its E. is neutral. This is the case with a sphere or a circular cylinder of uniform material placed on a horizontal plane. Any body whose center of gravity is at the: fixed point of support, or is always at the's ame height above’ the pomt of support, is in neutral E. Stable equilibrium.—But if when. the body is displaced very little in any ditection. from. its. E. position and. left to itself it commences and. continues vibrating without ever experiencing more than very: small deviation. from. the. position of E., the E. is said. to-be stable. This is the case. with a pendulum, or with. a, sphere loaded in its lowest part. Unstable equilibrium.—tIf, on the other hand, the system can be displaced in any way from a: position’ of E., so: that when left to itself it’ will not vibrate within very small limits about the position in E., but will move farther and, farther away from it, the E, is said to be. unstable, Thus an egg. or a billiard cue standing on’ end presents a case of unstable KE. In many cases the E. varies with the: direction of displacement; but if it is unstable for any’ po ible’ displacement, it is practically unstable on the whole. Thus a coin standing on its edge is-in neutral E. for displacements in its plane, but is in unstable EB. for those perpendicular to its plane. It is, therefore, practically in unstable E.: The conditions required for B: vary’ according to the number of forces and according as the forces are acting in the’ same plane or not. Thus two co-planar forces can only balance when they are equal in magnitude and directly opposed to each other. Three eo proger forces. acting ata point will be in K. if they can be represented in magnitude and direction by the three sides of a triangle taken in order.