CENTRE OF INERTIA (Lat. inertia. inac tivity, literally unskillfulness). The centre of inertia of two particles whose masses are m, and 20, is defined as follows: Draw in the plane which includes the two particles two lines OX and OX' at right angles to each other; let the dis tames of the particles from OX be y, and and from OY he x, and then the centre of inertia is such a point that its distances from OY and OX arc given by the equations _ .r, m x tn, m In,It is evident from these equations that this point coincides with the centre of gravity (q.v.); and that if the distance between the particles is h, the centre of inertia is upon a line joining the two particles at a distance equal to h M from the particle This is at once evident if the line ()X is chosen to pass through both particles, and if is made to coincide with the particle whose mass is in,. In this case g, = O. hence y = 7?1, = tl .r, = 11, hence x =— , In a perfectly similar manner. the position of the centre of inertia of any number of par ticles or of a solid body wade up of particles may be calculated.
The physical properties of the centre of in ertia are most interesting. They are a. follow:: 111 If a blow or a force is applied to a body in stud' a direction that the limb of action passe. through the centre of inertia. the whole body will receive a velocity in the direction of the force; there will be no rotation, mid the velocity and acceleration will be exactly what they would lie if the same blow or force were applied to a single particle whose mas: equals that of the body. (2) if the line of action does not pass
through the centre of inertia, there will be rota tion exactly as if the centre of inertia were pivoted; but the will also a: a whole so that the centre of inertia will describe the same path as it would if the line of action of the force had passed through it.. These two prop erties give a simple, .4-If-evident method of locat ing the centre of inertia of a body by direct experiment: l'Ia• it on a smooth table, and by trying different directions 4h-termitie one such that a blow in this direction produces. no rota tion, simply translation; draw a line in the body marking this direction: locate another similar line, and the centre of inertia is where these two lines intersect.
Illustrations of these two general properties of the centre of inertia are numerous. If a man falls from a building without striking the wall in his descent, his centre of inertia deseribes vertical line, however lie twists or turns. If a hammer is thrown obliquely upward in the air, it will revolve rapidly: but one point of the hammer—viz. its centre of inertia—will describe a smooth curve, cal a parabola, which a single pa•tiele would describe if it were thrown upward in the same manner. When a bomb shell explodes in its flight, the fragments thy off in different directions; but their centre of in ertia at any instant is on a parabola, the same that it would have followed if there had been no explosion. See ATECIIANICS.