Kinetics

Kinetics, the study of forces that are not in equilibrium. If a body be so small that the energy due to its rotation about any axis through its mass centre be negligible, the investigation of the force relations on that body is simple. The body is treated as a particle, of no dimensions, though it is, of course, impossible for such a thing to possess finite mass. Forces acting on it are assumed to act at one point, and the condition of their equilibrium is that the force-polygon (q.v.) shall be closed. The resultant motion of the body is rectilinear when the forces are not in equilibrium, and is identical with that produced by a single force represented in magnitude, direction, and sense by the line closing the force-polygon. The body, therefore, is impressed with a uniform and constant change of speed. If the body be not small, the operation of summing up the effects of the impressed forces will not always be so simple. The motion of the mass-centre of the body will be the same as if all the forces were shifted to that point, parallel to their actual positions. If the sum of the moments (q.v.) of the forces about an axis through the mass-centre be zero, there will be no rotation about that axis; if the sum of the moments have a finite value, there will be a rotation about the axis, with an angular acceleration proportional to the sum of the moments. Without entering into fuller detail, it is obvious that even for bodies that do not admit of rapid change of shape, the kinetic investigations may become exceedingly complicated; and for problems on liquids, gases, and flexible or elastic solids, processes involving most abstruse mathematical implements are in most cases necessary. [Dynamics.]