by the system is equal to the work done on it by the external forces. If no external forces act on a system, its energy remains constant, however the velocities of the separate particles may change in consequence of the action of internal forces.
A rigid body is one in which the particles retain the same relative positions. Whatever internal forces act between the particles, they are equilibrated by others due to the reactions in the system. The internal forces can therefore do no work, and the internal energy of such a body is wholly kinetic energy.
33. Conservation of Energy.— The theorem stated in the last section is the simplest illustration of the general principle known as the conservation of energy. If no external forces act on a system, and if the internal forces be conservative, the sum of the kinetic and potential energies of the system remains constant. In many operations in Nature, however, the internal forces are not all conservative, and the theorem just stated no longer holds true. Experiment has shown that when non-conservative forces act, other forms of energy are developed, which cannot as yet be expressed as the potential and kinetic energies of masses, and that if these forms of energy be taken into account, the sum of all the energies of the system remains constant so long as no external forces act on it. This principle is called the principle of the conservation of energy. It may be used as a working principle in solving questions in mechanics, and finds a very wide application in all departments of physical science. The evidence for it will appear in connection with many of the topics which are subsequently treated.
34. Systems to be Studied.— The description of the motions of a system of particles which are free to move among themselves, and between which forces act, cannot in most cases be given. Certain general theorems relating to this general case can be found, but the conditions which determine the individual motions of the particles are so complicated that they cannot be brought into a form suitable for mathematical discussion, and hence the motion of the system cannot be completely described. There are two cases, however, of very general character, in which, by the aid of
