5 - Work–Energy Theorem

Summary

The work–energy theorem in a general reference frame is presented. It relates the change of the mechanical energy of the system in a finite time interval to the impulse work of the interaction forces (and inertia forces, if the frame is a non-Galilean one). Different expressions for the calculation of the kinetic energy of a rigid body are provided. The concept of conservative system and conservative force are introduced, and from them, that of potential energy. The particular case of gravitational energy and energy associated with linear springs is studied. A section is devoted to the study of equilibrium configurations, and their stability, of systems of one degree of freedom. Finally, the impossibility of perpetual motion is proved. The rotation stability of a free rigid body is analyzed through Poinsot’s ellipsoid in an appendix.