4 - Vector Theorems

Summary

Formulation and application of the vector theorems (linear momentum theorem and the angular momentum theorem) for the case of systems with constant matter. Those theorems relate the rate of change of a vector associated with the system (the linear momentum and the angular momentum about a point, respectively) to the net interactions (forces and moments) exerted on the system. Three different versions of the angular momentum theorem are presented: about a point fixed to a Galilean frame, about the system's center of mass, and about a point moving relative to a Galilean frame. Rotational dynamics, where the behavior of rigid bodies is often counterintuitive, is analyzed in a general and rigorous way. The dynamic role of the principal axes of inertia is discussed through several didactic examples. The formulation of the vector theorems in non-Galilean frames is also included. An appendix is devoted to the static and dynamic balancing of a rotor.