Hypotheses and principles of Newtonian mechanics governing the dynamics of particles. Mach’s "empirical propositions” are presented as an alternative to Newton's laws, and the equivalences between both approaches is analyzed. The fundamental law governing particle dynamics (Newton’s second law) is presented both in Galilean and non-Galilean reference frames. A discussion of the frames which appear to behave as Galilean ones (according to the scope of the problem under study) is also included. The most usual interactions between particles are described. Formulation of forces associated with gravitation, springs, dampers, and friction phenomena are provided. Constraint forces on particles are introduced and characterized.

This chapter discusses the geometry of space and the notion of time assumed in Newtonian mechanics. This discussion will also serve to review aspects of mechanics and special relativity that will be important for later developments. Newtonian mechanics assumes a geometry for space and a particular idea for time. The laws of Newtonian mechanics take their standard and simplest forms in inertial frames. Using the laws of mechanics, an observer in an inertial frame can construct a clock that measures the time. Coordinate transformations can make the connection between different inertial frames. Newtonian mechanics assumes there is a single notion of time for all inertial observers. We explore Newtonian gravity and the Principle of Relativity: that identical experiments carried out in different inertial frames give identical results.

We begin our journey of discovery by reviewing the well-known laws of Newtonian mechanics. We set the stage by introducing inertial frames of reference and the Galilean transformation that translates between them, and then present Newton’s celebrated three laws of motion for both single particles and systems of particles. We review the three conservation laws of momentum, angular momentum, and energy, and illustrate how they can be used to provide insight and greatly simplify problem solving. We end by discussing the fundamental forces of Nature, and which of them are encountered in classical mechanics. All this is a preview to a relativistic treatment of mechanics in the following chapter.