hierarchy of models

The following hierarchical list has been developed and organized with several goals in mind:

• Each model must apply (approximately) to many situations in the world
• The models should cover mechanics as completely as possible
• The models should be ranked hierarchically with most general on top
• Each model should have a descriptive name and be accompanied by its most frequently used formula 

Even these requirements create some difficulties.  Firstly, we have to add a model for general energy conservation including thermal energy, even though this is usually considered part of Thermodynamics; Mechanics uses only the special case of Mechanical Energy, treating heat as "Lost Mechanical Energy".  Arranging the many models into a hierarchy with only four principle models (Kinematics, Energy, Momentum, and Angular Momentum) properly stresses that there are only a few basic models in Mechanics and that many of the most used ones are simply special cases of these few; however it obscures the logical chain of proof and derivation of the laws of mechanics from only F=ma and the definitions of kinematics.  (This usually starts with F=ma for point particles, then builds up and out to rigid bodies, systems of particles, momentum, angular momentum and energy.)  A further critique concerns the equations we associate with each model.  It is a simple operation of calculus to express the laws of physics in either differential (v = dx/dt, ΣF = m d²x/dt² , ΣT = I a), or integral form (E^final = E^initial + W^{nonConservative} ).  By presenting only the most frequently used form, we obscure this simplification for the benefit of helping students link titles and verbal concepts to equations. 

Hierarchy of Mechanics Models