heirarchy of models

We now present a list of models for Mechanics.  We have selected and organized our list 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, SF = m d²x/dt² , S T = 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. 
3-D Motion - General Point Particle

*          Circular motion - Two dimensional motion

            1-D Motion - General

*                      1-D Motion w. Constant Acceleration    [SF = m a ]

                                    1-D Motion w. Constant Velocity   [SF =0 ]

*                      Harmonic Motion   [ F = -k (x-x₀) ]

Energy Conservation - Work and Heat