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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, Σ{*}F* = m d{^}2{^}{*}x*/dt{^}2^ , Σ{*}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. 

h3. Hierarchy of Mechanics Models

* 3D Motion General
** 2D Motion
*** Circular Motion
**** Circular Motion with Constant Speed 
{latex} $ (\alpha = 0) $ {latex}
*** 1D Motion
**** 1D Motion with Constant Acceleration 
***** 1D Motion with Constant Velocity 
{latex} $ ( a = 0) $ {latex}
*** Simple Harmonic Motion 
{latex} $ (a = -\omega^2 x) $ latex


* Energy, Work and Heat

** [Work-Energy Theorem]
 {latex} $(Q = 0, \Delta U\_{int} = 0)$ {latex}
** [Mechanical Energy and Non-Conservative Work]
 {latex} $(Q = 0, \Delta U_{int} = 0)$ {latex}

*** [Constant Mechanical Energy]
{latex} $ (W\_{nc} = 0) $ {latex}
* h4. [Momentum and Force]
{latex}
$ \vec p(t_f) - \vec p(t_i) = \int\_
{t_i}^{t_f}\sum\vec{F^{ext}} $ {latex}

** [System Momentum Constant]
{latex} $ (\sum \vec F^{ext} = 0 ) $ {latex}
** Point Particle Dynamics
{latex} $ (\sum\vec F = m \vec a ) $ {latex}

* h4. Angular Momentum and Torque
{latex} $ \vec L(t_f) - \vec L(t_i) = \int_{t_i}
^
{t_f}
\sum\vec{\tau_o^{ext}} $ 
{latex}

** System Angular Momentum Constant
{latex} 
$ (\sum\vec{\tau_o^{ext}} = 0 ) $ 
{latex}
** Fixed-Axis Rotation
*** Statics
{latex}
$ (\sum \vec F^F\^
{ext} 
= 0 ) $ and $ (\sum\vec{\tau_o^{ext}} = 0 ) $ 
{latex}

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