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The following&nbsp;hierarchical list has been developed and organized&nbsp;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&nbsp;

Even these requirements create some difficulties.&nbsp; Firstly, we have to add a model for general energy conservation including thermal energy, even though this is usually considered part of Thermodynamics;&nbsp;Mechanics uses only the special case of Mechanical Energy, treating heat as "Lost Mechanical Energy".&nbsp; 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.&nbsp; (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.)&nbsp; A further critique concerns the equations we associate with each model.&nbsp; 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^ ).&nbsp; 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.&nbsp;

h3. Hierarchy of Mechanics Models

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[3D Motion General|Three-Dimensional Motion (General)]

[2D Motion General |2D motion (general)]
** [Circular Motion |Circular Motion]
*** [Circular Motion with Constant Speed |Circular Motion with Constant Speed ]
{latex} $ (\alpha = 0) $ {latex}
** [1D Motion General |1D motion (general)]
*** [One-Dimensional Motion with Constant Acceleration]
**** [1D Motion with Constant Velocity]
{latex} $ (a = 0) $  {latex}
* [Simple Harmonic Motion]
{latex}  $ (a = -\omega^2 x) $ {latex}\\

&nbsp;[Energy, Work and Heat|Energy, Work and Heat]
* [Work-Energy Theorem |Work-Energy Theorem]
{latex} $ (Q = 0, \Delta U_ {int} = 0)$ {latex}
* &nbsp;[Mechanical Energy and Non-Conservative Work]
{latex} $(Q = 0, \Delta U_{int} = 0)$ {latex}
** [System Mechanical Energy Constant]
{latex} $ (W^{nonConservative}= 0 ) $ {latex}

[Momentum and Force]
{latex} $ \vec p(t^{final}) - \vec p(t^{initial}) = \int_ {t^{initial}}^{t^{final}}\sum\vec F^{ext} $ {latex}
* [System Momentum Constant |Constant Momentum]
{latex} $ (\sum \vec F^{ext} = 0 ) $ {latex}
* [Point Particle Dynamics]
{latex} $ (\sum\vec F = m \vec a ) $ {latex}

[Angular Momentum and Torque]
&nbsp;
{latex} $ \vec L(t^{final}) - \vec L(t^{initial}) = \int_{t^{initial}}^{t^{final}} \sum\vec{\tau_o}^{ext} $ {latex}\\
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* [System Angular Momentum Constant |Constant Angular Momentum]
{latex} $ (\sum\vec\tau_o^{ext} = 0 ) $ {latex}
* [Fixed-Axis Rotation |Fixed-Axis Rotation]
** &nbsp;Statics&nbsp;
{latex} $ (\sum \vec F^{ext} = 0 ) ${latex}
&nbsp; and&nbsp;
{latex} $ (\sum\vec{\tau_o^{ext}} = 0 ) ${latex}

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