Page History

Goals and Caveats

The following heirarchical list has been developed and organized with 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  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, SΣF = m d²x/dt² , S 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.  3-D Motion - General Point Particle

*          Circular motion - Two dimensional motion

            1-D Motion - General

\*                      1-D Motion w. Constant Acceleration    \[S{*}F* = m *a* \]

                                    1-D Motion w. Constant Velocity   \[S{*}F* =0 \]

\*                      Harmonic Motion   \[ F = \-k (x-x{~}0~) \]

Energy Conservation - Work and Heat

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Heirarchy of Mechanics Models

• 3D Motion

  • 2D Circular Motion

    • Uniform Circular Motion

  • 1D Motion

    • 1D Motion with Constant Acceleration

      • 1D Motion with Constant Velocity

    • Simple Harmonic Motion

• Energy, Work and Heat

  • Work-Energy Theorem

  • Mechanical Energy and Non-Conservative Work

    • Constant Mechanical Energy

• Momentum and Force

  • Point Particle Dynamics

  • Constant Momentum

• Angular Momentum and Torque

  • Fixed Axis Rotation

    • Statics

  • Constant Angular Momentum

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