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{excerpt}In our version of [modeling physics|Models in Physics], a model is a specific Law of Change that is applied to a system.{excerpt}

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h2. Many Definitions of Model

The word "model" has many meanings in everyday language, and it has many meanings in physics as well.  The [Models in Physics] page gives a summary of what is usually called the modeling approach to mechanics.  In this WIKI, however, we will use a more narrow definition of model.  We will use it to refer to a specific Law of Change (which may have more than one equivalent form) that can be applied to [systems|system] which meet certain specified restrictions.

h2. Law of Change

h4. Definition

A Law of Change is an equation which expresses the _time evolution_ of some property of a system.  

h4h5. Example -- Momentum

For example, the equation:

{latex}\begin{large}\[ \vec{p}_{f} = \vec{p}_{i} + \int_{t_{i}}^{t_{f}} \vec{F}^{\;\rm ext}\;dt\]\end{large}{latex}

expresses the time evolution of the momentum of a system in terms of the external forces acting on the system.  It is therefore a Law of Change (in this case, belonging to the [Momentum and Force] model).

h4. Integral vs. Differential

Many Laws of Change can be equivalently expressed using derivatives or using integrals (or using explicitly integrated quantities).  

h4h5. Example -- Momentum

For example, the Law of Change from the momentum model that was discussed above is an integral form.  This Law could also be expressed as:

{latex}\begin{large}\[ \frac{d\vec{p}}{dt} = \vec{F}^{\;\rm ext}\]\end{large}{latex}

h2. Hierarchy of Models

h4. Restrictions to the Law of Change -- Sub-models

The [Model Hierarchy] presented in this WIKI classifies some models as _sub-models_ or _special cases_ of other models.