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{excerpt:hidden=true}*System:* One [point particle|point particle]. --- *Interactions:* Any.{excerpt}

h4. Description and Assumptions

This model is technically applicable to any [point particle] moving in three dimensions, and involves vector calculus.  Except for circular and rotational motion, however, one generally treats the vectors in Cartesian coordinates, so they split into three one-dimensional equations, allowing a solution with three applications of the [One-Dimensional Motion (General)] model.

h4. Problem Cues

This model is needed only for problems that clearly involve motion in three dimensions, and is not often used in introductory mechanics.


h2. Model

h4. Compatible Systems

A single [point particle|point particle] (or a system treated as a point particle with position specified by the center of mass).


h4. Relevant Interactions 

Only knowledge of the [net|net force] [external force|external force] is required to determine the acceleration of the system.  


h4. Laws of Change

The laws of change are simply the laws of calculus for vectors. 

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h5. Differential Forms
{latex}\begin{large}\[ \frac{d\vec{v}}{dt} = \vec{a}\]\end{large}{latex}\\
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{latex}\begin{large}\[ \frac{d\vec{x}}{dt} = \vec{v}\]\end{large}{latex}\\
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h5. Integral Forms
{latex}\begin{large}\[ \vec{v}(t) = \vec{v}(t_{0})+\int_{t_{0}}^{t} \vec{a}\;dt\]\end{large}{latex}\\
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{latex}\begin{large}\[ \vec{x}(t) = \vec{x}(t_{0})+\int_{t_{0}}^{t} \vec{v}\;dt\]\end{large}{latex}\\
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h2. Relevant Examples

None yet.
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