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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.

Problem Cues

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

Model

Compatible Systems

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

Relevant Interactions

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

Laws of Change

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

}\begin{large}\[ \frac{d\vec{v}}{dt} = \vec{a}\]\end{large}{latex}\\
\\
{latex}

\begin{large}\[ \frac{d\vec{x}}{dt} = \vec{v}\]\end{large}{latex}\\
\\

Integral

Forms

}\begin{large}\[ \vec{v}(t) = \vec{v}(t_{0})+\int_{t_{0}}^{t} \vec{a}\;dt\]\end{large}{latex}\\
\\
{latex}

\begin{large}\[ \vec{x}(t) = \vec{x}(t_{0})+\int_{t_{0}}^{t} \vec{v}\;dt\]\end{large}{latex}\\