Consider a composite atom P described by a repetitive chain of historically ordered events

$\Psi \left( \bar{r}, t \right) ^{\sf{P}} = \left( \sf{\Omega}_{1}, \sf{\Omega}_{2}, \sf{\Omega}_{3} \ldots \right)$

where each event is also characterized by its momentum $\bar{p}$. By Isaac Newton's second law of motion, any change in the momentum of P during this trajectory is related to the action of some force $\overline{F}$ according to$\begin{align} \overline{F} \equiv \frac{ \Delta \bar{p} }{ \Delta t } \end{align}$

So if there are no forces acting on P, then there are also no changes in P's momentum, and vice versa

$\overline{F} = \left(0, 0, 0 \right) \ \ \Longleftrightarrow \ \ \Delta \bar{p} = \left(0, 0, 0 \right)$

The forgoing statement is just a special case of the second law of motion. Yet Newton included this null relationship as part of his first law of motion. It may seem redundant, but the first law is more than simply a special case of the second law because it also establishes exactly what we mean by a *straight* line segment or a *straight* rod. The first law is also known as the law of inertia, it has been translated into modern English as

"Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.^{1}

For WikiMechanics this first law is uniquely important because by our premise we prefer to avoid mysteriously received knowledge about length and lines. So this aspect of Newton's first law is formally restated in the following explicit definition: If P has the same momentum for all events in its trajectory, then $\Psi$ describes uniform **linear** motion and we say that P is moving in a **straight** line. This sort of force-free motion is obtained if the frame of reference is ideal and P is isolated. It is only well-defined for particles that are at least as big as atoms.

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Newton's First Law of Motion |