Momentum

Momentum is the modern English word used for translating the phrase "quantity of motion" that Isaac Newton uses on the very first page of his great book, the Principia.

^{1}So to understand motion WikiMechanics starts by using sensation to define the momentum as follows. Consider some particle P characterized by its wavevector $\overline{ \kappa }$ and the total number of quarks it contains $N$. Report on any changes relative to a frame of reference F which is characterized using $\tilde{ \kappa }$ the average wavevector of the quarks in F. Definition: the**momentum**of particle P in reference frame F is the ordered set of three numbers$\begin{align} \overline{p} \equiv \frac{ h }{ 2 \pi } \left( \overline{ \kappa }^{ \sf{P}} \! - N^{ \sf{P}} \, \tilde{ \kappa }^{ \sf{F}} \right) \end{align}$

where $h$ and $\pi$ are constants. The norm of the momentum is marked without an overline

$p \equiv \left\| \, \overline{p} \, \right\|$

If $p=0$ we say that P is **stationary** or **at rest** in the F-frame. Alternatively, if $p \ne 0$ then we say that P is in **motion**.

page revision: 677, last edited: 26 Sep 2015 19:42