Momentum
//Sir Isaac Newton//. Painted by G Kneller 1689.
Sir Isaac Newton. Painted by G Kneller 1689.
Momentum is the modern English word used for translating the phrase "quantity of motion" that Isaac NewtonXlink.png 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.

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Sensory interpretation: The momentum is defined by a difference between the wavevector of P and a scaled-down version of the frame's wavevector. Recall that the wavevector has previously been interpreted as a mathematical representation of visual sensation. So momentum can be understood as the visual contrast between a particle and its reference frame.
Right.png Next step: conservation of momentum.
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