h3. Introduction to Linear Momentum [!images^EditSectionimages^SectionEdit.png!|Momentum (Intro)]
Although Newton is famous for the law F=ma, he actually stated his Second Law in terms of momentum and its change due to impressed forces or impulses (the time integral of the force). He defined Momentum as
_The [quantity of motion] is the measure of the same, arising from the [velocity] and quantity of matter conjointly_. - DEFINITION II, Principia (Motte and Cajori).
In modern terminology, this definion becomes:
{latex}\begin{large}\[ \vec{p} = m\vec{v} \]\end{large}{latex}
and [Newton's Second Law] can be written:
{latex}\begin{large}\[ \sum_{\rm ext} \vec{F} = \frac{d\vec{p}}{dt}\]\end{large}{latex}
This form is totally equivalent to _F_ = _ma_, provided that the [system] under consideration has constant [mass]. Unlike the traditional _F_ = _ma_ formulation, however, the formulation of Newton's Second Law in terms of momentum is accurate even for systems whose mass is variable.
|