...
Definition
...
and
...
Law
...
of Change 
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 |
|---|
Change [!images^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} [ |
...
...
...
can
...
be
...
written
...
in
...
terms
...
of
...
momentum,
...
and
...
represents
...
the
...
fundamental
...
law
...
of
...
change
...
for
...
the
...
...
...
...
...
...
:
| 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
...
...
under
...
consideration
...
has
...
constant
...
...
.
...
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.
...