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Definition
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and
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Law
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of
...
Change 
Although Newton is famous for the law F = ma,
...
he
...
actually
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stated
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his
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Second
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Law
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in
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terms
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of
...
momentum
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and
...
its
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change
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due
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to
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impressed
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forces
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or
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impulses
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(the
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time
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integral
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of
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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 |
|---|
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
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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
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is
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totally
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equivalent
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to
...
F
...
=
...
ma
...
,
...
provided
...
that
...
the
...
...
under
...
consideration
...
has
...
constant
...
...
.
...
Unlike
...
the
...
traditional
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F
...
=
...
ma
...
formulation,
...
however,
...
the
...
formulation
...
of
...
Newton's
...
Second
...
Law
...
in
...
terms
...
of
...
momentum
...
is
...
accurate
...
even
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for
...
systems
...
whose
...
mass
...
is
...
variable.
...