Definition and Law of Change 
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Although Newton is famous for the law
F = ma,
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he
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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
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momentum
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and
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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
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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 |
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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 [ |
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...
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can
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be written in terms of momentum, and represents the fundamental law of change for the Momentum and External Force model:
| Latex |
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written: {latex}\begin{large}\[ \sum_{\rm ext} \vec{F} = \frac{d\vec{p}}{dt}\]\end{large}{latex} |
This
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form
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is
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totally
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equivalent
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to
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F
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=
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ma
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,
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provided
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that
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the
...
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under
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consideration
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has
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constant
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.
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Unlike
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the
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traditional
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F
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=
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ma
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formulation,
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however,
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the
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formulation
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of
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Newton's
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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
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momentum
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is
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accurate
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even
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for
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systems
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whose
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mass
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is
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variable.
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