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Definition and Law of Change     null

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:

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\begin

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[ \vec

Unknown macro: {p}

= m\vec

Unknown macro: {v}

]\end

Newton's Second Law can be written in terms of momentum, and represents the fundamental law of change for the Momentum and External Force model:

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\begin

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[ \sum_

Unknown macro: {rm ext}

\vec

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= \frac{d\vec{p}}

Unknown macro: {dt}

]\end

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.

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