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Momentum

René Descartes and Christian Huygens together introduced the concept of momentum as the combination of an object's weight with its velocity, developing a rather powerful scheme for "before and after" analysis of isolated collisions and similar messy processes. I will be unfaithful to the historical sequence of conceptual evolution in this case primarily because I want to introduce the "impulse and momentum conservation law" later on as an example of the "emergence" of new paradigms from a desire to invent shortcuts around tedious mathematical calculations. Nevertheless, Newton actually formulated his Second Law in terms of momentum, so it would be too much of a distortion to omit at least a definition of momentum at this point, to wit:

$$\vec{\bf p} \; \equiv \; m \; \vec{\bf v}$$ (4)

I.e., the momentum of an object, a vector quantity which is almost always written   $\vec{\bf p}$  (magnitude $\vert\vec{\bf p}\vert \equiv p$), is the product of the object's mass m and its vector velocity $\vec{\bf v}$.