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[Phys-L] Did Newton really understand momentum?



From time to time we hear or read confident assertions that Newton
expressed his second law in terms of *momentum* rather than
*acceleration*. Interestingly, this is not a conclusion one can
reasonably infer directly from the statement of his second law, which
reads (in its most respected English translation by I. Bernard Cohen and
Anne Whitman):

"A change in motion is proportional to the motive force impressed and
takes place along the straight line in which that force is impressed."

However, few people take the time to read the many pages of preamble in
Newton's Principia, in which he ever-so-carefully lays all the
groundwork for the hundreds of propositions he will subsequently derive.

Of particular importance are his explicit definitions, which he urges
the reader to use (instead of everyday meanings) when interpreting his
kinematic and dynamic statements. And that's where it becomes clear what
he means by *change in motion*:

"Definition 2: Quantity of motion is a measure of motion that arises
from the velocity and the quantity of matter jointly."

After which he offers the elaboration:

"The motion of a whole is the sum of the motions of the individual parts
and thus if a body is twice as large as another and has equal velocity
there is twice as much motion, and if it has twice the velocity there is
four times as much motion."

So...

Did Newton understand momentum? You betcha!

Did Newton prefer to think in terms of momentum than acceleration?
Without a shadow of a doubt.

Did he ever use acceleration? Yep. In a few places, for technical
mathematical reasons. But he knew nature respected momentum more.

So how did it come to pass that we switched to the inferior
acceleration-speak? That's another story altogether ;-)

Takeaway: Don't let anyone accuse you of anachronism or hagiography when
you claim Newton understood (indeed discovered) the fundamental
importance of momentum.

Derek McKenzie
PhysicsFootnotes.com