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"If you believe that momentum is conserved, define force as dp/dt and --
shazzam! -- you've got a nice, general, robust version of the third law."
Really?
Didn't we just go through a lot of discussion about distinguishing
between a particular force and a sum of forces?
I can't just replace F/-F > with dp/dt's,
because dp/dt is equal to the NET force on an object. It
isn't equal to the F's in the historical Newton's 3rd law except in the
special case of there being just two objects that are interacting.
Oh, come now.
If your goal is to ensure Newton gets credit for his Holy Laws, then by
all means make sure students learn them by number. I know from
experience just how few of them understand which numbered law
corresponds to which physical principle. By contrast, my students who
learn the Matter and Interactions style of "kooky jargon" have no
trouble recognizing and applying the principle, and at the end of the
day can still attribute it to Saint Isaac.