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[Phys-l] Newton's version of the second law (was Re: Equations (causal relationship))



On May 1, 2006, at 2:38 PM, Larry Smith wrote:

As I understand it, part of the debate about forces causing (or not)
acceleration hinges on the meaning of the equal sign. In fact, Newton's
Principia doesn't even say F = ma at all (it's closer to F = p-dot).

Actually, it's closer to F * delta t = delta p.

IMO this isn't a trivial point. From my readings of the Principia, I have formed the opinion that Newton had a bit of difficulty thinking about acceleration or p-dot or any other quantity related to the second time derivative of position, much like our students do. He thought about motion and did his calculations in terms of the effects of a series of impulses (which Newton called "forces") each of which CHANGED the momentum (which he called "motion"), not in terms of a force (which he seems to have had no clear or consistent word for) resulting in a constantly CHANGING momentum.

Of course, we've been around this block a few times before! Entries into past threads treating the same point can be found at

<https://carnot.physics.buffalo.edu/archives/2002/04_2002/msg00089.html>

<https://carnot.physics.buffalo.edu/archives/2002/09_2002/msg00394.html>

<https://carnot.physics.buffalo.edu/archives/2003/11_2003/msg00411.html>

John "Slo" Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://www.csupomona.edu/~hsleff/OoPs.html>