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Re: F=ma: law or theory?



On Tuesday, October 16, 2001 12:58 PM, I wrote:

[snip]
It is _not_ true that F is defined in terms of ma. F=ma is
_not_ an axiom nor
a tautology. To say it in more positive terms: We have an
operational
definition of force. We have an operational definition of
mass. We have
an operational definition of acceleration. In Newtonian
mechanics, the
equality between F and ma is a law, an approximate law, based
on empirical
observations. We can design experiments to test whether F
does equal ma to
some greater or lesser degree of accuracy.


At 01:13 PM 10/16/01 -0400, Robert Cohen wrote:

I agree with the above. However, I was once informed by somebody
(two people, actually, who certainly acted as though *I* was the
misguided one) that F=ma is actually a theory, not a law. Is anyone
familiar with this alternate view who can provide the argument for it?

Well, the above was restricted to _Newtonian_ mechanics. If you lift that
restriction, the game changes. If you start from canonical mechanics
(Lagrangians and all that) you can derive F=ma or various generalizations
thereof.