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Re: Newton's Second Law of Motion



At 17:45 4/8/02 -0600, you wrote:
Introductory textbooks have routinely stated Newton's Second Law as: a =

Sigma(F)/m, or Sigma(F) = ma. (There are some exceptions; for example,
Eugene Hecht's text). This is a special case and is true only when the
mass is constant. There should also be an equal emphasis on the fact
that it is possible to generate a force at a constant velocity when the
mass changes as well, such as in rocket motion or in water jetting out
of a hose. Even Newton does not state his Second Law the same way,
instead indicating that force is proportional to the rate of change in
momentum. I think that should be the more general and the correct way to

state the second law. Please give me some feedback. Thank you.

- Abby

Perhaps it would be helpful to consider how the proposition was framed by
Newton [at least, in English translation]
Law II
The change of motion is proportional to the motive force impressed; and is
made in the direction of the right line in which that force is impressed.

- If any force generates a motion, a double force will generate double the
motion, a triple force triple the motion, whether that force be
impressed altogether and at once, or gradually and successively. And this
motion (being always directed the same way with the generating force), if
the body moved before, is added to or subtracted from the former motion,
according as they directly conspire with or are directly contrary to each
other; or obliquely joined, when they are oblique, so as to produce a new
motion compounded from the determination of both. [end of Law II]

Newton, Principia Axioms, transl: A Motte: Revised: F. Cajori