Newton's formulae

I dont like that answer.

Newton was a mathematician by nature, I know he didnt just thumbsuck an
formula. I am not asking about the goddamed format that we write F=ma in, I
am asking how he derived the formula.

How did Newton derive F=ma ?

"Mitchell B." wrote in message
...
I dont like that answer.

Newton was a mathematician by nature, I know he didnt just thumbsuck an
formula. I am not asking about the goddamed format that we write F=ma in,
I
am asking how he derived the formula.

How did Newton derive F=ma ?

http://en.wikipedia.org/wiki/Newton's_laws_of_motion

Newton was a mathematician (as you point out) and developed the method of
"fluxions" (a form of the calculus concurrently developed by Leibniz).
Newton also defined the "momentum" p (the product of the mass of an object m
and its velocity v - a consequence of his first law of motion) of a
particle. This made the analysis of the *change* of the momentum of the
particle the key to the study of the motion of objects. He applied the
concept of the derivative (from the calculus) to examine the *time rate of
change of momentum* dp/dt, which he called the force F.

http://en.wikipedia.org/wiki/Philoso...ia_Mathematica

Now this is rocket science to many, but if you allow that the mass is not
going to change (m is constant) then the calculus tells us that:

dp/dt = d(m*v)/dt = m * dv/dt

Then Newton dubbed dv/dt, the time rate of change of velocity, with the name
"acceleration."

Of course, with the mass constant, it is no longer rocket science:

F = m * a

The real triumph of his work (in 1687) came when he was able to apply his
laws of motion to objects moving in a central field (as he defined gravity)
to derive a rigorous mathematical basis for Kepler's Laws of Planetary
Motion (1609-1619):

http://en.wikipedia.org/wiki/Laws_of_Kepler

This was as much a clincher for his theory as accounting for the precession
of the perihelion of Mercury was for Einstein's General Relativity about 300
years later.


Tom Davidson
Richmond, VA

Thanks

"Mitchell B." wrote in message ...
I dont like that answer.

Newton was a mathematician by nature, I know he didnt just thumbsuck an
formula. I am not asking about the goddamed format that we write F=ma in, I
am asking how he derived the formula.

How did Newton derive F=ma ?


I already explained to you that he took the rate of change of momentum
with respect to time. It's all based on the first "law", which states
all bodies have default invariant momentum. When the momentum does
change, then the cause of the change is an abstraction called a
"force", which is simply defined AS the change in momentum over time.
Quite stupid reasoning if you think about it, since NOTHING is ever
observed to have constant momentum by default over a continuous time
interval.

Maybe one could derive that "the default" motion of bodies is not
necessarily linear in flat space, but curved in flat space, curved in
curved space or linear in curved space (as Einstein showed) or to make
things worse, curved/linear in curved/linear quantized space.

There are probably many "fundamental postulates" of physics which can
be shown to be empirically valid. Either way, all that really matters
is the empirical validity of the system, and Newton certainly prevails
over others such as Aristotle.

One should note that you can build a bicycle with Aristotlean physics
and still know Aristotle was wrong. Likewise with Newtonian physics
and its modern derivatives (Maxwell,SR,GR,QED,QFT).

JS

Dear John Schoenfeld:

"John Schoenfeld" wrote in message
m...
"Mitchell B." wrote in message
...
I dont like that answer.

Newton was a mathematician by nature, I know he didnt just thumbsuck an
formula. I am not asking about the goddamed format that we write F=ma
in, I
am asking how he derived the formula.

How did Newton derive F=ma ?


I already explained to you that he took the rate of change of momentum
with respect to time. It's all based on the first "law", which states
all bodies have default invariant momentum.

A body in motion tends to stay in motion unless acted on by an outside
force. He proposed it directly. Your derivation is (as is your memory)
flawed.

David A. Smith

"N:dlzc D:aol T:com \(dlzc\)" N: dlzc1 D:cox wrote in message news:2Slhc.25161$Yf6.9405@fed1read07...
Dear John Schoenfeld:

"John Schoenfeld" wrote in message
m...
"Mitchell B." wrote in message
...
I dont like that answer.

Newton was a mathematician by nature, I know he didnt just thumbsuck an
formula. I am not asking about the goddamed format that we write F=ma
in, I
am asking how he derived the formula.

How did Newton derive F=ma ?


I already explained to you that he took the rate of change of momentum
with respect to time. It's all based on the first "law", which states
all bodies have default invariant momentum.

A body in motion tends to stay in motion unless acted on by an outside
force. He proposed it directly. Your derivation is (as is your memory)
flawed.

Your definition is completely wrong. Your memory forgot to include "in
a straight line with constant velocity", which is exactly what i said
- "INVARIANT MOMENTUM".

David A. Smith

Dear John Schoenfeld:

"John Schoenfeld" wrote in message
om...
"N:dlzc D:aol T:com \(dlzc\)" N: dlzc1 D:cox wrote in
message news:2Slhc.25161$Yf6.9405@fed1read07...
Dear John Schoenfeld:

"John Schoenfeld" wrote in message
m...
"Mitchell B." wrote in message
...
I dont like that answer.

Newton was a mathematician by nature, I know he didnt just
thumbsuck an
formula. I am not asking about the goddamed format that we write
F=ma
in, I
am asking how he derived the formula.

How did Newton derive F=ma ?


I already explained to you that he took the rate of change of
momentum
with respect to time. It's all based on the first "law", which states
all bodies have default invariant momentum.

A body in motion tends to stay in motion unless acted on by an outside
force. He proposed it directly. Your derivation is (as is your
memory)
flawed.

Your definition is completely wrong. Your memory forgot to include "in
a straight line with constant velocity", which is exactly what i said
- "INVARIANT MOMENTUM".

I'm not the turkey that forgot that he described a relationship between
force and change in acceleration. And I'm not the turkey that then
produced a "broken" derivation to confuscate an honest question from an
unknowing poster. You've succeeded in acting like a troll. It may not
have been your intent, but that is what you managed to do.

David A. Smith

I'm not the turkey that forgot that he described a relationship between
force and change in acceleration. And I'm not the turkey that then
produced a "broken" derivation to confuscate an honest question from an
unknowing poster. You've succeeded in acting like a troll. It may not
have been your intent, but that is what you managed to do.

David A. Smith

What?