From: PointedEars@web.de
Thomas 'PointedEars' Lahn wrote:
> Ross Finlayson wrote:
>> F = ma
>
> This is a formulation of Newton's Second Law of Motion.
>
> Originally (in 1686/1687) Newton wrote this law in Latin words that as an
> equation he would have later written (or has written?)
>
> F = ṗ,
>
> (F = dot p, where by a dot above a symbol he defined the derivative of the
> corresponding quantity with respect to time, a notation that we are still
> using today), where he had previously defined the equivalent of
>
> p = m v.
To corroborate my claim, I should also have cited and quoted the law as
written by Newton, which can be found here:
,-
|
| [...]
|
| Lex II.
|
| Mutationem motus proportionalem esse vi motrici impressæ, & fieri se-
| cundum lineam rectam qua vis illa imprimitur.
|
| [Newton's detailed explanation]
Which I translate to:
"Law II
The change of motion is proportional to the impressed motive force, and is
done according to the straight line in which the force is impressed [i.e.,
the motion changes in the direction of the exerted force]."
> He called this [p], what we call "momentum" today, "the quantity of motion",
and
> defined that it "arises from Velocity [v] and the quantity of Matter [mass
> m] together" ("Philosophiæ Naturalis Principia Mathematica":
Definitiones").
>
> [...]
>
>
>
> (Cambridge University, Cambridge Digital Library. High resolution digitised
> version of Newton's own copy of the first edition, interleaved with blank
> pages for his annotations and corrections. Cited in:
> )
He wrote there:
| Def. I
|
| Quantitas Materiæ est mensura ejusdem orta ex illius Densitate &
| Magnitudine conjunctim.
|
| [...]
|
| Def. II.
|
| Quantitas motus est mensura ejusdem orta ex Velocitate et quantitate
| Materiæ conjunctum.
Which I translate to:
"Definition I
The Quantity of Matter is the measure of the same, arising from Density &
Size [volume] together.
[...]"
(this is equivalent to mass m = ρ V), and
"Definition II
The Quantity of motion is the measure of the same, arising from Velocity and
the quantity of Matter together."
(this is then equivalent to [non-relativistic] momentum, as I explained
before).
My translations are corroborated (and partially informed) by Andrew Motte's
official translation of 1729 of the second edition of the "Principia" into
English:
> One can see that this is equivalent to
>
> F = m a,
>
> considering that the mass is assumed to be constant¹, and that acceleration
> is the derivative of velocity with respect to time:
>
> F = ṗ = m v̇ = m a.
More precisely:
One can see from the Latin original that Newton never clearly stated (the
equivalent of) F = ṗ there, but merely a proportionality between the
exerted force and the change of motion (he previously defined motion to be
measured by the "quantity of motion", now called momentum).
However, the modern form of the law is implied because, following Newton's
definition of "(the quantity of) motion", the "change of motion/momentum"
can only be due to either a change of velocity, or "the quantity of matter"
(mass), or both. Then for the same change of velocity, i.e. acceleration,
a constant mass serves as the required proportionality constant.
And ISTM that Newton *meant* a constant mass because he had no reason to
assume that "the quantity of matter" would change due to an exerted force.
--
PointedEars
Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
|
