# 牛頓第二運動定律

## 概述

${\displaystyle \mathbf {F} \propto m\mathbf {a} }$

${\displaystyle \mathbf {F} =m\mathbf {a} }$

${\displaystyle 1\mathrm {N} =1\mathrm {kg} \cdot \mathrm {m} /\mathrm {s} ^{2}}$

${\displaystyle F_{x}=ma_{x}}$
${\displaystyle F_{y}=ma_{y}}$
${\displaystyle F_{z}=ma_{z}}$

## 牛頓的論述

The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

「motion」是「quantity of motion」的簡稱，在這裏指的是物體的動量。「impressed force」指的是衝量[3] [4]整個句子翻譯為

## 質量的操作定義

${\displaystyle F=m_{A}a_{A}=m_{B}a_{B}}$

${\displaystyle m_{B}={\frac {a_{A}}{a_{B}}}m_{A}}$

## 力的操作定義

${\displaystyle F_{s}=-kx}$

${\displaystyle F_{G}=-G{\frac {m_{A}m_{B}}{r^{2}}}}$

${\displaystyle F_{g}=mg}$

## 衝量

${\displaystyle \mathbf {J} =\int _{\Delta t}\mathbf {F} \,\mathrm {d} t}$

${\displaystyle \mathbf {F} =m\mathbf {a} }$

${\displaystyle \Delta \mathbf {p} =m\Delta \mathbf {v} =m\int _{\Delta t}\mathbf {a} \,\mathrm {d} t=\int _{\Delta t}\mathbf {F} \,\mathrm {d} t}$

${\displaystyle \mathbf {J} =\Delta \mathbf {p} }$

## 可變質量系統

${\displaystyle \mathbf {F} _{\mathrm {net} }=M\mathbf {a} _{\mathrm {cm} }}$

${\displaystyle \mathbf {F} _{g}+\mathbf {u} {\frac {\mathrm {d} m}{\mathrm {d} t}}=m{\mathrm {d} \mathbf {v} \over \mathrm {d} t}}$

${\displaystyle \mathbf {F} _{t}\ {\stackrel {def}{=}}\ \mathbf {u} {\frac {\mathrm {d} m}{\mathrm {d} t}}}$

${\displaystyle \mathbf {F} =m\mathbf {a} }$

## 參考文獻

1. ^ Serway 2006，第102頁
2. ^ Newton 1846，第83-93頁
3. 馬克士威, 詹姆斯. Matter and Motion. D.Van Nostrand. 1878: pp. 32–35.
4. Dugas 1988，第200-207頁
5. ^ See for example (1) I Bernard Cohen, "Newton’s Second Law and the Concept of Force in the Principia", in "The Annus Mirabilis of Sir Isaac Newton 1666–1966" (Cambridge, Massachusetts: The MIT Press, 1967), pages 143–185; (2) Stuart Pierson, "'Corpore cadente. . .': Historians Discuss Newton’s Second Law", Perspectives on Science, 1 (1993), pages 627–658; and (3) Bruce Pourciau, "Newton's Interpretation of Newton's Second Law", Archive for History of Exact Sciences, vol.60 (2006), pages 157–207; also an online discussion by G E Smith, in 5. Newton's Laws of Motion, s.5 of "Newton's Philosophiae Naturalis Principia Mathematica" in (online) Stanford Encyclopedia of Philosophy, 2007.
6. ^ Sommerfeld, Arnold, Mechanics (Lectures on Theoretical Physics, Volume I), Academic Press: pp. 5, 1952
7. ^ O'Sullivan, Colm. Newton's laws of motion: Some interpretations of the formalism. American Journal of Physics. Feb 1980, 48 (2): pp. 131. ISSN 0002-9505.
8. ^ Raymond A. Serway, Jerry S. Faughn. College Physics. Pacific Grove CA: Thompson-Brooks/Cole. 2006: pp. 160ff.
9. ^ I Bernard Cohen (Peter M. Harman & Alan E. Shapiro, Eds). The investigation of difficult things: essays on Newton and the history of the exact sciences in honour of D.T. Whiteside. Cambridge UK: Cambridge University Press. 2002: 353. ISBN 052189266X.
10. ^ WJ Stronge. Impact mechanics. Cambridge UK: Cambridge University Press. 2004: 12 ff. ISBN 0521602890.
11. ^ Plastino, Angel R.; Muzzio, Juan C. On the use and abuse of Newton's second law for variable mass problems. Celestial Mechanics and Dynamical Astronomy (Netherlands: Kluwer Academic Publishers). 1992, 53 (3): 227–232. Bibcode:1992CeMDA..53..227P. ISSN 0923-2958. doi:10.1007/BF00052611.
12. ^ Walter Lewin, Newton's First, Second, and Third Laws, Lecture 6. (6:53–11:06)