# 牛頓第二定律

## 方程式

${\displaystyle \mathbf {F_{net}} \propto m\mathbf {a} }$

${\displaystyle \mathbf {F_{net}} =m\mathbf {a} }$；又或者
${\displaystyle \mathbf {F_{net}} ={\frac {d{\vec {p}}}{dt}}=m{\vec {a}}}$${\displaystyle p}$ 係指動量（Momentum；舊物體嘅質量同佢嘅速度相乘），而 ${\displaystyle {\frac {d{\vec {p}}}{dt}}}$ 係動量隨住時間改變嘅率。

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

### 第二定律嘅三維化

${\displaystyle F_{x}=ma_{x}}$（沿住 X 軸嘅淨外力同加速度）、
${\displaystyle F_{y}=ma_{y}}$（沿住 Y 軸嘅淨外力同加速度）、
${\displaystyle F_{z}=ma_{z}}$（沿住 Z 軸嘅淨外力同加速度）；

### 喺可變質量系統嘅應用

${\displaystyle \mathbf {F} _{g}+\mathbf {u} {\frac {\mathrm {d} m}{\mathrm {d} t}}=m{\mathrm {d} \mathbf {v} \over \mathrm {d} t}}$
${\displaystyle \mathbf {u} {\frac {\mathrm {d} m}{\mathrm {d} t}}}$ 係氣體燃料由支火箭嗰度噴出嚟造成嘅推力（Thrust），佢同外力加埋就等於支火箭前前後後總共受咗幾多力；

## 牛頓嘅論述

"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."

「動量嘅變化同衝量方向一樣，而且成正比。」

## 理論方面嘅用途

### 質量嘅操作定義

${\displaystyle \mathbf {F} _{1}=(1)\mathbf {a} _{1}}$，舊標準質量當咗係等如 1 個單位嘅質量，而 ${\displaystyle {a}_{1}}$ 係佢受到 ${\displaystyle {F}_{1}}$ 呢股力嗰陣嘅加速度。
${\displaystyle \mathbf {F} _{1}=m\mathbf {a} _{2}}$${\displaystyle m}$ 係想知佢質量嗰舊物體嘅質量，而 ${\displaystyle {a}_{2}}$ 係佢受到 ${\displaystyle {F}_{1}}$ 呢股力嗰陣嘅加速度。因為 ${\displaystyle {F}_{1}}$ 喺兩舊物體上係相等，而兩個加速度可以用簡單方法揾到，所以有得靠兩舊物體各自嘅加速度之間嘅比例計出想知佢質量嗰舊物體：
${\displaystyle m\mathbf {a} _{2}=(1)\mathbf {a} _{1}}$
${\displaystyle m={\frac {{a}_{1}}{{a}_{2}}}}$

## 攷

1. Halliday, D.; Robert R., Jearl Walker. Fundamental of Physics, 7th Ed. USA: John Wiley and Sons, Inc., 2005.
2. Reif, F. Understanding Basic Mechanics 2, illustrated. Wiley: pp. 95, 1995.
3. O'Sullivan, C. Newton's laws of motion: Some interpretations of the formalism. American Journal of Physics. Feb 1980, 48 (2): pp. 131.
4. Raymond A. Serway, Jerry S. Faughn. College Physics. Pacific Grove CA: Thompson-Brooks/Cole. 2006: pp. 160ff.
5. 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.
6. 馬克士威詹姆斯 (1878). Matter and Motion. D.Van Nostrand. pp. pp. 32-35. {{cite book}}: |pages= has extra text (help)
7. 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.
8. 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.
9. Dugas, R. A History Of Mechanics, New York: Dover Publications, Inc., 1988.
10. Hecht, E. (2006). There is no really good definition of mass. The Physics Teacher, 44(1), 40-45.
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