# 牛頓第二運動定律

## 概述

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

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

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

$F_x =ma_x$
$F_y =ma_y$
$F_z =ma_z$

## 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

$F=m_Aa_A=m_Ba_B$

$m_B=\frac{a_A}{a_B}m_A$

## 力的操作定義

$F_s=-kx$

$F_G=-G\frac{m_A m_B}{r^2}$

$F_g=mg$

## 衝量

$\mathbf{J} = \int_{\Delta t} \mathbf F \,\mathrm{d}t$

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

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

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

## 可變質量系統

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

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

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

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

## 參考文獻

1. ^ Serway 2006，第102頁
2. ^ Newton 1846，第83-93頁
3. ^ 3.0 3.1 馬克士威, 詹姆斯. Matter and Motion. D.Van Nostrand. 1878: pp. 32–35.
4. ^ 4.0 4.1 Dugas 1988，第200-207頁
5. ^ See for example (1) I Bernard Cohen, "Newton’sSecond 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’sSecond 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. doi:10.1007/BF00052611. ISSN 0923-2958.
12. ^ Walter Lewin, Newton's First, Second, and Third Laws, Lecture 6. (6:53–11:06)