# 牛顿第三运动定律

（重定向自反作用力

1687年，英國物理泰斗艾萨克·牛顿在巨著《自然哲學的數學原理》裏，提出了牛頓運動定律，其中有三條定律，分別為牛顿第一運動定律牛顿第二運動定律與牛顿第三運動定律。[2]由於專門表述作用力與反作用力，牛顿第三運動定律又稱為「作用與反作用定律」，在本文內簡稱為「第三定律」。

${\displaystyle \sum \mathbf {F} _{A,B}=-\sum \mathbf {F} _{B,A}}$

## 牛頓的論述

To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

## 錯誤和正確的基本物理概念

### 正確分析實例

• 因為地球感受到太陽的萬有引力，所以地球環繞著太陽進行軌道運動，同時，太陽也會感受到地球的萬有引力。設定地球感受到的萬有引力為作用力，則太陽感受到的萬有引力是對應的反作用力，其與作用力大小相等、方向相反。因為太陽的質量超大於地球，所以地球的吸引似乎對於太陽並沒有造成甚麼影響，然而，太陽的確有被地球影響。對於這兩個天體的共同運動可以正確描述為，它們都環繞著整個太陽－地球系統的質心進行軌道運動。[11]
• 假設在一條不能延伸的鋼纜的一端懸掛著一個鉛球，鋼纜的另一端緊繫於實驗室的天花板。那麼，鉛球會被地球用萬有引力所吸引，因此傾向於朝著實驗室地板墜落。設定鉛球感受到的萬有引力為作用力，則鉛球吸引地球的萬有引力是對應的反作用力，這一對力的存在與鋼纜完全無關，實際而言，假若沒有鋼纜，作用力與反作用力依舊存在。從另一方面看，鋼纜施加於鉛球的力的方向朝上，阻止鉛球墜落，鉛球也同時施加力於鋼纜。設定鋼纜施加於鉛球的力為作用力，則鉛球同時施加於鋼纜的力是對應的反作用力，這一對作用力與反作用力的大小相等、方向相反。如果，相對於天花板，這簡單的系統是靜止不動的，則根據牛頓第一定律，鉛球感受到的淨外力等於零，這淨外力是地球施加於鉛球的地心引力與鋼纜施加於鉛球的力這兩種不同力的向量和。這兩種力的大小相等、方向相反；也就是說，它們互補。但是，這並不表示它們是一對作用力與反作用力，這可以從它們都作用於同一個物體（鉛球）的事實推斷出來，它們彼此之間的關係不遵循牛頓第三定律。[11]
• 為了要檢查這些概念的解釋是否正確，可以將鋼纜改換為彈簧。如果相對於實驗室參考系 ，這新系統最初是靜止的，則前面的分析也適合。但是，如果這系統現在遭到微擾（例如，鉛球被輕輕的推一下或拉一下），鉛球開始上下震動，則由於鉛球呈加速度運動，按照牛頓第一定律，淨外力不等於零，可是，鉛球與地球的質量都沒有改變，鉛球與地球質心之間的距離也幾乎一樣，所以，本質為萬有引力的作用力與反作用力仍舊不變，不同的是現在這系統已變為動力系統，鉛球感受到的萬有引力暫時地與彈力失去平衡。彈力的大小與方向都隨時間而改變（震動頻律跟彈簧的弹簧常数有關）。弹力和弹簧的长度变化量成線性關係。[12]

### 錯誤分析實例

• 第三定律時常會以一種簡單，但不完全或不正確的句子陳述：

• 作用力與反作用力問題時常會跟靜態平衡混淆；換句話說，假若作用力與反作用力大小相等、方向相反，則物體怎樣移動？[15]例如，思考以下句子：

• 另外一個常見的錯誤觀念：

## 註釋

1. ^ 應用諾特定理，可以從伽利略不變性推導出動量守恆。[5]
2. ^ 1711年，有一次牛頓在駁斥戈特弗里德·莱布尼茨的論述時表示，按照第三運動定律，離心力永遠與萬有引力大小相等、方向相反。[18]注意到萬有引力是一種向心力。

## 參考資料

1. Newton 1846，第83-84页
2. ^ Marion & Thornton 2004，第328-329页
3. ^ Goldstein 1980，第7页
4. Griffiths 1998，第349-351页
5. ^ Newton 1846，第86-87页
6. Gauld, Colin, THE HISTORICAL CONTEXT OF NEWTON'S THIRD LAW AND THE TEACHING OF MECHANICS, Research in Science Education, 1993, 23 (1): 95–103, doi:10.1007/BF02357049
7. Newton 1846，第92-93页
8. C Hellingman. Newton's third law revisited. Phys. Educ. 1992, 27 (2): 112–115. Bibcode:1992PhyEd..27..112H. doi:10.1088/0031-9120/27/2/011. The orlglnal formulathm of Newton’s third law is again under altack. Too many physicists-and not just undergraduates-fail to understand its core. … The answer most frequently given was: ‘The normal force the table exerts on the bottle’, a mistake I am sure I too would have made early in my career. ... It is not one action by which the Sun attracts Jupiter, and another by which Jupiter attracts the Sun; but it is one action by which the Sun and Jupiter mutually endeavour to come nearer together.
9. Brown, David. Students' concept of force: the importance of understanding Newton's third law. Phys. Educ. 1989, 24 (6): 353–358. doi:10.1088/0031-9120/24/6/007. A body cannot experience a force in isolation. There cannot be a force on a body A without a second body B to exert the force. A cannot exert a force in isolation. A cannot exert a force unless there is another body B to exert a force on A. … At all moments of time the force A exerts on B is of exactly the same magnitude as the force B exerts on A. … neither force precedes the other force. … The data from all three studies support the hypothesis that the persistence of preconceptions concerning the third law may result from students’ general naive view of force as a property of single objects rather than as a relation between objects.
10. Aiton 1995，第268页
11. ^ French 1966，第41-43页
12. ^ French 1971，第314页
13. ^ Hall, Nancy. Newton's Third Law Applied to Aerodynamics. NASA. （原始内容存档于2018-10-03）. for every action (force) in nature there is an equal and opposite reaction
14. ^ Lindsay 1950，第21页
15. ^
16. ^ Adair, Aaron, Student Misconceptions about Newtonian Mechanics: Origins and Solutions through Changes to Instruction, 2013, This was attacked by Newton who tried to have the centripetal force on the planets (from gravitational interactions) be matched by the centrifugal force so there would be a balance of forces based on his third law of motion
17. ^ Aiton 1995，第268-269页
18. ^ Roche, John. Introducing motion in a circle (PDF). Physics Education. September 2001, 43 (5): 399–405. A recent engineering mathematics textbook states that ‘The centripetal force. . . [and]. . . the centrifugal force. . . are in equilibrium at each instant of the motion. We might be forgiven for thinking that this is what theologians call the invincible blindness that can only be rectified by prayer. Unfortunately, this view is widespread. For example, many students are likely to have absorbed uncritically the statement that the Earth’s attraction on the Moon is balanced by a centrifugal force.
19. ^ Aiton 1995，第269页
20. ^ Singh, Chandralekha, Centripetal Acceleration: Often Forgotten or Misinterpreted, Physics Education, 2009, 44 (5): 464, doi:10.1088/0031-9120/44/5/001, Another difficulty is that students often consider the pseudo forces, e.g., the centrifugal force, as though they were real forces acting in an inertial reference frame.
21. Russel, John, Action and Reaction before Newton, British Journal for the History of Science, 1976, 9 (1): 25–38, JSTOR 4025704, doi:10.1017/S0007087400014473
22. ^ Walter Lewin, Newton's First, Second, and Third Laws 页面存档备份，存于互联网档案馆, Lecture 6. (14:11–16:00)