# Actio and Reactio

Body A (the apple) is attracted by gravity to body B (the earth ), so the force (“Actio”) acts on the apple's center of gravity . Due to the principle of interaction, the force ("Reactio") must now attack at the center of gravity of the earth . The apple is attached to the tree with its stem and thus an additional force acts on the apple, which prevents it from falling. Coercive force and action form a balance of forces (on the same body). Actio and Reactio, on the other hand, form the interaction pair described in this article (on two bodies).${\ displaystyle F_ {B \ to A}}$${\ displaystyle F_ {A \ to B}}$ ${\ displaystyle F_ {S}}$

The principle of Actio and Reactio (also counteraction principle , interaction principle or third Newtonian axiom ) is a Newtonian law and states that when two bodies interact, every action ( force from body A on B) simultaneously produces an equally large reaction (counterforce from body B on A), which affects the person who caused the action:

${\ displaystyle {\ vec {F}} _ {A \ to B} = - {\ vec {F}} _ {B \ to A}}$

It is part of Newton's laws . It is often also called "Actio et Reactio" (Latin for 'action and reaction'), "Actio est Reactio" (Latin for 'Action is [equal] reaction') or "Action equals reaction".

## Basics

The principle of Actio and Reactio is the lex tertia according to Sir Isaac Newton .

“Lex III. Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi. "

“Forces always appear in pairs. If a body A exerts a force on another body B (actio) , an equally large but opposing force from body B acts on body A (reaction) . "

- Isaac Newton : Philosophiae naturalis principia mathematica . Vol. 1 Tomus Primus. London 1726, p. 14.

From a modern point of view, the principle of interaction is equivalent to the conservation of momentum in closed systems . Forces correspond to temporal changes in the pulse, must therefore be the sum of all forces in a closed system (corresponding to the actio-and-Reactio principle) zero yield: . According to Noether's theorem , the conservation of momentum again corresponds to the homogeneity of space , i.e. the fact that the physical laws do not depend on the position in space. ${\ displaystyle {\ vec {F}} = {\ frac {\ mathrm {d} {\ vec {p}}} {\ mathrm {d} t}}}$${\ displaystyle \ sum _ {i} {\ vec {F_ {i}}} = {\ frac {\ mathrm {d}} {\ mathrm {d} t}} \ sum _ {i} {\ vec {p_ {i}}} = 0}$

It should be noted that a direct action at a distance has no validity in the special theory of relativity , in field theories such as electrodynamics and general relativity , rather the conservation of momentum or energy-momentum conservation of the overall system (particles and radiation) applies here.

## Interaction and balance

The principle of interaction, in which force and counterforce act on different bodies , must not be confused with an equilibrium of forces (see adjacent figure), in which two equally large but opposing forces balance each other on a body (and thus the state of movement of the body remains unchanged) . To make this distinction easier, the term “reaction force” or “interaction force” is sometimes used for the force that acts back on the basis of the principle of interaction.

## Explanations

In general, when a body exerts a force on another body, it is just as strongly (back) influenced by the other body. If the state of motion of one body is changed during this interaction, the same happens for the other body in the opposite direction. The change in the speeds of both bodies is only the same in special cases, in fact the change in momentum is meant.

In Newton's mechanics, the third axiom requires that two bodies must be involved in a force , which both experience exactly the same but opposite force at every moment. Forces can only emanate from bodies and only act on bodies. Therefore a vacuum or suction alone cannot exert force. With the apple on the tree, gravity acts between the bodies earth and apple; these two forces (on the one hand on the apple, on the other hand on the earth) are the interaction forces in the sense of actio and reaction. In addition, there is the holding force between apple and branch (which in turn has an interaction force between tree and earth). On the one Apple themselves act two forces. He stays calm, there is an equilibrium of forces. Only when the holding force is lost does the apple move evenly accelerated towards the earth and the earth falls accelerated towards the apple. The acceleration of the earth is much lower than the acceleration due to gravity of about 9.81 m / s 2 (with which the speed of the apple changes), since the mass of the earth exceeds that of the apple by many orders of magnitude.

Examples:

• When a horse pulls a stone over a rope, a force acts on the horse in the same way in the direction of the stone: For the rope, the horse pulls away from the stone in the same way as the stone offers resistance in the opposite direction, no object is preferred. It does not matter whether there is a stone on the other side or a second horse pulling with the same force.
• If two roller skaters face each other and one of them pulls the other towards him (or pushes away), the forces on both roller skaters are equal and opposite. The accelerations are usually not - the roller skater with the smaller mass experiences a greater acceleration (2nd Newton's axiom). It is important to note that the actio / reactio affects different objects.
• Another example of the principle of interaction is driving a rowboat : The oars are used to push the water backwards. The reaction of the water acts on the boat forwards.
• When you hold a ballpoint pen in your hand, you can feel its weight, i.e. the force with which it is being attracted to the earth. According to Newton's law of gravitation, however, this force of attraction works in both directions: The earth is in turn attracted by the ballpoint pen with the same force, only this goes under in view of the mass ratios, so to speak, and cannot be felt, but is present in physical reality.
• Baron Münchhausen cannot pull himself out of the swamp by the head. Hair and hand experience the same but opposite force and cancel each other out in the effect. Inside the closed system of hair, body and hand, the sum of the forces is zero. He would need a second body outside the swamp.
• Two bar magnets of different strength are connected at their poles. By simply pulling it apart, it is not possible to determine which is the stronger, as both experience exactly the same force. The same applies to two differently electrically charged bodies, they also experience the same force.
• A car (in forward gear) pushes its tires (body 1) backwards against the road surface (body 2). Its reaction force moves the car forward. Ice on the road decouples the road from the tire. No horizontal force can act and so there is no reaction either , the wheels spin and the car does not move.
• In propeller aircraft, the propeller and the air are the two bodies responsible for propulsive power. As actio the propeller accelerates the air to the rear. The reactio is the force of the air on the propeller, which drives the aircraft forward. When the aircraft is lifted, the wing is the one body that accelerates the air as the second body downwards. The upward reaction force of the air makes the airplane fly .
• In the case of rockets, the combustion chamber is one and the propellant is the second. In response to the exhaust of the combustion gases, the missile is accelerated. In this case the law of interaction is also called the recoil principle and one speaks of the recoil drive .
• A difficult case is the tug of war . The same force always acts in both directions in the rope at any moment, even with jerky movements. Apparently no team could win that way. But: Every team exerts a force on the ground with their feet. The two of you together are one body, connected by an internal force through the rope, the ground is the other. Whoever exerts the greater force on the ground and produces the greater reaction force there will win.
• The centrifugal force is an apparent force because the second body is missing, from which an outward pulling force emanates. A “correct” force is the centripetal force , which acts on the rotating body in the direction of the center of the circle and keeps it on the path.

## Individual evidence

1. ^ Digitized version ( Memento from December 22, 2015 in the Internet Archive ) - word for word in the Geneva 1739 edition, p. 23 ( digitized version , 60 of 589)