Action and reaction

                                          

The third of Newton's laws of motion of classical mechanics states that forces always occur in pairs. This is related to the fact that a force results from the interaction of two objects. Every force ('action') on one object is accompanied by a 'reaction' on another, of equal magnitude but opposite direction. The attribution of which of the two forces is action or reaction is arbitrary. Each of the two forces can be consider.

The reaction is one of the least understood of the basic physical concepts, perhaps because it is often poorly taught or incorrectly described in many publications.

Causal misinterpretation

The terms 'action' and 'reaction' have the unfortunate suggestion of causality, as if the 'action' is the cause and 'reaction' is the effect. It is therefore easy to think of the second force of being there because of the first, and even happening some time after the first. This is incorrect; the forces are perfectly simultaneous, and are there for the same reason.

When the forces are caused by a person's volition (e.g. a soccer player kicks a ball), this volitional cause often leads to an asymmetric interpretation, where the force by the player on the ball is considered the 'action' and the force by the ball on the player, the 'reaction'. But physically, the situation is symmetric. The forces on ball and player are both explained by their nearness, which results in a pair of contact forces (ultimately due to electric repulsion). That this nearness is caused by a decision of the player has no bearing on the physical analysis. As far as the physics is concerned, the labels 'action' and 'reaction' can be flipped.

'Equal and opposite'              

One problem frequently observed by physics educators is that students tend to apply Newton's Third Law to pairs of 'equal and opposite' forces acting on the same object. This is incorrect; the Third Law refers to forces on two different objects. For example, a book lying on a table is subject to a downward gravitational force (exerted by the earth) and to an upward normal force by the table. Since the book is not accelerating, these forces must be exactly balanced, according to Newton's First or Second law. They are therefore 'equal and opposite'. However, these forces are not always equally strong; they will be different if the book is pushed down by a third force, or if the table is slanted, or if the table-and-book system is in an accelerating elevator. The case of three or more forces is covered by considering sum of all forces.A possible cause of this problem is that the Third Law is often stated in an abbreviated form: For every action there is an equal and opposite reaction, without the details, namely that these forces act on two different objects. Moreover, there is a causal connection between the weight of something and the normal force: if an object had no weight, it would not experience support force from the table, and the weight dictates how strong the support force will be. This causal relationship is not due to the Third Law but to other physical relations in the system; but this point is often lost on students.