Newton’s Third Law

Every action has an equal and opposite reaction.

Everyone knows this catchphrase but Newton’s Third Law still causes much misunderstanding.

The first two laws concern the balance or imbalance of forces acting on a single object and its resulting motion (or stasis – non-motion.) Newton’s Third Law concerns the forces that act when two bodies interact.

A more accurate way of describing Newton’s Third Law is:

If body A exerts a force on body B then body B exerts a force on body A – ALWAYS AND WITHOUT EXCEPTION.

The two forces are

• Equal in magnitude.
• Opposite in direction
• The same type of force (e.g. magnetic, gravitational)
• Strictly A acting on B and B acting on A. I.e. if a third body is involved, there must be another pair of forces involved.

Consider a book placed on a shelf. We are taught in school that the book remains at rest because it is acted on by gravity (producing the downwards force of weight) and an upwards reaction force from the shelf. This is true but it is important to realise that this is an example of Newton’s First Law, not Newton’s Third Law of Motion.

Let us examine the forces acting on the book. They satisfy the first two criteria of a Third Law force pair: they are equal in magnitude and opposite in direction. However, they are not the same type of force: the book’s weight is due to gravity while the reaction force from the shelf is actually an electrostatic force, as are all contact forces. Furthermore, both the forces act on the same body, the book. The reaction force is due to the shelf acting on the book and the book’s weight is due to the earth’s gravitational field.

We must then consider the forces acting between book and shelf and between book and earth:

One Third Law force pair is: book pushes on shelf, shelf pushes back on book. These are the electrostatic contact forces that the two bodies exert on each other where they touch. They fulfil all four criteria: they are equal in magnitude and opposite in direction, they are the same type of force and they are also mutually between two bodies (A on B, B on A)

The other Third Law force pair is the earth’s gravitational pull on the book and the book’s gravitational pull on the earth. Again these two fulfil all the criteria of a third law force pair.

This helps to answer a common student question when introducing the first law: “If every force has an equal and opposite reaction force, how can anything ever move in the first place? Don’t the forces cancel out?”

What we have to remember is that, yes, every force does have an equal an opposite pair force BUT that opposite force does NOT act on the same body as the “action” force: if you punch the wall hard enough, you may indeed be able to move (accelerate) the wall but you would be ill-advised to do so because the wall will exert an equal and opposite force on your hand!