Action–Reaction Principle

Newton's Third Law states that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force back on the first. These two forces — called an action–reaction pair or an interaction pair — are always equal in magnitude and opposite in direction. Crucially, they act on different objects, which is what distinguishes them from balanced forces. This law applies universally: it holds whether you are pushing a wall, firing a rocket, or simply sitting on a chair. No force ever exists in isolation; every force is one half of a mutual interaction. A useful everyday analogy is swimming. When you push water backwards with your hands (action), the water pushes you forwards (reaction). The magnitudes are identical, but the forces act on different bodies — one on the water, one on you. This is why swimmers accelerate forward even though the two forces are equal: they cause accelerations on different masses. The swimmer, being less massive than the body of water, accelerates noticeably, while the water's acceleration is imperceptible. Newton's Third Law governs the motion of rockets, cars, birds, and even the Earth itself. It is vital not to confuse an action–reaction pair with two balanced forces on the same object. If you stand still on the ground, the ground pushes you up (normal force) and gravity pulls you down — those two forces are equal and opposite but they both act on you, so they are not a Newton's Third Law pair. The Third Law pair to gravity pulling you down is you pulling the Earth upward with exactly the same magnitude of force.

Key takeaways
  • Identify the two interacting objects
  • Name both forces in the pair
  • Check the three key properties
  • Understand why equal forces can cause unequal accelerations
  • Apply to real-world propulsion

Identify the two interacting objects

Every application of Newton's Third Law begins by naming two distinct objects. Force is always the result of an interaction between two bodies. For example: a bat and a ball, a rocket engine and exhaust gas, or your foot and the floor. Without two objects, there is no interaction and no force pair to speak of.

Name both forces in the pair

Once you have identified objects A and B, the action–reaction pair consists of: (1) the force that A exerts on B, and (2) the force that B exerts on A. These are always equal in magnitude and opposite in direction. A good naming convention helps: 'Force of A on B' and 'Force of B on A'. For instance, 'Force of bat on ball' (forward) and 'Force of ball on bat' (backward).

Check the three key properties

A genuine Newton's Third Law pair satisfies three conditions simultaneously: (a) Equal magnitude — |F_AB| = |F_BA|; (b) Opposite direction — they point exactly 180° apart; (c) Different objects — one force acts on A, the other acts on B. If both forces act on the same object, they cannot be a Third Law pair, regardless of whether they happen to be equal and opposite.

Understand why equal forces can cause unequal accelerations

Because the two forces in a pair act on different objects with potentially different masses, they produce different accelerations. By Newton's Second Law, a = F/m. A gun and a bullet experience equal and opposite forces during firing, but the bullet (tiny mass) accelerates enormously while the gun (large mass) recoils only slightly. The forces are identical in magnitude; the accelerations are not — and that is perfectly consistent with Newton's laws.

Apply to real-world propulsion

Rockets work entirely because of Newton's Third Law. Hot exhaust gas is expelled backwards at high speed (action). The rocket is pushed forwards (reaction). There is no ground or air required — this works in the vacuum of space. Similarly, a car's tyres push backward on the road; the road pushes forward on the car. Understanding interaction pairs explains how propulsion and locomotion work at a fundamental level.

The Key Equation

F⃗AB=−F⃗BA\vec{F}_{AB} = -\vec{F}_{BA}
  • \vec{F}_{AB} — Force of A on B (Newton (N)): The vector force that object A exerts upon object B. This is one member of the interaction pair.
  • \vec{F}_{BA} — Force of B on A (Newton (N)): The vector force that object B exerts upon object A. This is the other member of the interaction pair, equal in size but opposite in direction.
  • - — Negative sign (dimensionless): Indicates that the two force vectors are antiparallel — they point in exactly opposite directions, differing by 180°.

Worked Example

Problem. A skater of mass 50 kg pushes off a wall with a force of 120 N. (a) What force does the wall exert on the skater? (b) If the skater starts from rest, what is their initial acceleration away from the wall? (Ignore friction.)

Fwall on skater=120 N,a=12050=2.4 m s−2F_{\text{wall on skater}} = 120\text{ N},\quad a = \frac{120}{50} = 2.4\text{ m s}^{-2}

Answer. The wall exerts 120 N on the skater (away from the wall), and the skater's initial acceleration is 2.4 m s⁻² away from the wall.

Figure
Diagram
Newton's Third Law: Skater Pushing Off a WallWallSkaterm = 50 kgF skater→wall120 NF wall→skater120 Naccelerationa = 2.4 m s⁻²Action (skater on wall)Reaction (wall on skater)Resulting acceleration of skaterBoth forces equal 120 N — but act on DIFFERENT objects
Origins · 1 minIsaac Newton and how this was discovered
IN
Isaac Newton
1643–1727 · English

Newton formulated his three laws of motion in his landmark 1687 work Philosophiæ Naturalis Principia Mathematica. The Third Law — that every action has an equal and opposite reaction — appeared there for the first time in rigorous mathematical form. This single principle unified the physics of collisions, rocket propulsion, planetary orbits, and structural forces under one elegant statement, forming a cornerstone of classical mechanics that remained the definitive framework for over 200 years. Newton reportedly said he made his greatest discoveries during the plague years of 1665–1666 when Cambridge University sent students home. Confined to his family farm in Lincolnshire, he developed calculus, his theory of colours, and the foundations of gravitational theory — all before his 24th birthday.

  • Newton's First Law & Inertia — Newton's First Law defines what happens when net force is zero — understanding all three laws together gives a complete picture of how forces govern motion.
  • Newton's Second Law (F = ma) — The Second Law tells you how each force in an action–reaction pair separately accelerates its respective object, explaining why equal forces cause different accelerations on different masses.
  • Free-Body Diagrams — Drawing free-body diagrams is the essential skill for correctly identifying which forces act on which object, helping you avoid confusing Third Law pairs with balanced forces.
  • Momentum & Impulse — Newton's Third Law is the physical basis for conservation of momentum — equal and opposite forces acting for the same time interval produce equal and opposite changes in momentum.