Newton's Third Law
Newton's third law states that when one body exerts a force on a second body, the second body simultaneously exerts a force of equal magnitude and opposite direction on the first.
Curious
Stand on a skateboard and push against a wall. You roll backward. The wall didn't move, but it pushed back on your hand with the same force you pushed on it — and since you're the one free to move, that reaction force is what sends you rolling.
This is true everywhere, all the time, for every force: gravity, contact pushes, magnetic pulls, everything. When you sit in a chair, you push down on the chair with your weight, and the chair pushes up on you with an equal force — that's why you don't fall through it.
The key thing people get wrong: the two forces in a "third law pair" act on different objects. Your push on the wall acts on the wall. The wall's push acts on you. They never cancel each other out for the same object, because they're not both acting on the same thing.
Exploring
Formally, if body A exerts force F_AB on body B, then body B simultaneously exerts a force F_BA on body A such that:
Both forces act along the same line, have equal magnitude, and point in opposite directions — but they act on two different bodies, so they never appear together in a single free-body diagram of one object, and they never cancel in the way two opposing forces on the same object would.
Worked example: An astronaut of mass 80 kg pushes off a 1,000 kg space capsule with a force that lasts long enough to reach a recoil speed of 0.5 m/s. By the third law, the capsule receives an equal and opposite impulse. Since impulse = momentum change, and momentum must balance (total momentum conserved, starting from rest): 80 × 0.5 = 1,000 × v_capsule, giving v_capsule = 0.04 m/s in the opposite direction.
Deep Dive
Newton's third law is the foundation of the conservation of linear momentum in isolated systems. Consider two bodies A and B interacting only with each other. By the second law, F_AB = dp_B/dt and F_BA = dp_A/dt. By the third law, F_AB = −F_BA, so dp_A/dt + dp_B/dt = 0, meaning the total momentum p_A + p_B is constant in time. This is not a coincidence — the third law is essentially the local, force-based statement whose global consequence is momentum conservation.
Limits of validity: The strong form of Newton's third law (equal, opposite, and acting along the line connecting the two bodies) holds for contact forces and for the gravitational and electrostatic forces between bodies at rest relative to each other. It famously breaks down for the magnetic force between moving charges and, more generally, in any situation involving time-delayed field interactions — a consequence of no signal or field disturbance being able to propagate faster than the speed of light. In these cases, momentum conservation is rescued not by force pairs but by including the momentum carried by the electromagnetic field itself. This is one of the conceptual seams where classical field theory (Maxwell's equations) must supplement Newtonian point-particle mechanics.
In general relativity and quantum field theory, the third law in its Newtonian form is not fundamental; conservation of momentum survives as a consequence of the translational symmetry of physical laws (via Noether's theorem), a deeper and more general justification than the pairwise force statement Newton gave in 1687.
Concept Relationship Map
Requires: force, Newton's Second Law
Enables: conservation of momentum, rocket propulsion analysis
Commonly confused with: the misconception that action-reaction pairs cancel and prevent motion — they act on different bodies and never cancel for either one
Sources
- Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica, Book I, Axioms, Law III. Public domain.
- Goldstein, H., Poole, C., Safko, J. (2002). Classical Mechanics, 3rd ed. Addison Wesley, Ch. 1, 9.
- Griffiths, D.J. (2017). Introduction to Electrodynamics, 4th ed. Cambridge University Press — on the breakdown of the strong third law for moving charges.