Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

Just some minor additional information:

The two forces generated have equal magnitudes, but opposite directions. It is also important to note that the forces act on different bodies.

Symbolically:

FA on B= (-)FB on A (the forces are vectors)

Note that the Third Law only applies to central forces. A central force is a force which is exerted by one object on another directed along a line connecting the centers of the two objects. Gravity and the electrostatic force are both examples.

Any force which is depends on the velocities of the interacting objects is noncentral, and the third law does not apply. The force between two moving electric charges would be noncentral because the force propagates at the speed of light.

A related statement is:

In a closed system, the sum of the (net) forces acting on the particles is zero.

This statement is "almost" equivalent to Newton's 3rd law. It certainly holds in Newtonian mechanics, so it is implied by the 3rd law and in the case of ony two particles in the system it reduces to it. However, it does not say anything about where the forces come from.

In a way, that is very appealing. The only thing we can actually observe about a particle is the net force (by measuring its acceleration). We can not tell which particle is exerting that force. Thus the above statement is a generalised version of the 3rd law: it admits both theories that assign forces between individual pairs of particles (like Newtonian mechanics does), and those that don't.

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