section_path: Newtonian mechanics/Third law
section_name: Third law
paragraph_text: Third law
  
  Whenever one body exerts a force on another, the latter simultaneously exerts an equal and opposite force on the first. In vector form, if F 1, 2 {\displaystyle \mathbf {F} _{1,2}} is the force of body 1 on body 2 and F 2, 1 {\displaystyle \mathbf {F} _{2,1}} that of body 2 on body 1, then F 1, 2 = − F 2, 1. {\displaystyle \mathbf {F} _{1,2}=-\mathbf {F} _{2,1}.} This law is sometimes referred to as the action-reaction law, with F 1, 2 {\displaystyle \mathbf {F} _{1,2}} called the action and − F 2, 1 {\displaystyle -\mathbf {F} _{2,1}} the reaction.
  
  Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are interactions between different bodies. and thus that there is no such thing as a unidirectional force or a force that acts on only one body.
  
  In a system composed of object 1 and object 2, the net force on the system due to their mutual interactions is zero: F 1, 2 + F 2, 1 = 0. {\displaystyle \mathbf {F} _{1,2}+\mathbf {F} _{2,1}=0.} More generally, in a closed system of particles, all internal forces are balanced. The particles may accelerate with respect to each other but the center of mass of the system will not accelerate. If an external force acts on the system, it will make the center of mass accelerate in proportion to the magnitude of the external force divided by the mass of the system.
  
  Combining Newton's Second and Third Laws, it is possible to show that the linear momentum of a system is conserved in any closed system. In a system of two particles, if p 1 {\displaystyle \mathbf {p} _{1}} is the momentum of object 1 and p 2 {\displaystyle \mathbf {p} _{2}} the momentum of object 2, then d p 1 d t + d p 2 d t = F 1, 2 + F 2, 1 = 0. {\displaystyle {\frac {\mathrm {d} \mathbf {p} _{1}}{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {p} _{2}}{\mathrm {d} t}}=\mathbf {F} _{1,2}+\mathbf {F} _{2,1}=0.} Using similar arguments, this can be generalized to a system with an arbitrary number of particles. In general, as long as all forces are due to the interaction of objects with mass, it is possible to define a system such that net momentum is never lost nor gained.