Newton’s Third Law
“To every action [change of momentum] there is always opposed an equal reaction; or, the mutual actions of two bodies are always equal, and directed to contrary parts.”
Consider collision of m1 with m2:
- Newton’s Second Law says that the force acting on m2 (= F12) during a time ?t results in a change in the momentum of m2 (=?p2) equal to the force times the time ( ?p2 = F12 ?t ). Similarly the change in momentum of m1 is given by: ?p1 = F21 ?t
- Newton’s Third Law says that the force m1 exerts on m2 (= F12) must be equal in magnitude, but in the opposite direction of the force m2 exerts on m1 (= F21), i.e., F12 = -F21
- Therefore, the change in momentum of m1 (= ?p1) is equal in magnitude, but in the opposite direction of the change in momentum of m2 (= ?p2).
- THE TOTAL MOMENTUM DOES NOT CHANGE!