{"id":239,"date":"2026-06-15T22:30:34","date_gmt":"2026-06-15T22:30:34","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=239"},"modified":"2026-06-15T22:30:36","modified_gmt":"2026-06-15T22:30:36","slug":"conservation-of-momentum","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/conservation-of-momentum\/","title":{"rendered":"What Is Conservation of Momentum?"},"content":{"rendered":"\n
Definition<\/div>

\nConservation of momentum is the physical law stating that the total momentum of an isolated system stays constant: the vector sum of every object’s momentum (mass \u00d7 velocity) before an interaction equals the total momentum afterward. With no external force, collisions, explosions and recoil only redistribute momentum \u2014 they never create or destroy it.\n<\/p><\/div>\n\n

Step off a small boat onto a jetty and the boat darts backwards beneath your foot. Fire a rifle and your shoulder takes the kick. Break a rack of pool balls and a single cue strike scatters fifteen of them across the felt.<\/p>\n\n

Every one of these is the same rule quietly balancing its books. Momentum \u2014 the “quantity of motion” a moving object carries \u2014 is never simply lost. It only shifts from one object to another, and the totals always match. That single idea is one of the most powerful problem-solving tools in all of physics.<\/p>\n\n

What Is Conservation of Momentum?<\/h2>\n\n

Picture two ice skaters drifting toward each other. They grab hands, spin, and push apart. Track every push and shove, and you find the books always balance \u2014 what one skater gains, the other loses.<\/p>\n\n

Conservation of momentum<\/strong> is the law that the total momentum of an isolated system never changes. Momentum is the product of an object’s mass and its velocity, written p = mv<\/em>. Add up the momentum of every object before an event, and you get the exact same total afterward.<\/p>\n\n

The key word is isolated<\/em>. As long as no outside force pushes on the system, momentum has nowhere to go. Objects can swap it between themselves through collisions, but the grand total is locked.<\/p>\n\n

Momentum is also a vector<\/strong> \u2014 it has direction. A 2 kg cart rolling left does not cancel an identical cart rolling right by accident; their momenta point in opposite directions and sum to zero. Keeping track of sign and direction is half the skill of momentum problems, which is why it pays to be clear about velocity versus speed<\/a> before you start.<\/p>\n\n\n \n <\/path><\/marker>\n <\/defs>\n <\/rect>\n Total momentum before = total momentum after<\/text>\n BEFORE<\/text>\n <\/line>\n <\/rect>\n m\u2081 = 2 kg<\/text>\n <\/line>\n u\u2081 = 3 m\/s<\/text>\n <\/rect>\n m\u2082 = 1 kg<\/text>\n u\u2082 = 0<\/text>\n total p = (2)(3) + (1)(0) = 6 kg\u00b7m\/s<\/tspan><\/text>\n <\/line>\n AFTER<\/text>\n <\/line>\n <\/rect>\n m\u2081 = 2 kg<\/text>\n <\/line>\n v\u2081 = 1 m\/s<\/text>\n <\/rect>\n m\u2082 = 1 kg<\/text>\n <\/line>\n v\u2082 = 4 m\/s<\/text>\n total p = (2)(1) + (1)(4) = 6 kg\u00b7m\/s<\/tspan><\/text>\n<\/svg>\n

The carts trade velocity in the collision, yet the total momentum (6 kg\u00b7m\/s) is identical before and after.<\/p>\n\n

The Conservation of Momentum Formula<\/h2>\n\n

For two objects colliding in a straight line, the law is written as a single, balanced equation. Initial velocities use u<\/em>; final velocities use v<\/em>.<\/p>\n\n

m\u2081u\u2081 + m\u2082u\u2082 = m\u2081v\u2081 + m\u2082v\u2082<\/div>\n\n

Every term is built from one simpler quantity \u2014 the momentum of a single object:<\/p>\n\n

p = m\u00b7v<\/div>\n\n

Here is what each symbol means, with its SI unit:<\/p>\n\n