Conservation of Momentum
Total momentum of an isolated system stays constant.
Formula
Variables
Example
When two skaters push apart, their momenta are equal and opposite — total stays zero.
How it works
Momentum is the quantity of motion in a system, defined as mass times velocity, and in an isolated system the total before an interaction must equal the total after it. This happens because the forces during the interaction come in equal-and-opposite pairs, so the system’s internal pushes and pulls cannot change the total momentum. In practice, momentum can be redistributed among objects, but without a net external impulse the sum stays the same.
When to use it
Use this when objects collide, explode apart, or push off each other, especially if external forces are negligible over the interaction time. It is also useful for recoil, rocket motion, and two-body collision problems in mechanics.
Worked example, step by step
A 2.0 kg cart moves east at 3.0 m/s and collides with a 1.0 kg cart initially at rest. After the collision, the 2.0 kg cart slows to 1.0 m/s east. Find the final velocity of the 1.0 kg cart. Initial total momentum: p_i = (2.0)(3.0) + (1.0)(0) = 6.0 kg·m/s east Final total momentum: p_f = (2.0)(1.0) + (1.0)(v_f) Set initial equal to final: 6.0 = 2.0 + v_f Solve: v_f = 4.0 m/s east Final answer: the 1.0 kg cart moves east at 4.0 m/s
Common mistakes to avoid
- Forgetting momentum is a vector and mixing up directions
- Using conservation when an external force like friction is significant
- Adding velocities instead of adding mass times velocity for each object
Did You Know?
Total momentum before and after any collision is identical — even in a chaotic multi-car pileup.
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More in Physics Laws & Theorems
View allNewton's First Law (Inertia)
BasicAn object stays at rest or in uniform motion unless acted on by a net force.
Newton's Second Law
BasicNet force equals mass times acceleration (rate of change of momentum).
Newton's Third Law
BasicFor every action there is an equal and opposite reaction.
Conservation of Energy
BasicEnergy cannot be created or destroyed, only transformed.
Archimedes' Principle
IntermediateBuoyant force equals the weight of fluid displaced.
Pascal's Law
IntermediatePressure applied to a confined fluid transmits equally in all directions.