4.2 Conservation of Momentum in Isolated Systems

Apply system-level momentum conservation and distinguish internal versus external forces.

Estimated time: 22 minutes

Statement of the Law

When the net external force on a system is zero, total momentum of that system remains constant. This rule is independent of whether interacting bodies stick, bounce, deform, or break apart. What changes is kinetic-energy behavior, not total momentum.

$\sum \vec{p}_{\text{before}} = \sum \vec{p}_{\text{after}}$

Apply vector conservation to the whole chosen system.

Choosing the Correct System Boundary

The same physical event may appear to violate conservation if the system is chosen too narrowly. A falling ball alone does not conserve momentum because gravity is external to that system. A ball-plus-Earth system does conserve total momentum, with Earth receiving a tiny opposite momentum change.

In table-top collisions, weight and normal often cancel vertically, leaving negligible net external horizontal force. Under those conditions, horizontal momentum conservation is an excellent model for impact problems.

Conservation with Mass Flow

For rockets, momentum conservation is applied to the rocket-plus-exhaust system over short intervals. Ejected propellant carries momentum in one direction while the rocket gains momentum in the other. The core idea remains unchanged: account for all relevant masses in the system model.

Test Yourself

Which condition is required to apply momentum conservation directly to a chosen system?

4.1 Newton's Second Law in Momentum Form and Impulse

4.3 Collision Models: Elastic, Inelastic, and Total Inelastic