Momentum · 03 / 04

Conservation of Momentum

Internal interactions can redistribute momentum between objects, but the total momentum of an isolated system remains unchanged.

The learner question

How can both objects change momentum while the system total stays fixed?

Internal forces come in equal-and-opposite interaction pairs, so the impulses exchanged inside the system cancel in the total accounting.

System statement

\sum \vec p_{before} = \sum \vec p_{after}

This requires negligible external impulse during the interaction.

Internal-exchange lab

Object A

before p

8.0

after p

4.0

after velocity 2.00 m/s

Object B

before p

-3.0

after p

1.0

after velocity 0.33 m/s

internal impulse on A-4.0 N·s

internal impulse on B4.0 N·s

system before

5.0 kg·m/s

system after

5.0 kg·m/s

mA2.0 kg

vA4.0 m/s

mB3.0 kg

vB-1.0 m/s

internal J on A-4.0 N·s

Individual momentum can change

Each object experiences an internal impulse, so neither object's momentum is generally conserved by itself.

Internal impulses cancel

The impulse on A is equal and opposite to the impulse on B. Added together, their contribution to system Δp is zero.

External impulse changes the total

If an outside force delivers a significant impulse, include it: system momentum changes by that external impulse.

Transfer check