Conservation of Momentum

Objective: Explain the concepts and assumptions used in conservation of momentum.

Linear momentum is the vector p=mv in classical mechanics. Add signed or vector components for a multi-object system. The total momentum is conserved over an interval if net external impulse is negligible; internal third-law forces transfer momentum between objects. Momentum and kinetic energy are different quantities and need not share the same conservation condition. State the system before applying the law; a single colliding cart usually receives an external impulse from the other cart if considered alone.

Objective: Apply conservation of momentum to calculations, evidence, and specified situations.

For the application problems, define the system and list the quantities supplied before choosing a relation. Use p=mv; p_initial=p_final when net external impulse≈0. The relation must match the stated conditions. Convert to compatible units before substitution, preserve intermediate precision, and report the requested quantity with its unit or sign. When comparing alternatives, check the defining condition rather than a superficial word match. The worked examples below show the setup and calculation separately.