\section{Linear Momentum and Collisions}

This unit develops the momentum viewpoint for interactions between objects and systems. We begin by defining linear momentum $\vec{p}$ for a particle and total momentum $\vec{P}$ for a system, using consistent vector notation and emphasizing that momentum conservation is applied componentwise in both one and two dimensions.

We then connect external forces to momentum transfer through impulse $\vec{J}$, use isolated-system reasoning to establish conservation of momentum, and apply those ideas to collisions, recoil, and explosions. Throughout, the AP focus is on classifying collisions correctly, recognizing that kinetic energy is not always conserved, and relating system motion to the center-of-mass velocity $\vec{v}_{\mathrm{cm}}$ when helpful.

\input{concepts/mechanics/u4/m4-1-linear-momentum.tex}

\input{concepts/mechanics/u4/m4-2-impulse.tex}

\input{concepts/mechanics/u4/m4-3-momentum-conservation.tex}

\input{concepts/mechanics/u4/m4-4-collisions.tex}

\input{concepts/mechanics/u4/m4-5-recoil-explosions.tex}