content(warnings): Add W8-W11, X4-X5 — collision, inertia, and torque cross-refs
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@@ -27,6 +27,12 @@ A collision is \emph{perfectly inelastic} if the objects stick together after th
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Every perfectly inelastic collision is inelastic.}
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\wc{Momentum is conserved in every collision type}{Total momentum of an isolated system is conserved in elastic, inelastic, \emph{and} perfectly inelastic collisions. The word ``elastic'' only tells you whether kinetic energy is also conserved. A common exam error is to drop the momentum equation for inelastic collisions --- \emph{never} do this.}
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\wc{``Momentum is lost'' in a collision}{Momentum of the \emph{system} is never lost in any isolated collision. What is ``lost'' in an inelastic collision is \emph{kinetic energy}, which is converted to thermal energy, sound, deformation, etc. Momentum conservation holds regardless of how ``bouncy'' the collision is.}
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Collisions connect momentum conservation (Unit 4) with energy conservation (Unit 3): elastic collisions conserve both, inelastic conserve only momentum. See also the coefficient of restitution in Section 4.5 for explosive separation.
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\nt{Do not decide whether momentum is conserved by asking whether the collision is elastic. Those are different ideas. Momentum conservation depends on the net external impulse on the chosen system. If the system is isolated during the collision, then total momentum is conserved for elastic, inelastic, and perfectly inelastic collisions alike. Kinetic energy supplies an \emph{extra} condition only in the elastic case. In two-dimensional AP problems, conserve momentum separately in the $x$- and $y$-directions.}
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\ex{Illustrative example}{On a frictionless track, cart 1 has mass $m_1=0.40\,\mathrm{kg}$ and initial velocity
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