content(warnings): Add W12-W16, N5-N6 — rolling, pendulum, and inertia enhancements

concepts/mechanics/u5/m5-4-moment-of-inertia.tex

@@ -32,6 +32,8 @@ I=I_{\mathrm{cm}}+Md^2.
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 Therefore moment of inertia depends on the chosen axis as well as on the mass distribution. Moving the axis farther from the center of mass increases $I$.}
 
+\nt{The parallel-axis theorem relates the moment of inertia about any axis to the moment of inertia about a parallel axis through the center of mass: $I_{\mathrm{any}}=I_{\mathrm{cm}}+Md^2$, where $d$ is the perpendicular distance between the axes. This is useful for computing $I$ about arbitrary pivot points. The perpendicular-axis theorem ($I_z=I_x+I_y$) applies only to flat planar objects and relates the moment of inertia about an axis perpendicular to the plane to the moments of inertia about two orthogonal in-plane axes.}
+
 \ex{Illustrative example}{A light turntable carries two small clay balls, each of mass $m=0.40\,\mathrm{kg}$. In arrangement A, each ball is at distance $r_A=0.10\,\mathrm{m}$ from the axis. In arrangement B, each ball is at distance $r_B=0.20\,\mathrm{m}$ from the axis.
 
 For arrangement A,