content(warnings): Add W8-W11, X4-X5 — collision, inertia, and torque cross-refs

concepts/mechanics/u5/m5-3-torque.tex

@@ -30,6 +30,8 @@ For rotation about a chosen fixed axis with unit vector $\hat{k}$,
 \]
 so the scalar $\tau$ is positive or negative according to the declared sign convention.}
 
+Torque about a fixed axis connects directly to angular acceleration through Newton's second law for rotation (Section 5.6), just as net force connects to linear acceleration through Newton's second law (Section 2.1).
+
 \pf{Why $rF\sin\phi$ equals $F\ell$}{From the cross-product magnitude formula,
 \[
 |\vec{\tau}|=|\vec{r}\times \vec{F}|=rF\sin\phi.

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

@@ -16,6 +16,8 @@ I=mr_\perp^2.
 \]
 The SI unit of moment of inertia is $\mathrm{kg\cdot m^2}$. Because the distance to the axis is squared, mass farther from the axis contributes much more strongly to $I$.}
 
+\wc{Moment of inertia does not depend on speed or rotation}{The moment of inertia $I$ is a geometric property of the mass distribution about an axis. It depends only on the object's mass, shape, and axis position --- \emph{not} on angular velocity, angular acceleration, or torque. A spinning top and a stationary top have the same $I$.}
+
 \thm{Key fixed-axis relations and axis dependence}{Consider a rigid body rotating about a fixed axis with unit vector $\hat{k}$. Let $\vec{\alpha}=\alpha\hat{k}$ denote its angular acceleration, let $\vec{\tau}_{\mathrm{net}}=\tau_{\mathrm{net}}\hat{k}$ denote the net external torque about that axis, and let $I$ denote the moment of inertia about that same axis. Then
 \[
 \tau_{\mathrm{net}}=I\alpha,

concepts/mechanics/u5/m5-6-rotation-dynamics.tex

@@ -13,6 +13,8 @@ The net torque about the axis is the sum of the signed torques:
 
 Let $I$ denote the moment of inertia of the body about that same axis, and let $\alpha$ denote the signed angular acceleration. The quantity $I$ measures the rotational inertia of the body: for the same net torque, a larger $I$ gives a smaller $\alpha$. Thus $I$ plays the rotational role that mass plays in translational motion.}
 
+\wc{Heavier objects do not fall faster (in vacuum)}{In the absence of air resistance, all objects fall with the same acceleration $g$, regardless of mass. The gravitational force is larger on a heavier object ($F_g=mg$), but so is the object's inertia ($F=ma$), and the $m$ cancels: $a=g$. Air resistance is what makes feathers fall slower in real life.}
+
 \thm{Newton's second law for fixed-axis rotation}{Consider a rigid body rotating about a fixed axis with unit vector $\hat{k}$. Let $I$ denote the moment of inertia about that axis, let $\alpha$ denote the signed angular acceleration, and let $\sum \tau$ denote the net external torque about the axis using the declared sign convention. Then
 \[
 \sum \tau = I\alpha.