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

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2026-05-04 23:44:35 -05:00
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commit a1c4ab93c0
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@@ -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.