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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@@ -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,