Question
A thin rod has mass M and length L. Its perpendicular rotation axis crosses the rod one-third of the length from one end, leaving segments L/3 and 2L/3. Determine its moment of inertia using direct integration, and independently verify the result using the parallel-axis theorem.
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Evidence boundary
This is a worked solution of OpenStax University Physics Volume 1, Chapter 10, Problem 70. The axis geometry is preserved in words from the source figure. The calculation explicitly uses the section’s standard uniform thin-rod model; the problem supplies no nonuniform density. The answer is independently derived, not attributed to an official solution key.