---
title: "A laboratory setup uses a thin uniform rod of mass \\(M\\) and length \\(L\\). When the rod is rotated about an axis perpendicular to the rod and passing through its center of mass, its moment of inertia is \\(I_0\\). The pivot point is then moved to a position midway between the center of mass and one end of the rod. In terms of \\(I_0\\), what is the moment of inertia of the rod about this new axis?"
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url: "https://nerd-notes.com/ubq/109960/"
date_modified: "2026-03-31T09:09:39+00:00"
---

# A laboratory setup uses a thin uniform rod of mass \(M\) and length \(L\). When the rod is rotated about an axis perpendicular to the rod and passing through its center of mass, its moment of inertia is \(I_0\). The pivot point is then moved to a position midway between the center of mass and one end of the rod. In terms of \(I_0\), what is the moment of inertia of the rod about this new axis?

A laboratory setup uses a thin uniform rod of mass \(M\) and length \(L\). When the rod is rotated about an axis perpendicular to the rod and passing through its center of mass, its moment of inertia is \(I_0\). The pivot point is then moved to a position midway between the center of mass and one end of the rod. In terms of \(I_0\), what is the moment of inertia of the rod about this new axis?

![A horizontal uniform thin rod of length L. A dot at the center is labeled 'CM'. A vertical dashed line passes through the CM, representing the initial axis. A second vertical dashed line is drawn parallel to the first, located at a distance L/4 to the right of the CM. A horizontal dimension line below the rod shows the total length L. A small horizontal arrow indicates the distance L/4 between the two dashed lines.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/ubq-frq-generatedstem-fig-1-1774948179-IInGOg.jpg)

- **A.** \(\dfrac{3}{4} I_0\)
- **B.** \(\dfrac{5}{4} I_0\)
- **C.** \(\dfrac{7}{4} I_0\)
- **D.** \(4 I_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109960/*