---
title: "Two identical uniform rods, each of mass \\(M\\) and length \\(L\\), are used to construct two rotating systems. In System 1, two small spheres, each of mass \\(m = M/6\\), are attached to the opposite ends of the rod. In System 2, the same two spheres are attached to the center of the rod. Both systems are rotated about an axis through the center of the rod and perpendicular to its length. What is the ratio \\(I_1 / I_2\\) of the rotational inertia of System 1 to the rotational inertia of System 2?"
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url: "https://nerd-notes.com/ubq/111287/"
date_modified: "2026-04-10T01:21:06+00:00"
---

# Two identical uniform rods, each of mass \(M\) and length \(L\), are used to construct two rotating systems. In System 1, two small spheres, each of mass \(m = M/6\), are attached to the opposite ends of the rod. In System 2, the same two spheres are attached to the center of the rod. Both systems are rotated about an axis through the center of the rod and perpendicular to its length. What is the ratio \(I_1 / I_2\) of the rotational inertia of System 1 to the rotational inertia of System 2?

Two identical uniform rods, each of mass \(M\) and length \(L\), are used to construct two rotating systems. In System 1, two small spheres, each of mass \(m = M/6\), are attached to the opposite ends of the rod. In System 2, the same two spheres are attached to the center of the rod. Both systems are rotated about an axis through the center of the rod and perpendicular to its length. What is the ratio \(I_1 / I_2\) of the rotational inertia of System 1 to the rotational inertia of System 2?

![Two diagrams labeled System 1 and System 2. System 1 shows a horizontal rod of length L with a vertical axis of rotation through its center. Two small circles representing masses m are at the very ends of the rod, each at a distance L/2 from the axis. System 2 shows the same horizontal rod and axis, but the two small circles are placed directly at the center axis.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775784065-3PHlqP.jpg)

- **A.** \(1\)
- **B.** \(2\)
- **C.** \(3\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111287/*