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title: "Two identical uniform thin rods, each of mass \\(M\\) and length \\(L\\), are held horizontally and released from rest. Rod 1 is pivoted about a frictionless horizontal axis passing through its center of mass, and a small point mass of mass \\(M\\) is attached to one of its ends. Rod 2 is pivoted about a frictionless horizontal axis passing through one of its ends, and an identical point mass of mass \\(M\\) is attached to its opposite, free end. Immediately after release, what is the ratio of the angular acceleration of Rod 1 to the angular acceleration of Rod 2, \\(\\dfrac{\\alpha_1}{\\alpha_2}\\)?"
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url: "https://nerd-notes.com/ubq/120850/"
date_modified: "2026-08-23T04:43:37+00:00"
---

# Two identical uniform thin rods, each of mass \(M\) and length \(L\), are held horizontally and released from rest. Rod 1 is pivoted about a frictionless horizontal axis passing through its center of mass, and a small point mass of mass \(M\) is attached to one of its ends. Rod 2 is pivoted about a frictionless horizontal axis passing through one of its ends, and an identical point mass of mass \(M\) is attached to its opposite, free end. Immediately after release, what is the ratio of the angular acceleration of Rod 1 to the angular acceleration of Rod 2, \(\dfrac{\alpha_1}{\alpha_2}\)?

Two identical uniform thin rods, each of mass \(M\) and length \(L\), are held horizontally and released from rest. Rod 1 is pivoted about a frictionless horizontal axis passing through its center of mass, and a small point mass of mass \(M\) is attached to one of its ends. Rod 2 is pivoted about a frictionless horizontal axis passing through one of its ends, and an identical point mass of mass \(M\) is attached to its opposite, free end. Immediately after release, what is the ratio of the angular acceleration of Rod 1 to the angular acceleration of Rod 2, \(\dfrac{\alpha_1}{\alpha_2}\)?

![A grayscale schematic showing two horizontal rods viewed from the side, positioned one above the other. The upper rod, labeled Rod 1, has uniform length \(L\) and mass \(M\); a triangular pivot support and small circular axle are located exactly at its center, and a filled circle labeled \(M\) is attached at its right end. The lower rod, labeled Rod 2, has uniform length \(L\) and mass \(M\); a triangular pivot support and small circular axle are located at its left end, and an identical filled circle labeled \(M\) is attached at its right end. A horizontal dashed line with dimension arrows marks the length \(L\) for each rod. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460217-RKu2i0.jpg)

- **A.** \(\dfrac{4}{3}\)
- **B.** \(\dfrac{3}{2}\)
- **C.** \(\dfrac{16}{9}\)
- **D.** \(2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120850/*