---
title: "A circular disk rotates about a fixed axis through its center and slows down with a constant angular acceleration of magnitude \\(\\alpha\\). Point 1 and Point 2 are located at radial distances \\(R\\) and \\(2R\\) from the axis, respectively, such that Point 2 traverses twice the linear path length of Point 1 as the disk comes to rest. At the instant when the radial acceleration of Point 1 is equal in magnitude to its tangential acceleration, what is the ratio of the magnitude of the net linear acceleration of Point 2 to that of Point 1, \\(\\dfrac{a_2}{a_1}\\)?"
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url: "https://nerd-notes.com/ubq/124422/"
date_modified: "2026-09-28T14:05:18+00:00"
---

# A circular disk rotates about a fixed axis through its center and slows down with a constant angular acceleration of magnitude \(\alpha\). Point 1 and Point 2 are located at radial distances \(R\) and \(2R\) from the axis, respectively, such that Point 2 traverses twice the linear path length of Point 1 as the disk comes to rest. At the instant when the radial acceleration of Point 1 is equal in magnitude to its tangential acceleration, what is the ratio of the magnitude of the net linear acceleration of Point 2 to that of Point 1, \(\dfrac{a_2}{a_1}\)?

A circular disk rotates about a fixed axis through its center and slows down with a constant angular acceleration of magnitude \(\alpha\). Point 1 and Point 2 are located at radial distances \(R\) and \(2R\) from the axis, respectively, such that Point 2 traverses twice the linear path length of Point 1 as the disk comes to rest. At the instant when the radial acceleration of Point 1 is equal in magnitude to its tangential acceleration, what is the ratio of the magnitude of the net linear acceleration of Point 2 to that of Point 1, \(\dfrac{a_2}{a_1}\)?

![A top-down view of a circular disk of radius 2R centered on a fixed central axis marked with a small black dot. A horizontal dashed line segment extends from the center dot to the right edge of the disk. On this dashed line, Point 1 is indicated by a filled black dot at distance R from the center, labeled 1. Point 2 is indicated by a filled black dot at distance 2R from the center on the outer boundary, labeled 2. A curved counterclockwise arrow labeled \omega indicates the direction of rotation. A curved clockwise arrow labeled \alpha indicates the angular deceleration opposing the rotation. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604318-eT5aqt.jpg)

- **A.** \(1\)
- **B.** \(\sqrt{2}\)
- **C.** \(2\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124422/*