---
title: "A thin circular disc rotates in a horizontal plane about a fixed central axis with a constant angular speed \\(\\omega\\). Point \\(X\\) is located at a radial distance \\(r\\) from the axis of rotation, where its tangential speed is \\(v_X\\) and the magnitude of its centripetal acceleration is \\(a_{c,X}\\). Point \\(Y\\) is located on the disc at a radial distance \\(2r\\) from the axis of rotation.  Which row in the table correctly compares the tangential speed \\(v_Y\\) and centripetal acceleration \\(a_{c,Y}\\) of Point \\(Y\\) to those of Point \\(X\\)?"
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url: "https://nerd-notes.com/ubq/120776/"
date_modified: "2026-08-23T04:43:18+00:00"
---

# A thin circular disc rotates in a horizontal plane about a fixed central axis with a constant angular speed \(\omega\). Point \(X\) is located at a radial distance \(r\) from the axis of rotation, where its tangential speed is \(v_X\) and the magnitude of its centripetal acceleration is \(a_{c,X}\). Point \(Y\) is located on the disc at a radial distance \(2r\) from the axis of rotation.

Which row in the table correctly compares the tangential speed \(v_Y\) and centripetal acceleration \(a_{c,Y}\) of Point \(Y\) to those of Point \(X\)?

A thin circular disc rotates in a horizontal plane about a fixed central axis with a constant angular speed \(\omega\). Point \(X\) is located at a radial distance \(r\) from the axis of rotation, where its tangential speed is \(v_X\) and the magnitude of its centripetal acceleration is \(a_{c,X}\). Point \(Y\) is located on the disc at a radial distance \(2r\) from the axis of rotation.

Which row in the table correctly compares the tangential speed \(v_Y\) and centripetal acceleration \(a_{c,Y}\) of Point \(Y\) to those of Point \(X\)?

![A circle representing a rotating disc viewed from above. A central dot marks the fixed axis of rotation with a curved arrow labeled \(\omega\) indicating counterclockwise rotation. A horizontal dashed radial line extends from the center to the right edge. Point \(X\) is marked as a solid dot on the line at a distance labeled \(r\) from the center. Point \(Y\) is marked as a solid dot farther along the same line at a distance labeled \(2r\) from the center. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460197-v4wQtW.jpg)

- **A.** | Tangential Speed \(v_Y\) | Centripetal Acceleration \(a_{c,Y}\) | |---|---| | \(v_X\) | \(a_{c,X}\) |
- **B.** | Tangential Speed \(v_Y\) | Centripetal Acceleration \(a_{c,Y}\) | |---|---| | \(2v_X\) | \(\dfrac{1}{2}a_{c,X}\) |
- **C.** | Tangential Speed \(v_Y\) | Centripetal Acceleration \(a_{c,Y}\) | |---|---| | \(2v_X\) | \(4a_{c,X}\) |
- **D.** | Tangential Speed \(v_Y\) | Centripetal Acceleration \(a_{c,Y}\) | |---|---| | \(2v_X\) | \(2a_{c,X}\) |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120776/*