---
title: "A uniform disk is initially at rest and begins to rotate about its center with a constant angular acceleration \\(\\alpha\\). Let \\(a_t\\) be the magnitude of the tangential acceleration and \\(a_c\\) be the magnitude of the centripetal acceleration of a point on the outer rim of the disk. At time \\(t = T\\), the magnitudes of these two accelerations are equal, such that \\(a_c = a_t\\). At time \\(t = 2T\\), what is the ratio \\(\\dfrac{a_c}{a_t}\\) for the same point on the rim?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/109565/"
date_modified: "2026-03-25T07:03:52+00:00"
---

# A uniform disk is initially at rest and begins to rotate about its center with a constant angular acceleration \(\alpha\). Let \(a_t\) be the magnitude of the tangential acceleration and \(a_c\) be the magnitude of the centripetal acceleration of a point on the outer rim of the disk. At time \(t = T\), the magnitudes of these two accelerations are equal, such that \(a_c = a_t\). At time \(t = 2T\), what is the ratio \(\dfrac{a_c}{a_t}\) for the same point on the rim?

A uniform disk is initially at rest and begins to rotate about its center with a constant angular acceleration \(\alpha\). Let \(a_t\) be the magnitude of the tangential acceleration and \(a_c\) be the magnitude of the centripetal acceleration of a point on the outer rim of the disk. At time \(t = T\), the magnitudes of these two accelerations are equal, such that \(a_c = a_t\). At time \(t = 2T\), what is the ratio \(\dfrac{a_c}{a_t}\) for the same point on the rim?

![A top-down view of a circular disk of radius R. A point P is marked on the outer rim. An arrow labeled alpha indicates a counterclockwise angular acceleration around the center axis.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774422232-gWaamL.jpg)

- **A.** \(1\)
- **B.** \(2\)
- **C.** \(4\)
- **D.** \(8\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109565/*