---
title: "A disk of radius \\(R\\) rotates about a fixed axis through its center. The angular speed of the disk as a function of time \\(t\\) is given by \\(\\omega(t) = bt^2\\), where \\(b\\) is a positive constant. At what time \\(t > 0\\) does a point on the rim of the disk experience tangential and radial accelerations of equal magnitude?"
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url: "https://nerd-notes.com/ubq/117558/"
date_modified: "2026-08-04T07:49:04+00:00"
---

# A disk of radius \(R\) rotates about a fixed axis through its center. The angular speed of the disk as a function of time \(t\) is given by \(\omega(t) = bt^2\), where \(b\) is a positive constant. At what time \(t > 0\) does a point on the rim of the disk experience tangential and radial accelerations of equal magnitude?

A disk of radius \(R\) rotates about a fixed axis through its center. The angular speed of the disk as a function of time \(t\) is given by \(\omega(t) = bt^2\), where \(b\) is a positive constant. At what time \(t > 0\) does a point on the rim of the disk experience tangential and radial accelerations of equal magnitude?

- **A.** \(\left(\dfrac{1}{b}\right)^{1/3}\)
- **B.** \(\left(\dfrac{1}{2b}\right)^{1/3}\)
- **C.** \(\left(\dfrac{2}{bR}\right)^{1/3}\)
- **D.** \(\left(\dfrac{2}{b}\right)^{1/3}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117558/*