---
title: "A rigid disk rotates about a fixed axis through its center. Its angular position as a function of time \\(t\\) is given by \\(\\theta(t) = at^3 – bt^4\\), where \\(a\\) and \\(b\\) are positive constants, \\(\\theta\\) is in radians, and \\(t\\) is in seconds. Which of the following correctly pairs the non-zero time \\(t\\) at which the angular acceleration of the disk is zero with the direction of rotation of the disk at that instant?"
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url: "https://nerd-notes.com/ubq/117582/"
date_modified: "2026-08-04T07:49:12+00:00"
---

# A rigid disk rotates about a fixed axis through its center. Its angular position as a function of time \(t\) is given by \(\theta(t) = at^3 – bt^4\), where \(a\) and \(b\) are positive constants, \(\theta\) is in radians, and \(t\) is in seconds. Which of the following correctly pairs the non-zero time \(t\) at which the angular acceleration of the disk is zero with the direction of rotation of the disk at that instant?

A rigid disk rotates about a fixed axis through its center. Its angular position as a function of time \(t\) is given by \(\theta(t) = at^3 - bt^4\), where \(a\) and \(b\) are positive constants, \(\theta\) is in radians, and \(t\) is in seconds. Which of the following correctly pairs the non-zero time \(t\) at which the angular acceleration of the disk is zero with the direction of rotation of the disk at that instant?

- **A.** Time: \(t = \dfrac{3a}{4b}\) | Direction: Counterclockwise (\(\omega > 0\))
- **B.** Time: \(t = \dfrac{3a}{4b}\) | Direction: Clockwise (\(\omega < 0\))
- **C.** Time: \(t = \dfrac{a}{2b}\) | Direction: Clockwise (\(\omega < 0\))
- **D.** Time: \(t = \dfrac{a}{2b}\) | Direction: Counterclockwise (\(\omega > 0\))

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117582/*