---
title: "A disk rotates about a fixed axis through its center. Starting from rest at time \\(t = 0\\), its angular acceleration as a function of time is given by \\(\\alpha(t) = bt – ct^2\\), where \\(b\\) and \\(c\\) are positive constants. Which of the following expressions represents the maximum angular velocity achieved by the disk?"
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url: "https://nerd-notes.com/ubq/117552/"
date_modified: "2026-08-04T07:49:01+00:00"
---

# A disk rotates about a fixed axis through its center. Starting from rest at time \(t = 0\), its angular acceleration as a function of time is given by \(\alpha(t) = bt – ct^2\), where \(b\) and \(c\) are positive constants. Which of the following expressions represents the maximum angular velocity achieved by the disk?

A disk rotates about a fixed axis through its center. Starting from rest at time \(t = 0\), its angular acceleration as a function of time is given by \(\alpha(t) = bt - ct^2\), where \(b\) and \(c\) are positive constants. Which of the following expressions represents the maximum angular velocity achieved by the disk?

- **A.** \(\dfrac{b^3}{6c^2}\)
- **B.** \(\dfrac{b^3}{3c^2}\)
- **C.** \(\dfrac{b^3}{2c^2}\)
- **D.** \(\dfrac{2b^3}{3c^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117552/*