---
title: "A heavy flywheel rotates about a fixed axis. Due to fluid friction, the flywheel experiences an angular acceleration given by \\(\\alpha = -k \\omega^{3/2}\\), where \\(k\\) is a positive constant and \\(\\omega\\) is its instantaneous angular velocity. At time \\(t = 0\\), the flywheel has an initial angular velocity \\(\\omega_0\\). Which of the following expressions represents the time \\(t\\) required for the flywheel’s angular velocity to decrease to \\(\\dfrac{\\omega_0}{4}\\)?"
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url: "https://nerd-notes.com/ubq/117608/"
date_modified: "2026-08-04T07:49:18+00:00"
---

# A heavy flywheel rotates about a fixed axis. Due to fluid friction, the flywheel experiences an angular acceleration given by \(\alpha = -k \omega^{3/2}\), where \(k\) is a positive constant and \(\omega\) is its instantaneous angular velocity. At time \(t = 0\), the flywheel has an initial angular velocity \(\omega_0\). Which of the following expressions represents the time \(t\) required for the flywheel’s angular velocity to decrease to \(\dfrac{\omega_0}{4}\)?

A heavy flywheel rotates about a fixed axis. Due to fluid friction, the flywheel experiences an angular acceleration given by \(\alpha = -k \omega^{3/2}\), where \(k\) is a positive constant and \(\omega\) is its instantaneous angular velocity. At time \(t = 0\), the flywheel has an initial angular velocity \(\omega_0\). Which of the following expressions represents the time \(t\) required for the flywheel's angular velocity to decrease to \(\dfrac{\omega_0}{4}\)?

- **A.** \(\dfrac{1}{2k\sqrt{\omega_0}}\)
- **B.** \(\dfrac{1}{k\sqrt{\omega_0}}\)
- **C.** \(\dfrac{3}{2k\sqrt{\omega_0}}\)
- **D.** \(\dfrac{2}{k\sqrt{\omega_0}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117608/*