---
title: "A uniform solid disk with rotational inertia \\(I\\) rotates about a fixed frictionless axle through its center. The disk has an initial angular velocity \\(\\omega_0\\) at time \\(t = 0\\) and is subjected to a retarding drag torque \\(\\tau = -b\\omega\\), where \\(b\\) is a positive constant and \\(\\omega\\) is the instantaneous angular velocity. Which of the following expressions represents the total number of revolutions the disk completes before coming to rest?"
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url: "https://nerd-notes.com/ubq/117681/"
date_modified: "2026-08-04T07:50:16+00:00"
---

# A uniform solid disk with rotational inertia \(I\) rotates about a fixed frictionless axle through its center. The disk has an initial angular velocity \(\omega_0\) at time \(t = 0\) and is subjected to a retarding drag torque \(\tau = -b\omega\), where \(b\) is a positive constant and \(\omega\) is the instantaneous angular velocity. Which of the following expressions represents the total number of revolutions the disk completes before coming to rest?

A uniform solid disk with rotational inertia \(I\) rotates about a fixed frictionless axle through its center. The disk has an initial angular velocity \(\omega_0\) at time \(t = 0\) and is subjected to a retarding drag torque \(\tau = -b\omega\), where \(b\) is a positive constant and \(\omega\) is the instantaneous angular velocity. Which of the following expressions represents the total number of revolutions the disk completes before coming to rest?

![A flat circular disk viewed at a three-quarter tilt. A vertical dashed line passes through the center of the disk along the rotational z-axis. A counterclockwise curved arrow above the disk is labeled with angular velocity \(\omega_0\). A clockwise curved arrow near the outer edge indicates a drag torque labeled \(\tau = -b\omega\). The disk is labeled with rotational inertia \(I\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829816-3AHxQm.jpg)

- **A.** \(\dfrac{I\omega_0}{8\pi b}\)
- **B.** \(\dfrac{I\omega_0}{4\pi b}\)
- **C.** \(\dfrac{I\omega_0}{2\pi b}\)
- **D.** \(\dfrac{I\omega_0}{\pi b}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117681/*