---
title: "A thick hollow cylinder of length \\(L\\), inner radius \\(R\\), and outer radius \\(2R\\) rotates about its central axis with a constant angular speed \\(\\omega\\). The cylinder has a non-uniform volume mass density given by \\(\\rho(r) = \\dfrac{c}{r^2}\\), where \\(r\\) is the radial distance from the central axis and \\(c\\) is a positive constant. Which of the following expressions represents the rotational kinetic energy of the cylinder?"
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url: "https://nerd-notes.com/ubq/117604/"
date_modified: "2026-08-04T07:49:17+00:00"
---

# A thick hollow cylinder of length \(L\), inner radius \(R\), and outer radius \(2R\) rotates about its central axis with a constant angular speed \(\omega\). The cylinder has a non-uniform volume mass density given by \(\rho(r) = \dfrac{c}{r^2}\), where \(r\) is the radial distance from the central axis and \(c\) is a positive constant. Which of the following expressions represents the rotational kinetic energy of the cylinder?

A thick hollow cylinder of length \(L\), inner radius \(R\), and outer radius \(2R\) rotates about its central axis with a constant angular speed \(\omega\). The cylinder has a non-uniform volume mass density given by \(\rho(r) = \dfrac{c}{r^2}\), where \(r\) is the radial distance from the central axis and \(c\) is a positive constant. Which of the following expressions represents the rotational kinetic energy of the cylinder?

![A 3D perspective diagram of a thick hollow cylinder of length L oriented along a central longitudinal dashed axis z. The cylinder has an inner circular radius labeled R and an outer circular radius labeled 2R. A curved rotational arrow near the top indicates rotation about the z-axis with angular velocity \omega. Cross-hatching on the annular face illustrates the thick cylindrical wall. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829757-GTajNc.jpg)

- **A.** \(\dfrac{3}{4}\pi c L R^2 \omega^2\)
- **B.** \(\pi c L R^2 \omega^2\)
- **C.** \(\dfrac{3}{2}\pi c L R^2 \omega^2\)
- **D.** \(3\pi c L R^2 \omega^2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117604/*