---
title: "An energy storage system uses a uniform solid cylindrical flywheel of mass \\(M\\) and radius \\(R\\) rotating about its central symmetry axis with angular speed \\(\\omega\\). An engineer considers replacing it with a thin-walled hollow cylindrical shell of the same mass \\(M\\) and radius \\(R\\), rotating at the same angular speed \\(\\omega\\) about its central symmetry axis. What is the ratio of the rotational kinetic energy of the solid cylindrical flywheel to the rotational kinetic energy of the thin-walled cylindrical shell, \\(\\dfrac{K_{\\text{solid}}}{K_{\\text{shell}}}\\)?"
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url: "https://nerd-notes.com/ubq/120872/"
date_modified: "2026-08-23T04:43:56+00:00"
---

# An energy storage system uses a uniform solid cylindrical flywheel of mass \(M\) and radius \(R\) rotating about its central symmetry axis with angular speed \(\omega\). An engineer considers replacing it with a thin-walled hollow cylindrical shell of the same mass \(M\) and radius \(R\), rotating at the same angular speed \(\omega\) about its central symmetry axis. What is the ratio of the rotational kinetic energy of the solid cylindrical flywheel to the rotational kinetic energy of the thin-walled cylindrical shell, \(\dfrac{K_{\text{solid}}}{K_{\text{shell}}}\)?

An energy storage system uses a uniform solid cylindrical flywheel of mass \(M\) and radius \(R\) rotating about its central symmetry axis with angular speed \(\omega\). An engineer considers replacing it with a thin-walled hollow cylindrical shell of the same mass \(M\) and radius \(R\), rotating at the same angular speed \(\omega\) about its central symmetry axis. What is the ratio of the rotational kinetic energy of the solid cylindrical flywheel to the rotational kinetic energy of the thin-walled cylindrical shell, \(\dfrac{K_{\text{solid}}}{K_{\text{shell}}}\)?

- **A.** \(\dfrac{1}{2}\)
- **B.** \(1\)
- **C.** \(2\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120872/*