---
title: "A uniform disk of mass \\(M\\) and radius \\(R\\) rotates about a fixed axis through its center. The angular speed of the disk as a function of time \\(t\\) is given by \\(\\omega(t) = bt^2\\), where \\(b\\) is a positive constant. What is the ratio of the rotational kinetic energy of the disk at time \\(t = 2t_0\\) to its rotational kinetic energy at time \\(t = t_0\\)?"
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url: "https://nerd-notes.com/ubq/117557/"
date_modified: "2026-08-04T07:49:04+00:00"
---

# A uniform disk of mass \(M\) and radius \(R\) rotates about a fixed axis through its center. The angular speed of the disk as a function of time \(t\) is given by \(\omega(t) = bt^2\), where \(b\) is a positive constant. What is the ratio of the rotational kinetic energy of the disk at time \(t = 2t_0\) to its rotational kinetic energy at time \(t = t_0\)?

A uniform disk of mass \(M\) and radius \(R\) rotates about a fixed axis through its center. The angular speed of the disk as a function of time \(t\) is given by \(\omega(t) = bt^2\), where \(b\) is a positive constant. What is the ratio of the rotational kinetic energy of the disk at time \(t = 2t_0\) to its rotational kinetic energy at time \(t = t_0\)?

- **A.** \(2\)
- **B.** \(4\)
- **C.** \(16\)
- **D.** \(32\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117557/*