---
title: "A uniform disk is initially rotating with rotational kinetic energy \\(K_0\\) about a fixed, frictionless axis through its center. Starting at angular displacement \\(\\theta = 0\\), a braking mechanism applies a resistive torque of magnitude \\(\\tau(\\theta) = c\\theta\\) to the disk, where \\(c\\) is a positive constant and \\(\\theta\\) is the angular displacement of the disk after the brake is engaged. Which of the following graphs best represents the rotational kinetic energy \\(K\\) of the disk as a function of \\(\\theta\\) until the disk momentarily comes to rest at \\(\\theta_f\\)?"
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url: "https://nerd-notes.com/ubq/120947/"
date_modified: "2026-08-23T04:44:37+00:00"
---

# A uniform disk is initially rotating with rotational kinetic energy \(K_0\) about a fixed, frictionless axis through its center. Starting at angular displacement \(\theta = 0\), a braking mechanism applies a resistive torque of magnitude \(\tau(\theta) = c\theta\) to the disk, where \(c\) is a positive constant and \(\theta\) is the angular displacement of the disk after the brake is engaged. Which of the following graphs best represents the rotational kinetic energy \(K\) of the disk as a function of \(\theta\) until the disk momentarily comes to rest at \(\theta_f\)?

A uniform disk is initially rotating with rotational kinetic energy \(K_0\) about a fixed, frictionless axis through its center. Starting at angular displacement \(\theta = 0\), a braking mechanism applies a resistive torque of magnitude \(\tau(\theta) = c\theta\) to the disk, where \(c\) is a positive constant and \(\theta\) is the angular displacement of the disk after the brake is engaged. Which of the following graphs best represents the rotational kinetic energy \(K\) of the disk as a function of \(\theta\) until the disk momentarily comes to rest at \(\theta_f\)?

![A flat circular disk viewed in perspective at a slight oblique tilt, centered on a vertical dashed rotation axle that extends above and below the disk. A curved counterclockwise arrow near the axle is labeled \omega_0. A small rectangular brake block is positioned adjacent to the outer rim on the right. A curved arrow directed opposite to the rotation at the rim is labeled \tau(\theta). An angular sector on the upper surface of the disk is outlined by two thin radial lines with an arc arrow between them labeled \theta. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460276-MQ6twg.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120947/*