---
title: "A uniform disk with rotational inertia \\(I = 2.0\\text{ kg}\\cdot\\text{m}^2\\) is free to rotate about a fixed frictionless axle through its center. At time \\(t = 0\\text{ s}\\), the disk is rotating clockwise with an angular speed of \\(5.0\\text{ rad/s}\\). A net torque \\(\\tau\\) is exerted on the disk along the rotational axis as a function of time \\(t\\) as shown in the graph, where counterclockwise torque is defined as positive. What is the angular velocity of the disk at \\(t = 6.0\\text{ s}\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120926/"
date_modified: "2026-08-23T04:44:22+00:00"
---

# A uniform disk with rotational inertia \(I = 2.0\text{ kg}\cdot\text{m}^2\) is free to rotate about a fixed frictionless axle through its center. At time \(t = 0\text{ s}\), the disk is rotating clockwise with an angular speed of \(5.0\text{ rad/s}\). A net torque \(\tau\) is exerted on the disk along the rotational axis as a function of time \(t\) as shown in the graph, where counterclockwise torque is defined as positive. What is the angular velocity of the disk at \(t = 6.0\text{ s}\)?

A uniform disk with rotational inertia \(I = 2.0\text{ kg}\cdot\text{m}^2\) is free to rotate about a fixed frictionless axle through its center. At time \(t = 0\text{ s}\), the disk is rotating clockwise with an angular speed of \(5.0\text{ rad/s}\). A net torque \(\tau\) is exerted on the disk along the rotational axis as a function of time \(t\) as shown in the graph, where counterclockwise torque is defined as positive. What is the angular velocity of the disk at \(t = 6.0\text{ s}\)?

![A grayscale Cartesian graph with time \(t\text{ (s)}\) on the horizontal axis from 0 to 6 with integer tick marks, and net torque \(\tau\text{ (N}\cdot\text{m)}\) on the vertical axis from -6 to 6 with tick marks every 2 units. Light dashed gridlines extend across the grid at every labeled tick mark. A thick solid line starts at \((0, 0)\), rises linearly to \((2, 6)\), extends horizontally to \((4, 6)\), and descends linearly through \((5, 0)\) to end at \((6, -6)\). No other labels, lines, curves, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/torque-time-graph-1787460262-ysy4Yl.jpg)

- **A.** \(4.0\text{ rad/s}\), clockwise
- **B.** \(4.0\text{ rad/s}\), counterclockwise
- **C.** \(9.0\text{ rad/s}\), counterclockwise
- **D.** \(14.0\text{ rad/s}\), counterclockwise

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120926/*