---
title: "A rigid wheel with rotational inertia \\(I = 2.0\\text{ kg}\\cdot\\text{m}^2\\) is mounted on a frictionless horizontal axle and is initially rotating with an angular speed of \\(\\omega_i = 3.0\\text{ rad/s}\\) at angular position \\(\\theta = 0\\text{ rad}\\). A variable net torque \\(\\tau\\) is applied to the wheel as a function of its angular displacement \\(\\theta\\), as shown in the graph.  What is the angular speed of the wheel when it reaches \\(\\theta = 10\\text{ rad}\\)?"
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url: "https://nerd-notes.com/ubq/120951/"
date_modified: "2026-08-23T04:44:39+00:00"
---

# A rigid wheel with rotational inertia \(I = 2.0\text{ kg}\cdot\text{m}^2\) is mounted on a frictionless horizontal axle and is initially rotating with an angular speed of \(\omega_i = 3.0\text{ rad/s}\) at angular position \(\theta = 0\text{ rad}\). A variable net torque \(\tau\) is applied to the wheel as a function of its angular displacement \(\theta\), as shown in the graph.

What is the angular speed of the wheel when it reaches \(\theta = 10\text{ rad}\)?

A rigid wheel with rotational inertia \(I = 2.0\text{ kg}\cdot\text{m}^2\) is mounted on a frictionless horizontal axle and is initially rotating with an angular speed of \(\omega_i = 3.0\text{ rad/s}\) at angular position \(\theta = 0\text{ rad}\). A variable net torque \(\tau\) is applied to the wheel as a function of its angular displacement \(\theta\), as shown in the graph.

What is the angular speed of the wheel when it reaches \(\theta = 10\text{ rad}\)?

![A 2D Cartesian coordinate graph showing net torque \(\tau\) in \(\text{N}\cdot\text{m}\) on the vertical axis versus angular displacement \(\theta\) in \(\text{rad}\) on the horizontal axis. The horizontal axis ranges from \(0\) to \(10\) with labeled tick marks at intervals of \(2\) (\(0, 2, 4, 6, 8, 10\)) and light gridlines. The vertical axis ranges from \(-6\) to \(10\) with labeled tick marks at \(-4, 0, 4, 8\) and light gridlines. A thick solid black line consists of four connected line segments: starting at \((0, 0)\), rising linearly to \((3, 8)\), descending linearly to \((6, 0)\), descending linearly to \((8, -4)\), and rising linearly to end at \((10, 0)\). No other curves, labels, shading, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/torque-vs-theta-graph-1787460279-8cD5ao.jpg)

- **A.** \(5.0\text{ rad/s}\)
- **B.** \(6.4\text{ rad/s}\)
- **C.** \(8.5\text{ rad/s}\)
- **D.** \(11\text{ rad/s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120951/*