---
title: "A rigid wheel rotating about a fixed frictionless axle is initially at rest at \\(t = 0\\). A net torque applied to the wheel produces an angular acceleration \\(\\alpha\\) as a function of time \\(t\\) shown in the graph. Which of the following statements correctly identifies the maximum angular velocity of the wheel on the interval \\(0 \\le t \\le 6\\text{ s}\\) and provides a correct justification?"
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url: "https://nerd-notes.com/ubq/124268/"
date_modified: "2026-09-28T14:04:35+00:00"
---

# A rigid wheel rotating about a fixed frictionless axle is initially at rest at \(t = 0\). A net torque applied to the wheel produces an angular acceleration \(\alpha\) as a function of time \(t\) shown in the graph. Which of the following statements correctly identifies the maximum angular velocity of the wheel on the interval \(0 \le t \le 6\text{ s}\) and provides a correct justification?

A rigid wheel rotating about a fixed frictionless axle is initially at rest at \(t = 0\). A net torque applied to the wheel produces an angular acceleration \(\alpha\) as a function of time \(t\) shown in the graph. Which of the following statements correctly identifies the maximum angular velocity of the wheel on the interval \(0 \le t \le 6\text{ s}\) and provides a correct justification?

![A two-dimensional Cartesian graph on a white background with thin dashed gridlines. The horizontal axis is labeled t (s) at the right end, with numerical labels at tick marks for 0, 2, 4, and 6. The vertical axis is labeled \alpha (rad/s^2) at the top, with numerical labels at tick marks for -3, 0, 3, and 6. A single solid straight line with a constant negative slope begins at coordinates (0, 6) on the vertical axis, extends downward and rightward through the horizontal axis intercept at (4, 0), and ends at coordinates (6, -3). Small filled circular points mark the endpoints at (0, 6) and (6, -3) as well as the horizontal intercept at (4, 0). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604275-yrH3Z1.jpg)

- **A.** The wheel reaches its maximum angular velocity of \(12\text{ rad/s}\) at \(t = 4\text{ s}\), because the area under the \(\alpha\text{-}t\) curve represents the change in angular velocity, and this positive area accumulates until \(\alpha\) drops to zero.
- **B.** The wheel reaches its maximum angular velocity of \(6\text{ rad/s}\) at \(t = 0\text{ s}\), because the magnitude of the angular acceleration is greatest at the start of the motion.
- **C.** The wheel reaches its maximum angular velocity of \(9\text{ rad/s}\) at \(t = 6\text{ s}\), because the total area accumulated across the entire time interval represents the peak speed of the wheel.
- **D.** The wheel reaches its maximum angular velocity of \(1.5\text{ rad/s}\) at \(t = 4\text{ s}\), because the slope of the \(\alpha\text{-}t\) curve represents the rate of change of angular position.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124268/*