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title: "A flywheel with rotational inertia \\(I\\) is mounted on a fixed, frictionless axle and is initially at rest at time \\(t = 0\\). A net external torque \\(\\tau\\) is applied to the flywheel about the axle, varying with time \\(t\\) as shown in the graph. The torque decreases linearly from \\(\\tau_0\\) at \\(t = 0\\), crosses zero at \\(t = T\\), and reaches \\(-\\tau_0\\) at \\(t = 2T\\). Which of the following statements correctly identifies the maximum angular velocity of the flywheel and characterizes its subsequent rotational motion?"
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url: "https://nerd-notes.com/ubq/124417/"
date_modified: "2026-09-28T14:05:18+00:00"
---

# A flywheel with rotational inertia \(I\) is mounted on a fixed, frictionless axle and is initially at rest at time \(t = 0\). A net external torque \(\tau\) is applied to the flywheel about the axle, varying with time \(t\) as shown in the graph. The torque decreases linearly from \(\tau_0\) at \(t = 0\), crosses zero at \(t = T\), and reaches \(-\tau_0\) at \(t = 2T\). Which of the following statements correctly identifies the maximum angular velocity of the flywheel and characterizes its subsequent rotational motion?

A flywheel with rotational inertia \(I\) is mounted on a fixed, frictionless axle and is initially at rest at time \(t = 0\). A net external torque \(\tau\) is applied to the flywheel about the axle, varying with time \(t\) as shown in the graph. The torque decreases linearly from \(\tau_0\) at \(t = 0\), crosses zero at \(t = T\), and reaches \(-\tau_0\) at \(t = 2T\). Which of the following statements correctly identifies the maximum angular velocity of the flywheel and characterizes its subsequent rotational motion?

![A two-dimensional Cartesian graph with a horizontal axis labeled t and a vertical axis labeled \tau. The horizontal axis has tick marks labeled 0, T, and 2T. The vertical axis has tick marks labeled \tau_0 above the horizontal axis and -\tau_0 below the horizontal axis. A single, solid straight line begins at the point (0, \tau_0) on the vertical axis, extends downward and to the right with a constant negative slope, crosses the horizontal axis at (T, 0), and terminates at the point (2T, -\tau_0). Dashed reference lines extend horizontally from -\tau_0 to (2T, -\tau_0) and vertically from 2T to (2T, -\tau_0). No other labels, lines, text, or gridlines appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604317-QSOXqf.jpg)

- **A.** The flywheel attains a maximum angular velocity of \(\dfrac{\tau_0 T}{2I}\) at \(t = T\) and momentarily comes to rest at \(t = 2T\).
- **B.** The flywheel attains a maximum angular velocity of \(\dfrac{\tau_0 T}{I}\) at \(t = T\) and reverses its direction of rotation at \(t = T\).
- **C.** The flywheel momentarily comes to rest at \(t = T\) and attains a maximum angular speed of \(\dfrac{\tau_0 T}{2I}\) in the reverse direction at \(t = 2T\).
- **D.** The flywheel attains a maximum angular velocity of \(\dfrac{\tau_0 T}{4I}\) at \(t = \dfrac{T}{2}\) and momentarily comes to rest at \(t = T\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124417/*