---
title: "A uniform flywheel with rotational inertia \\(I\\) is initially at rest. Starting at time \\(t = 0\\), a net torque \\(\\tau(t) = kt^2\\) is applied to the flywheel, where \\(k\\) is a positive constant. Which of the following expressions represents the angular speed \\(\\omega\\) of the flywheel at time \\(t = T\\)?"
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url: "https://nerd-notes.com/ubq/117559/"
date_modified: "2026-08-04T07:49:05+00:00"
---

# A uniform flywheel with rotational inertia \(I\) is initially at rest. Starting at time \(t = 0\), a net torque \(\tau(t) = kt^2\) is applied to the flywheel, where \(k\) is a positive constant. Which of the following expressions represents the angular speed \(\omega\) of the flywheel at time \(t = T\)?

A uniform flywheel with rotational inertia \(I\) is initially at rest. Starting at time \(t = 0\), a net torque \(\tau(t) = kt^2\) is applied to the flywheel, where \(k\) is a positive constant. Which of the following expressions represents the angular speed \(\omega\) of the flywheel at time \(t = T\)?

- **A.** \(\dfrac{kT^3}{6I}\)
- **B.** \(\dfrac{kT^3}{3I}\)
- **C.** \(\dfrac{kT^3}{2I}\)
- **D.** \(\dfrac{kT^3}{I}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117559/*