---
title: "A rotor with rotational inertia \\(I\\) is mounted on a frictionless axle and is initially at rest. Starting at time \\(t = 0\\), a net external torque given by \\(\\tau(t) = bt\\) is applied to the rotor, where \\(b\\) is a positive constant. Which of the following expressions represents the total work done on the rotor by the torque from \\(t = 0\\) to \\(t = T\\)?"
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url: "https://nerd-notes.com/ubq/120914/"
date_modified: "2026-08-23T04:44:17+00:00"
---

# A rotor with rotational inertia \(I\) is mounted on a frictionless axle and is initially at rest. Starting at time \(t = 0\), a net external torque given by \(\tau(t) = bt\) is applied to the rotor, where \(b\) is a positive constant. Which of the following expressions represents the total work done on the rotor by the torque from \(t = 0\) to \(t = T\)?

A rotor with rotational inertia \(I\) is mounted on a frictionless axle and is initially at rest. Starting at time \(t = 0\), a net external torque given by \(\tau(t) = bt\) is applied to the rotor, where \(b\) is a positive constant. Which of the following expressions represents the total work done on the rotor by the torque from \(t = 0\) to \(t = T\)?

![A circular disk of rotational inertia \(I\) shown in perspective as a flat horizontal ellipse tilted slightly forward. A central dashed vertical line represents the fixed rotation axis passing through the center of the disk. A curved arrow labeled \(\tau(t) = bt\) wraps counterclockwise around the top surface of the disk to indicate the applied torque. Near the disk, the initial condition is labeled \(\omega_0 = 0\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460256-Oykig5.jpg)

- **A.** \(\dfrac{b^2 T^4}{2I}\)
- **B.** \(\dfrac{b^2 T^4}{4I}\)
- **C.** \(\dfrac{b^2 T^4}{6I}\)
- **D.** \(\dfrac{b^2 T^4}{8I}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120914/*