---
title: "A rigid flywheel mounted on a frictionless axle is initially at rest at time \\(t = 0\\). For \\(t \\ge 0\\), a net torque \\(\\tau(t) = \\beta t – \\gamma t^2\\) is exerted on the flywheel, where \\(\\beta\\) and \\(\\gamma\\) are positive constants. Which of the following expressions represents the maximum angular momentum achieved by the flywheel?"
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url: "https://nerd-notes.com/ubq/117586/"
date_modified: "2026-08-04T07:49:13+00:00"
---

# A rigid flywheel mounted on a frictionless axle is initially at rest at time \(t = 0\). For \(t \ge 0\), a net torque \(\tau(t) = \beta t – \gamma t^2\) is exerted on the flywheel, where \(\beta\) and \(\gamma\) are positive constants. Which of the following expressions represents the maximum angular momentum achieved by the flywheel?

A rigid flywheel mounted on a frictionless axle is initially at rest at time \(t = 0\). For \(t \ge 0\), a net torque \(\tau(t) = \beta t - \gamma t^2\) is exerted on the flywheel, where \(\beta\) and \(\gamma\) are positive constants. Which of the following expressions represents the maximum angular momentum achieved by the flywheel?

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117586/*