---
title: "A wheel rotates under the influence of a motor that exerts a variable torque given by \\(\\tau(\\theta) = C\\theta^3\\), where \\(C\\) is a positive constant and \\(\\theta\\) is the angular displacement in radians. The wheel starts from rest and rotates from \\(\\theta = 0\\) to \\(\\theta = \\Phi\\). What is the total work done on the wheel by the motor during this angular displacement?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/117548/"
date_modified: "2026-08-04T07:48:59+00:00"
---

# A wheel rotates under the influence of a motor that exerts a variable torque given by \(\tau(\theta) = C\theta^3\), where \(C\) is a positive constant and \(\theta\) is the angular displacement in radians. The wheel starts from rest and rotates from \(\theta = 0\) to \(\theta = \Phi\). What is the total work done on the wheel by the motor during this angular displacement?

A wheel rotates under the influence of a motor that exerts a variable torque given by \(\tau(\theta) = C\theta^3\), where \(C\) is a positive constant and \(\theta\) is the angular displacement in radians. The wheel starts from rest and rotates from \(\theta = 0\) to \(\theta = \Phi\). What is the total work done on the wheel by the motor during this angular displacement?

- **A.** \(\dfrac{1}{4} C \Phi^4\)
- **B.** \(\dfrac{1}{3} C \Phi^3\)
- **C.** 3 C \Phi^2
- **D.** C \Phi^4

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117548/*