---
title: "A rigid flywheel with rotational inertia \\(I\\) is mounted on a frictionless central axle and is initially at rest at time \\(t = 0\\). A time-dependent torque \\(\\tau(t) = \\tau_0 \\cos(\\omega_0 t)\\) is applied to the flywheel, where \\(\\tau_0\\) and \\(\\omega_0\\) are positive constants. Which of the following expressions gives the instantaneous power \\(P(t)\\) delivered to the flywheel as a function of time \\(t\\)?"
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/117661/"
date_modified: "2026-08-04T07:49:36+00:00"
---

# A rigid flywheel with rotational inertia \(I\) is mounted on a frictionless central axle and is initially at rest at time \(t = 0\). A time-dependent torque \(\tau(t) = \tau_0 \cos(\omega_0 t)\) is applied to the flywheel, where \(\tau_0\) and \(\omega_0\) are positive constants. Which of the following expressions gives the instantaneous power \(P(t)\) delivered to the flywheel as a function of time \(t\)?

A rigid flywheel with rotational inertia \(I\) is mounted on a frictionless central axle and is initially at rest at time \(t = 0\). A time-dependent torque \(\tau(t) = \tau_0 \cos(\omega_0 t)\) is applied to the flywheel, where \(\tau_0\) and \(\omega_0\) are positive constants. Which of the following expressions gives the instantaneous power \(P(t)\) delivered to the flywheel as a function of time \(t\)?

![A circular disk representing a flywheel of radius R, mounted on a central axle. A curved arrow around the perimeter indicates an applied torque \tau(t). A rotational axis z extends vertically through the center of the flywheel. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785829776-tkbyCy.jpg)

- **A.** \(\dfrac{\tau_0^2}{I\omega_0} \cos^2(\omega_0 t)\)
- **B.** \(\dfrac{\tau_0^2}{I\omega_0} \sin^2(\omega_0 t)\)
- **C.** \(\dfrac{\tau_0^2}{I\omega_0} \sin(\omega_0 t) \cos(\omega_0 t)\)
- **D.** \(\dfrac{\tau_0^2}{2I\omega_0} \sin(2\omega_0 t)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117661/*