---
title: "At time \\( t = 0 \\), a disk starts from rest and begins spinning about its center with a constant angular acceleration of magnitude \\( \\alpha \\). At time \\( t_f \\), the disk has angular speed \\( \\omega_f \\). Which of the following expressions correctly compares the final angular displacement \\( \\theta_f \\) of the disk at time \\( t_f \\) to the angular displacement \\( \\theta_{1/2} \\) at time \\( \\frac{t_f}{2} \\)?"
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/80606/"
date_modified: "2025-03-11T06:22:44+00:00"
---

# At time \( t = 0 \), a disk starts from rest and begins spinning about its center with a constant angular acceleration of magnitude \( \alpha \). At time \( t_f \), the disk has angular speed \( \omega_f \). Which of the following expressions correctly compares the final angular displacement \( \theta_f \) of the disk at time \( t_f \) to the angular displacement \( \theta_{1/2} \) at time \( \frac{t_f}{2} \)?

At time \( t = 0 \), a disk starts from rest and begins spinning about its center with a constant angular acceleration of magnitude \( \alpha \). At time \( t_f \), the disk has angular speed \( \omega_f \). Which of the following expressions correctly compares the final angular displacement \( \theta_f \) of the disk at time \( t_f \) to the angular displacement \( \theta_{1/2} \) at time \( \frac{t_f}{2} \)?

- **A.** \[ \theta_f = \frac{\theta_{1/2}}{4} \]
- **B.** \[ \theta_f = \theta_{1/2} \]
- **C.** \[ \theta_f = 2\theta_{1/2} \]
- **D.** \[ \theta_f = 4\theta_{1/2} \]

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/80606/*