---
title: "A uniform door of mass \\(M\\) and length \\(L\\) is initially at rest and is free to rotate about a vertical axis through its hinges. A student applies a constant force of magnitude \\(F\\) to the door. The force is always directed perpendicular to the door’s surface. In Trial 1, the force is applied at the outer edge of the door, a distance \\(L\\) from the hinges. In Trial 2, the force is applied at the door’s midpoint, a distance \\(L/2\\) from the hinges. In Trial 3, the force is applied at a distance \\(L/4\\) from the hinges. Which of the following correctly ranks the magnitude of the door’s angular acceleration \\(\\alpha\\) during each trial?"
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url: "https://nerd-notes.com/ubq/109834/"
date_modified: "2026-05-01T22:20:10+00:00"
---

# A uniform door of mass \(M\) and length \(L\) is initially at rest and is free to rotate about a vertical axis through its hinges. A student applies a constant force of magnitude \(F\) to the door. The force is always directed perpendicular to the door’s surface. In Trial 1, the force is applied at the outer edge of the door, a distance \(L\) from the hinges. In Trial 2, the force is applied at the door’s midpoint, a distance \(L/2\) from the hinges. In Trial 3, the force is applied at a distance \(L/4\) from the hinges. Which of the following correctly ranks the magnitude of the door’s angular acceleration \(\alpha\) during each trial?

A uniform door of mass \(M\) and length \(L\) is initially at rest and is free to rotate about a vertical axis through its hinges. A student applies a constant force of magnitude \(F\) to the door. The force is always directed perpendicular to the door's surface. In Trial 1, the force is applied at the outer edge of the door, a distance \(L\) from the hinges. In Trial 2, the force is applied at the door's midpoint, a distance \(L/2\) from the hinges. In Trial 3, the force is applied at a distance \(L/4\) from the hinges. Which of the following correctly ranks the magnitude of the door's angular acceleration \(\alpha\) during each trial?

![A top-down view of a rectangular door of length L. The left end is attached to a hinge (pivot). Three horizontal arrows labeled F are shown at different positions along the door length, pointing perpendicular to the door. F1 is at the far right edge (distance L from pivot). F2 is at the center (distance L/2 from pivot). F3 is halfway between the pivot and the center (distance L/4 from pivot).](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/ubq-frq-generatedstem-fig-1-1777674010-Y3bWpF.jpg)

- **A.** \(\alpha_1 > \alpha_2 > \alpha_3\)
- **B.** \(\alpha_3 > \alpha_2 > \alpha_1\)
- **C.** \(\alpha_1 = \alpha_2 = \alpha_3\)
- **D.** \(\alpha_1 > \alpha_2 = \alpha_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109834/*