---
title: "Four identical uniform solid disks, each of mass \\(M\\) and radius \\(R\\), are mounted on frictionless fixed axles perpendicular to the plane of each disk. External forces of magnitude \\(F_0\\) or \\(2F_0\\) act in the plane of the disks as described in the table.  | Disk | Axle Location | Force Magnitude | Point of Application and Direction | | :—: | :—: | :—: | :—: | | 1 | Center | \\(F_0\\) | Tangent to outer edge at radius \\(R\\) | | 2 | Rim | \\(2F_0\\) | Perpendicular to the diameter through the axle, at the opposite rim | | 3 | Rim | \\(F_0\\) | Perpendicular to the diameter through the axle, at the opposite rim | | 4 | Center | \\(F_0\\) | Tangent to an inner track at radius \\(\\dfrac{R}{2}\\) |  Which of the following correctly ranks the magnitudes of the initial angular accelerations \\(\\alpha_1\\), \\(\\alpha_2\\), \\(\\alpha_3\\), and \\(\\alpha_4\\) of the disks?"
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url: "https://nerd-notes.com/ubq/120817/"
date_modified: "2026-08-23T04:43:28+00:00"
---

# Four identical uniform solid disks, each of mass \(M\) and radius \(R\), are mounted on frictionless fixed axles perpendicular to the plane of each disk. External forces of magnitude \(F_0\) or \(2F_0\) act in the plane of the disks as described in the table.

| Disk | Axle Location | Force Magnitude | Point of Application and Direction |
| :—: | :—: | :—: | :—: |
| 1 | Center | \(F_0\) | Tangent to outer edge at radius \(R\) |
| 2 | Rim | \(2F_0\) | Perpendicular to the diameter through the axle, at the opposite rim |
| 3 | Rim | \(F_0\) | Perpendicular to the diameter through the axle, at the opposite rim |
| 4 | Center | \(F_0\) | Tangent to an inner track at radius \(\dfrac{R}{2}\) |

Which of the following correctly ranks the magnitudes of the initial angular accelerations \(\alpha_1\), \(\alpha_2\), \(\alpha_3\), and \(\alpha_4\) of the disks?

Four identical uniform solid disks, each of mass \(M\) and radius \(R\), are mounted on frictionless fixed axles perpendicular to the plane of each disk. External forces of magnitude \(F_0\) or \(2F_0\) act in the plane of the disks as described in the table.

| Disk | Axle Location | Force Magnitude | Point of Application and Direction |
| :---: | :---: | :---: | :---: |
| 1 | Center | \(F_0\) | Tangent to outer edge at radius \(R\) |
| 2 | Rim | \(2F_0\) | Perpendicular to the diameter through the axle, at the opposite rim |
| 3 | Rim | \(F_0\) | Perpendicular to the diameter through the axle, at the opposite rim |
| 4 | Center | \(F_0\) | Tangent to an inner track at radius \(\dfrac{R}{2}\) |

Which of the following correctly ranks the magnitudes of the initial angular accelerations \(\alpha_1\), \(\alpha_2\), \(\alpha_3\), and \(\alpha_4\) of the disks?

![A 2-by-2 grid showing four identical circular disks labeled Disk 1, Disk 2, Disk 3, and Disk 4. Disk 1 (top-left) has a central black pivot dot, a radius labeled \(R\), and a tangential upward arrow labeled \(F_0\) at the right edge. Disk 2 (top-right) has a black pivot dot at the leftmost edge, a horizontal dashed diameter line labeled with total length \(2R\), and an upward arrow labeled \(2F_0\) at the opposite right edge. Disk 3 (bottom-left) has a black pivot dot at the leftmost edge, a horizontal dashed diameter line, and an upward arrow labeled \(F_0\) at the opposite right edge. Disk 4 (bottom-right) has a central black pivot dot, a concentric dashed inner circle of radius \(\dfrac{R}{2}\), and a tangential upward arrow labeled \(F_0\) at the right edge of the inner circle. No other lines, labels, or decorative shading appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460207-TxHURq.jpg)

- **A.** \(\alpha_2 > \alpha_3 > \alpha_1 > \alpha_4\)
- **B.** \(\alpha_1 > \alpha_2 > \alpha_3 > \alpha_4\)
- **C.** \(\alpha_2 > \alpha_1 > \alpha_3 > \alpha_4\)
- **D.** \(\alpha_1 > \alpha_2 > \alpha_4 > \alpha_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120817/*