---
title: "Two uniform solid disks, Disk 1 and Disk 2, have the same mass \\(M\\). The radius of Disk 2 is twice the radius of Disk 1 (\\(R_2 = 2R_1\\)). Both disks are initially at rest and are mounted on frictionless axles through their centers. The same constant net torque \\(\\tau\\) is applied to each disk. Which of the following correctly relates the magnitude of the angular acceleration of Disk 1 (\\(\\alpha_1\\)) to that of Disk 2 (\\(\\alpha_2\\)) and provides a correct justification?"
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url: "https://nerd-notes.com/ubq/109819/"
date_modified: "2026-03-26T05:52:32+00:00"
---

# Two uniform solid disks, Disk 1 and Disk 2, have the same mass \(M\). The radius of Disk 2 is twice the radius of Disk 1 (\(R_2 = 2R_1\)). Both disks are initially at rest and are mounted on frictionless axles through their centers. The same constant net torque \(\tau\) is applied to each disk. Which of the following correctly relates the magnitude of the angular acceleration of Disk 1 (\(\alpha_1\)) to that of Disk 2 (\(\alpha_2\)) and provides a correct justification?

Two uniform solid disks, Disk 1 and Disk 2, have the same mass \(M\). The radius of Disk 2 is twice the radius of Disk 1 (\(R_2 = 2R_1\)). Both disks are initially at rest and are mounted on frictionless axles through their centers. The same constant net torque \(\tau\) is applied to each disk. Which of the following correctly relates the magnitude of the angular acceleration of Disk 1 (\(\alpha_1\)) to that of Disk 2 (\(\alpha_2\)) and provides a correct justification?

- **A.** \(\alpha_1 = 4\alpha_2\), because the rotational inertia of a uniform disk is proportional to the square of its radius.
- **B.** \(\alpha_1 = 2\alpha_2\), because the rotational inertia of a uniform disk is proportional to its radius.
- **C.** \(\alpha_2 = 4\alpha_1\), because for a fixed torque, a disk with a larger radius will experience a larger angular acceleration.
- **D.** \(\alpha_1 = \alpha_2\), because the disks have the same mass and the same net torque is applied to both.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109819/*