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title: "Two uniform solid disks, Disk 1 and Disk 2, are mounted on separate frictionless horizontal axles. Disk 1 has rotational inertia \\(I_1 = I_0\\) and Disk 2 has rotational inertia \\(I_2 = 2I_0\\). Starting from rest, each disk is rotated through the same angular displacement \\(\\Delta\\theta\\) by an identical constant net torque \\(\\tau_0\\). Which of the following correctly pairs the relationship between the total work \\(W_1\\) and \\(W_2\\) done on the disks with the relationship between their final rotational kinetic energies \\(K_1\\) and \\(K_2\\)?"
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url: "https://nerd-notes.com/ubq/124316/"
date_modified: "2026-09-28T14:04:46+00:00"
---

# Two uniform solid disks, Disk 1 and Disk 2, are mounted on separate frictionless horizontal axles. Disk 1 has rotational inertia \(I_1 = I_0\) and Disk 2 has rotational inertia \(I_2 = 2I_0\). Starting from rest, each disk is rotated through the same angular displacement \(\Delta\theta\) by an identical constant net torque \(\tau_0\). Which of the following correctly pairs the relationship between the total work \(W_1\) and \(W_2\) done on the disks with the relationship between their final rotational kinetic energies \(K_1\) and \(K_2\)?

Two uniform solid disks, Disk 1 and Disk 2, are mounted on separate frictionless horizontal axles. Disk 1 has rotational inertia \(I_1 = I_0\) and Disk 2 has rotational inertia \(I_2 = 2I_0\). Starting from rest, each disk is rotated through the same angular displacement \(\Delta\theta\) by an identical constant net torque \(\tau_0\). Which of the following correctly pairs the relationship between the total work \(W_1\) and \(W_2\) done on the disks with the relationship between their final rotational kinetic energies \(K_1\) and \(K_2\)?

![A schematic showing two disks mounted on fixed horizontal axles. On the left, a circular disk labeled Disk 1 has a rotational inertia labeled \(I_1 = I_0\). On the right, a second circular disk labeled Disk 2 has a rotational inertia labeled \(I_2 = 2I_0\). A dashed horizontal line passes through the center of both disks to represent their fixed axes of rotation. Around the circumference of Disk 1 is a curved arrow indicating a net torque labeled \(\tau_0\). Around the circumference of Disk 2 is an identical curved arrow in the same rotational direction, also labeled \(\tau_0\). Both disks are shown facing forward as flat circles. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604286-ybY9u2.jpg)

- **A.** Work done: \(W_1 < W_2\) ; Final kinetic energy: \(K_1 > K_2\)
- **B.** Work done: \(W_1 < W_2\) ; Final kinetic energy: \(K_1 = K_2\)
- **C.** Work done: \(W_1 = W_2\) ; Final kinetic energy: \(K_1 > K_2\)
- **D.** Work done: \(W_1 = W_2\) ; Final kinetic energy: \(K_1 = K_2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124316/*