---
title: "Three identical uniform solid disks of mass \\(M\\) and radius \\(R\\) rotate freely about frictionless vertical axes through their centers with the same initial angular velocity \\(\\omega_0\\). Three identical small lumps of clay, each of mass \\(m\\), are dropped vertically from rest just above the disks and stick to the surfaces at different radial distances from the rotation axes.  | Turntable | Distance from axle of clay landing point | |—|—| | 1 | \\(r_1 = \\dfrac{1}{4}R\\) | | 2 | \\(r_2 = \\dfrac{1}{2}R\\) | | 3 | \\(r_3 = \\dfrac{3}{4}R\\) |  Which of the following correctly ranks the magnitudes of the final angular velocities of the three turntables, \\(\\omega_1\\), \\(\\omega_2\\), and \\(\\omega_3\\)?"
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url: "https://nerd-notes.com/ubq/120924/"
date_modified: "2026-08-23T04:44:20+00:00"
---

# Three identical uniform solid disks of mass \(M\) and radius \(R\) rotate freely about frictionless vertical axes through their centers with the same initial angular velocity \(\omega_0\). Three identical small lumps of clay, each of mass \(m\), are dropped vertically from rest just above the disks and stick to the surfaces at different radial distances from the rotation axes.

| Turntable | Distance from axle of clay landing point |
|—|—|
| 1 | \(r_1 = \dfrac{1}{4}R\) |
| 2 | \(r_2 = \dfrac{1}{2}R\) |
| 3 | \(r_3 = \dfrac{3}{4}R\) |

Which of the following correctly ranks the magnitudes of the final angular velocities of the three turntables, \(\omega_1\), \(\omega_2\), and \(\omega_3\)?

Three identical uniform solid disks of mass \(M\) and radius \(R\) rotate freely about frictionless vertical axes through their centers with the same initial angular velocity \(\omega_0\). Three identical small lumps of clay, each of mass \(m\), are dropped vertically from rest just above the disks and stick to the surfaces at different radial distances from the rotation axes.

| Turntable | Distance from axle of clay landing point |
|---|---|
| 1 | \(r_1 = \dfrac{1}{4}R\) |
| 2 | \(r_2 = \dfrac{1}{2}R\) |
| 3 | \(r_3 = \dfrac{3}{4}R\) |

Which of the following correctly ranks the magnitudes of the final angular velocities of the three turntables, \(\omega_1\), \(\omega_2\), and \(\omega_3\)?

![Three identical horizontal circular disks are shown side-by-side, labeled Turntable 1, Turntable 2, and Turntable 3 from left to right. Each disk has a central black dot representing the axle. A curved counterclockwise arrow is drawn above each disk, labeled \omega_0. On Turntable 1, a small filled circle is located along the horizontal radius at a distance of r_1 = \dfrac{1}{4}R from the center. On Turntable 2, an identical small filled circle is located along the horizontal radius at a distance of r_2 = \dfrac{1}{2}R from the center. On Turntable 3, an identical small filled circle is located along the horizontal radius at a distance of r_3 = \dfrac{3}{4}R from the center. A dashed horizontal line extends from the center of each disk to its outer perimeter to indicate the disk radius R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460260-sBaWsH.jpg)

- **A.** \(\omega_3 > \omega_2 > \omega_1\)
- **B.** \(\omega_1 = \omega_2 = \omega_3\)
- **C.** \(\omega_2 > \omega_1 > \omega_3\)
- **D.** \(\omega_1 > \omega_2 > \omega_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120924/*