---
title: "A uniform flat disk of radius \\(R\\) has a circular hole of radius \\(R/2\\) removed from it, as shown in the figure. The center of the circular hole is located at a distance of \\(R/2\\) from the center \\(O\\) of the original disk. The remaining planar object has a total mass \\(M\\). In terms of \\(M\\) and \\(R\\), what is the rotational inertia of the remaining object about an axis perpendicular to the plane of the disk and passing through the original center \\(O\\)?"
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url: "https://nerd-notes.com/ubq/120780/"
date_modified: "2026-08-23T04:43:19+00:00"
---

# A uniform flat disk of radius \(R\) has a circular hole of radius \(R/2\) removed from it, as shown in the figure. The center of the circular hole is located at a distance of \(R/2\) from the center \(O\) of the original disk. The remaining planar object has a total mass \(M\). In terms of \(M\) and \(R\), what is the rotational inertia of the remaining object about an axis perpendicular to the plane of the disk and passing through the original center \(O\)?

A uniform flat disk of radius \(R\) has a circular hole of radius \(R/2\) removed from it, as shown in the figure. The center of the circular hole is located at a distance of \(R/2\) from the center \(O\) of the original disk. The remaining planar object has a total mass \(M\). In terms of \(M\) and \(R\), what is the rotational inertia of the remaining object about an axis perpendicular to the plane of the disk and passing through the original center \(O\)?

![A large circle representing a flat disk of outer radius \(R\) is centered at point \(O\). The interior of the large circle is shaded with a light uniform gray fill. Inside the large circle, a smaller circular cutout of radius \(R/2\) is positioned with its center shifted horizontally to the right of \(O\) by a distance \(R/2\), drawn with a white interior fill. A solid black dot marks the original center \(O\). A dashed horizontal reference line extends from \(O\) through the center of the cutout to the right edge of the disk. A double-headed dimension arrow indicates the distance \(R/2\) between \(O\) and the cutout center, and a dimension line indicates the outer radius \(R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460199-rb9r39.jpg)

- **A.** \(\dfrac{13}{24} M R^2\)
- **B.** \(\dfrac{5}{8} M R^2\)
- **C.** \(\dfrac{13}{32} M R^2\)
- **D.** \(\dfrac{19}{24} M R^2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120780/*