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title: "A thin, uniform square sheet of mass \\(M\\) and side length \\(L\\) has a rotational inertia \\(I_0\\) about a diagonal axis in its plane. The sheet is folded in half along this diagonal to form a flat triangular sheet of mass \\(M\\). Axes \\(x’\\) and \\(y’\\) lie in the plane of the folded sheet and pass through its new center of mass, oriented parallel and perpendicular to the fold line, respectively, while axis \\(z’\\) is perpendicular to the sheet through the new center of mass. Which row in the table correctly compares the rotational inertias \\(I_{\\text{fold}}\\) (about the fold line) and \\(I_{x’}\\) to \\(I_0\\), and correctly ranks the moments of inertia about the axes through the new center of mass?"
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url: "https://nerd-notes.com/ubq/124388/"
date_modified: "2026-09-28T14:05:07+00:00"
---

# A thin, uniform square sheet of mass \(M\) and side length \(L\) has a rotational inertia \(I_0\) about a diagonal axis in its plane. The sheet is folded in half along this diagonal to form a flat triangular sheet of mass \(M\). Axes \(x’\) and \(y’\) lie in the plane of the folded sheet and pass through its new center of mass, oriented parallel and perpendicular to the fold line, respectively, while axis \(z’\) is perpendicular to the sheet through the new center of mass. Which row in the table correctly compares the rotational inertias \(I_{\text{fold}}\) (about the fold line) and \(I_{x’}\) to \(I_0\), and correctly ranks the moments of inertia about the axes through the new center of mass?

A thin, uniform square sheet of mass \(M\) and side length \(L\) has a rotational inertia \(I_0\) about a diagonal axis in its plane. The sheet is folded in half along this diagonal to form a flat triangular sheet of mass \(M\). Axes \(x'\) and \(y'\) lie in the plane of the folded sheet and pass through its new center of mass, oriented parallel and perpendicular to the fold line, respectively, while axis \(z'\) is perpendicular to the sheet through the new center of mass. Which row in the table correctly compares the rotational inertias \(I_{\text{fold}}\) (about the fold line) and \(I_{x'}\) to \(I_0\), and correctly ranks the moments of inertia about the axes through the new center of mass?

![Two diagrams side by side labeled 'Before Folding' and 'After Folding'. On the left, a square sheet with vertices oriented horizontally and vertically, showing a dashed diagonal line extending from bottom-left to top-right labeled 'Fold line'. The center of the square is marked with an open circle labeled 'Initial center of mass'. On the right, an isosceles right triangle representing the folded sheet with its hypotenuse along the bottom-left to top-right diagonal. A filled circle marks the new center of mass, displaced perpendicular to the fold line into the interior of the triangle. Three mutually perpendicular axes pass through this new center of mass: a dashed line parallel to the fold line labeled x', a dashed line perpendicular to the fold line labeled y', and a circled dot labeled z' indicating an axis pointing out of the plane. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604307-os5OSV.jpg)

- **A.** \(I_{\text{fold}}\): Decreases | \(I_{x'}\): Decreases | Ranking: \(I_{x'} = I_{y'} < I_{z'}\)
- **B.** \(I_{\text{fold}}\): Remains the same | \(I_{x'}\): Decreases | Ranking: \(I_{x'} < I_{y'} < I_{z'}\)
- **C.** \(I_{\text{fold}}\): Remains the same | \(I_{x'}\): Increases | Ranking: \(I_{y'} < I_{x'} < I_{z'}\)
- **D.** \(I_{\text{fold}}\): Increases | \(I_{x'}\): Remains the same | Ranking: \(I_{z'} < I_{x'} < I_{y'}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124388/*