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A thin uniform rod of length 3L and mass M is bent into an L-shape, such that one leg has length L and the other has length 2L (the legs are perpendicular to each other). 1. Find its moment of inertia about an axis perpendicular to its plane and passing through the corner where it bends. 2. Find its moment of inertia about an axis perpendicular to its plane and passing through the midpoint of the line connecting the two ends. Hint: break the L-shaped piece into two pieces.

A thin uniform rod of length 3L and mass M is bent into an L-shape, such that one leg has length L and the other has length 2L (the legs are perpendicular to each other). 1. Find its moment of inertia about an axis perpendicular to its plane and passing through the corner where it bends. 2. Find its moment of inertia about an axis perpendicular to its plane and passing through the midpoint of the line connecting the two ends. Hint: break the L-shaped piece into two pieces.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Problem Statement: A thin uniform rod of length \(3L\) and mass \(M\) is bent into an L-shape, such that one leg has length \(L\) and the other has length \(2L\) (the legs are perpendicular to each other). 1. **Find its moment of inertia about an axis perpendicular to its plane and passing through the corner where it bends.** 2. **Find its moment of inertia about an axis perpendicular to its plane and passing through the midpoint of the line connecting the two ends.** **Hint:** Break the L-shaped piece into two pieces. ### Diagram Explanation: The diagram below the problem statement represents the L-shaped rod with its specific dimensions. The two segments of the rod are perpendicular to each other. - The vertical segment has a length of \(L\). - The horizontal segment has a length of \(2L\). The diagram shows: - The \(L\)-shaped rod with one segment vertical and one segment horizontal. - The vertical segment is labeled with a length \(L\). - The horizontal segment is labeled with a length \(2L\). - There is a black dot at the corner where the rod bends, indicating the axis for part 1 of the problem. - There is another black dot at the midpoint of the diagonal line connecting the two ends of the L-shaped rod, indicating the axis for part 2 of the problem. The diagonal line suggests the connecting line whose midpoint is where the second axis (for part 2 of the problem) passes through.
Transcribed Image Text:### Problem Statement: A thin uniform rod of length \(3L\) and mass \(M\) is bent into an L-shape, such that one leg has length \(L\) and the other has length \(2L\) (the legs are perpendicular to each other). 1. **Find its moment of inertia about an axis perpendicular to its plane and passing through the corner where it bends.** 2. **Find its moment of inertia about an axis perpendicular to its plane and passing through the midpoint of the line connecting the two ends.** **Hint:** Break the L-shaped piece into two pieces. ### Diagram Explanation: The diagram below the problem statement represents the L-shaped rod with its specific dimensions. The two segments of the rod are perpendicular to each other. - The vertical segment has a length of \(L\). - The horizontal segment has a length of \(2L\). The diagram shows: - The \(L\)-shaped rod with one segment vertical and one segment horizontal. - The vertical segment is labeled with a length \(L\). - The horizontal segment is labeled with a length \(2L\). - There is a black dot at the corner where the rod bends, indicating the axis for part 1 of the problem. - There is another black dot at the midpoint of the diagonal line connecting the two ends of the L-shaped rod, indicating the axis for part 2 of the problem. The diagonal line suggests the connecting line whose midpoint is where the second axis (for part 2 of the problem) passes through.
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