Lo the ry-plane at the point I = I, + m(x² + y) where I, is the moment of inertia about (0,0). (This is a version of the theorem of paralle mechanics. This theorem, along with a table of moments of inertia for standard shapes gi books, allows us to quickly find the moment of inertia around other axes as needed.)
Lo the ry-plane at the point I = I, + m(x² + y) where I, is the moment of inertia about (0,0). (This is a version of the theorem of paralle mechanics. This theorem, along with a table of moments of inertia for standard shapes gi books, allows us to quickly find the moment of inertia around other axes as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![**Theorem of Parallel Axes in Mechanics**
**Section D:**
Suppose that the center of mass of a uniform plate is at \((0,0)\), and that the plate has a total mass \(m\). Show that its moment of inertia about an axis perpendicular to the \(xy\)-plane at the point \((x_0, y_0)\) is
\[ I = I_0 + m(x_0^2 + y_0^2) \]
where \(I_0\) is the moment of inertia about \((0,0)\). This is a version of the theorem of parallel axes from mechanics. This theorem, along with a table of moments of inertia for standard shapes given in most books, allows us to quickly find the moment of inertia around other axes as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc740e8b2-d410-40ba-b674-1beb1e9bb454%2F952f6695-c7ca-4ef8-a323-c06bd296fe3b%2Fxhrjihp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Theorem of Parallel Axes in Mechanics**
**Section D:**
Suppose that the center of mass of a uniform plate is at \((0,0)\), and that the plate has a total mass \(m\). Show that its moment of inertia about an axis perpendicular to the \(xy\)-plane at the point \((x_0, y_0)\) is
\[ I = I_0 + m(x_0^2 + y_0^2) \]
where \(I_0\) is the moment of inertia about \((0,0)\). This is a version of the theorem of parallel axes from mechanics. This theorem, along with a table of moments of inertia for standard shapes given in most books, allows us to quickly find the moment of inertia around other axes as needed.
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