Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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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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