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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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D. Suppose that the center of mass of a uniform plate is at (0,0), and that the plate has total mass m. Show that its moment of inertia about an axis perpendicular to the ry-plane at the point (ro, Yo) is I = 1, + m(r² + v where I. 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.)
Transcribed Image Text:D. Suppose that the center of mass of a uniform plate is at (0,0), and that the plate has total mass m. Show that its moment of inertia about an axis perpendicular to the ry-plane at the point (ro, Yo) is I = 1, + m(r² + v where I. 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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