Parallel and perpendicular axis theorems
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Proof of the Perpendicular Axis Theorem
Let p be a plane thin uniform lamina. Let mi be a mass element with perpendicular distance ri from an axis Oz perpendicular to the plane and passing through O in the plane. [Diagram goes here - download the original to see it. Let Ox and Oy be two perpendicular axes lying in the plane. Let ai be the perpendicular lying in the plane. Let ai be the perpendicular distance of mi from Ox and bi be the perpendicular distance of mi from Oy. Let [Equation goes here - download the original to see it.] be the moment of inertia of p about Ox and [Equation goes here - download the original to see it.] be the moment of inertia of p about Oy. The moment of inertia of p about Oz is given by [Equation goes here - download the original to see it.]
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Contents of
Parallel and perpendicular axis theorems
1 Parallel Axis Theorem
2 Proof of the parallel axis theorem
3 Perpendicular Axis Theorem
4 Proof of the Perpendicular Axis Theorem
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