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Find the indicated moment of inertia or radius of gyration.Find the radius of gyration of a plate covering the region bounded by $x=2, x=4, y=0,$ and $y=4,$ with respect to the $y$ -axis.

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 5

Moments of Inertia

Harvey Mudd College

Baylor University

Idaho State University

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well given their wash up too equal to four And there was born the zero and the X. Up to it's B. And x. sub one. It's a. Also equal to two. No. To calculate the moment of inertia we have K times the integral of for X squared With the limits being two and 4. That's equal to Forte Tom's excellent. Third over three. I give this 22,000. I give this 224 k. Over three and then the mass of the plate stealing by the former. So we have K times the integral of four X. Dx. There are limits being 24 and we get a K. Now on the rages. Our sub Y is equal to the moment of inertia over the mets. And that gives us 3.06.

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