134_Problem CHAPTER 9

134_Problem CHAPTER 9 - PROBLEM 9.110 Using Mohr's circle,...

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PROBLEM 9.110 Using Mohr’s circle, show that for any regular polygon (such as a pentagon) ( a ) the moment of inertia with respect to every axis through the centroid is the same, ( b ) the product of inertia with respect to every pair of rectangular axes through the centroid is zero. SOLUTION Consider the regular pentagon shown, with centroidal axes x and y . Because the y axis is an axis of symmetry, it follows that 0. xy I = Since 0, xy I = the x and y axes must be principal axes. Assuming max min and , xy I II I == the Mohr’s circle is then drawn as shown. Now rotate the coordinate axes through an angle α as shown; the resulting moments of inertia,
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This note was uploaded on 07/11/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.

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