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 xand y. Because the yaxis is an axis of symmetry, it follows that 0.xyI=Since 0,xyI=the xand yaxes must be principal axes. Assuming maxminand ,xyIIII==the Mohr’s circle is then drawn as shown. Now rotate the coordinate axes through an angle αas 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.