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- Determine the product of inertia with respect to the x- and y-axes for the quarter circular, thin ring (tR) by integration.The product of inertia of triangle (a) with respect to its centroid is Ixy=b2h2/72. What is Ixy for triangles (b)-(d)? (Hint: Investigate the signs in the expression Ixy=IxyAxy.)Using integration, compute the polar moment of inertia about point O for the circular sector. Check your result with Table 9.2.
- Using Ix and Iu from Table 9.2, determine the moment of inertia of the circular sector about the OB-axis. Check your result for =45 with that given for a quarter circle in Table 9.2.The moments of inertia of the plane region about the x- and u-axes are Ix=0.4ft4 and Iu=0.6ft4, respectively. Determine y (the y-coordinate of the centroid C) and Ix (the moment of inertia about the centroidal x-axis).The moment of inertia of the plane region about the x-axis and the centroidal x-axis are Ix=0.35ft4 and Ix=0.08in.4, respectively. Determine the coordinate y of the centroid and the moment of inertia of the region about the u-axis.
- Compute the principal centroidal moments of inertia for the plane area.The L806010-mm structural angle has the following cross-sectional properties: Ix=0.808106mm4,Iy=0.388106mm4, and I2=0.213106mm4, where I2 is a centroidal principal moment of inertia. Assuming that Ixy is negative, compute (a) I1 (the other centroidal principal moment of inertia); and (b) the principal directions at the centroid.Consider the plate shown below (shaded area) [b = 4 mm]. What is the moment of inertia about the X-axis? What is the moment of inertia about the Y-axis? What is the polar radius of gyration (Ko)?
- a. Locate the centroid of the cross-sectional área. B. Determine the moments of inertia and the product of inertia about the XY axes with origin at C. C. Determine the principal moments of inertia with respect to the axes Ѵ,ꭒ rotated 60° as shown in figure N°3. D. Draw Mohr's circle for principal moments Ix, Iy.what is the right answer and solution? Determine the moments of inertia of the shaded area about the x- and y-axes. Also determine the polar moment of inertia about point O.