Determine the centroidal moment of inertia I, and I, of the plane area shown.
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Q: Determine the moment of inertia (mm4) Īx of the area shown with respect to the horizontal line that…
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Q: Determine the moments of inertia I, and I, of the area shown with respect to centroidal axes…
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- 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 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.
- 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.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.Determine the centroid of the shaded area shown in figure 2. Determine the moment of inertia about y-axis of the shaded area shown in figure 2
- A17. Determine the moment of inertia of the area represented in figure P-A17, with respect to the centroidal axes X, and Y.. materialesDetermine the product of inertia of the beam’s cross-sectional area, shown in Figure, about the x and y centroidal axes.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.
- Determine the product of inertia of the beam’s cross-sectional area,shown in Fig. A–a, about the x and y centroidal axes.Determine the moment of inertia about the horzontal axis through the centroid, x bar of the composite shape. Also, determine the moment of inertia about the vertical axis through the centroid, y bar of the composite shapeProve that the centroidal polar moment of inertia of a given area A cannot be smaller than A2/2π (Hint:Compare the moment of inertia of the given area with the moment of inertia of a circle that has the same area and the same centroid.)