༡། a a 0. X 2a -2a- PROBLEM 9.36 Determine the moments of inertia of the shaded area shown with respect to the x and y axes.
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- 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.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.)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).Compute the principal centroidal moments of inertia for the plane area.
- | 6"! ارچی 0 y = kx² -X 6" Determine the moment of inertia Ix, Iy and the product of inertia Ixy of the shaded area using any integration scheme.4) Calculate the moment of inertia Ix for the shaded area given below. Ay 10 cm r=10 cm 19 ➤xConsider a circular, semi-circular, and a quarter-circular steel plate, whose moment of inertia about the z-axis are Izc, Izs, and Izq, respectively. They have equal mass densities and thicknesses. Which of the following is correct? a. Izc=Izs greater than Izqb. Izcgreater thanIzs=Izqc.Izcgreater thanIzsgreater thanIzq
- Determine by direct integration the moments of inertia of the trapezoidal area about the x- and y- axes. Find the polar moment of inertia about point O. 0.8b b 1.2b Answers: Ix = .3 ly = %3D i .304 b4 lo = i .604 b42. Locate the X-X and Y-Y centroidal axes, and calculate the moments of inertia with respect to both centroidal axes for the areas shown below. 1 Inswer: (1) X: (2) y: (3) With respect to the X-X centroidal axis: With respect to the Y-Y centroidal axis: in in.What is the moment of inertia (in relativos about x axis Ixx) of the following area below?