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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.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).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 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.
- Determine the mass moment of inertia of the figure shown about the x, y and z axis. The materials weighs 500N/m3. Also determine the radius of gyration about each axis.Find the moment of inertia of a solid parallelepiped of homogeneous mass density, mass M, and sides of length a, b, and c with respect to: a) One of its principal axes of inertia b) An axis at a distance d from its center and parallel to the previous axis of rotation.In the figure the L- shaped machine part is composed of two homogeneous bars . Bar 1 is tungsten alloy with mass density 14,000 kg/m3 , and bar 2 is steel with mass density 7800 kg/m3 . Determine its moment of inertia about the x axis.