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- The uniform lamina of density 2.2 kg/m2. for a=2.2 m,b=4.8 m,c=8 m,d=8.9 m 1-The x-co-ordinate of total area centroid is: (a.8.27 - b.13.17 - c.7.05 - d.8.88 - e.6.13) 2- The y-co-ordinate of total area centroid is: (a.1.96 - b.2.68 - c.3.04 - d.1.61 - e.3.57) 3- The total mass is : ( a. 163.00 - b. 326.00 - c. 244.50 - d. 81.50 - e. 40.75 )For the surface shown in the figure below, determine:a) The xc and yc coordinates of its centroid;b)The moments of inertia and product of inertia in relation to the centroidal axes x' and y' (axes parallel to x and y , which pass through the centroid);c)Using Mohr's circle, the new moments and product of inertia obtained by rotating these centroidal axes by 35° counterclockwise.The uniform lamina of density 2.2 kg/m2. for a=2.2 m,b=4.8 m,c=8 m,d=8.9 m, 1- x-co-ordinate of shape (1) is: (a. 1.78 - b. 2.23 - c. 4.45 - d.8.90 - e. 2.97 ) 2- y-co-ordinate of centroid of shape (2) is: (a. 3.80 - b. 4.52 - c.2.33 - d. 5.28 - e. 4.60 ) 3- The total area is: (a.81.50 - b. 150.78 - c. 52.98 - d. 69.27 - e. 110.03) 4- The total mass is: ( a. 163.00 - b. 326.00 - c. 244.50 - d. 81.50 - e. 40.75 )
- For the entire section shown, the moments of inertia with respect to the centroidal x and y axes at point C are Ix = 0.162(106) mm4 and Iy = 0.454(106) mm4, respectively. a. Determine the product of inertia with respect to the centroid at C, in mm4. b. Use a Mohr's Circle to determine the orientation (in degrees) of the principal axes of the section about the centroid C. c. Use the same Mohr's Circle to determine the values of the principal moments of inertia about the centroid C, in mm4.For the in-plane composite shape shown; a) Determine the location of centroid C(x,y) b) Moments of inertia components w.r.t x and y axes (Ix, Iy,Ixy) c) Principle moments of inertia (Imax, Imin) using Mohr’s circleFind the centroid (x̄, ȳ) of the cross-sectional area, given: L1 = 7 in, L2 = 9 in, L3 = 3.6 in, L4 = 2.8 in, L5 = 1.5 in
- A circular cylinder is welded on the center of the base of a rectangular prism, forming a hammer-like object. The mass of the cylinder is 2kg, and the mass of the rectangular prism is 10kg. The origin of the rectangular axes is at the centroid of the cylinder. Determine the following: 1. moment of intertia about the z-axis 2. radius of gyration about the z-axisA 100×100 paper was punched from its left lower corner. A 25×25 square hole was created there. The 25×25 scrap was subsequently glued onto right upper corner of the paper. By neglecting the thickness of the paper,a) Determine the centroid of this composite area,b) Calculate the moments of inertia Ix, Iy and product of inertia, Ixy.c) Determine the principal moments of inertia and the orientation of the principal axes.(a=3 b=1)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.
- For the composite area shown in the image below, if the dimensions are a=28mm, b=218mm, c=282mm, and d=148mm, determine its area moment of inertia Ix' (in 10^6 mm^4) about the centroidal horizontal x'-axis (not shown) that passes through point C. Have 2 places after the decimal point.It is known that for a given area Iy = 48 x 106 mm4 and Ixy = -20 x 106 mm4, where the x and y axes are rectangular centroidal axes. If the axis corresponding to the maximum product of inertia is obtained by rotating the x axis 67.5° counterclockwise about C , use Mohr’s circle to determine (a) the moment of inertia Ix of the area, (b) the principal centroidal moments of inertia.Determine the Moment of Inertia about both Centroids I-sub-x, and I-sub-y -Divide into shapes -Determine the centroid -Set up TABLE - Shape, AREA, x, y, x^2*AREA, y^2*AREA - Compute the Moment of Inertias with PARALLEL AXIS THEREOM I-sub-x =SUM(I-sub-x-sub-(SELF) + Ad^2)