Problem 2. Two uniform thin plates of mass 2 kg each are welded into a shaft...

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Problem 2. Two uniform thin plates of mass 2 kg each are welded into a shaft of negligible mass. Each plate is a spare plate of length b = 0.4 m and width b = 0.4 m. Find: a. The location of the composite mass center for the assembly. b. The moment of inertia of the assembly about the assembly's center of mass G. c. Use Matlab to find the principal moments of inertia and the principal axes. Draw these axes (approximately) on the provided figure. B b 12 clear 2 clc 3 4 % The value below is the inertia tensor for the problem in the Moment of 569 % Inertia handout. Each row is seperated by a ; 6 I = [0.0258, -0.0037, -0.0022; -0.0037, 0.0102, -0.0101; -0.0022, -0.0101, 0.0183] 7 8 % Finding the principal Moments of Inertia and the axes of inertia 9 10 [v, d] = eig(1) %v: principal moments of inertia, d directional cosines for axes of inertia 11 12 plot3([0,1],[0,0], [0,0], 'k', 'LineWidth', 1.5) 13 hold on 14 plot3([0,0], [0,1],[0,0], 'k', 'LineWidth', 1.5) 15 plot3([0,0], [0,0],[0,1], 'k', 'LineWidth', 1.5) 16 xlabel 'x' 17 ylabel 'y' 18 zlabel 'z' 19 222222 20 21 23 24 grid 25 v = [0.1819, -0.1587, -0.9704; 0.8156, -0.5269, 0.2391; 0.5492, 0.8350, -0.0336] cosines = acosd (v) %angles between the principal axes and x,y,z plot3([0,v(1,1)], [0,v(2,1)],[0,v(3,1)], 'LineWidth',1.5) plot3([0,v(1,2)], [0, v(2,2)], [0,v(3,2)], 'LineWidth',1.5) plot3([0,v(1,3)], [0,v(2,3)], [0,v(3,3)], 'LineWidth', 1.5) Problem 2. Two uniform thin plates of mass 2 kg each are welded into a shaft of negligible mass. Each plate is a spare plate of length b = 0.4 m and width b = 0.4 m. Find: a. The location of the composite mass center for the assembly. b. The moment of inertia of the assembly about the assembly's center of mass G. c. Use Matlab to find the principal moments of inertia and the principal axes. Draw these axes (approximately) on the provided figure. B b 12 clear 2 clc 3 4 % The value below is the inertia tensor for the problem in the Moment of 569 % Inertia handout. Each row is seperated by a ; 6 I = [0.0258, -0.0037, -0.0022; -0.0037, 0.0102, -0.0101; -0.0022, -0.0101, 0.0183] 7 8 % Finding the principal Moments of Inertia and the axes of inertia 9 10 [v, d] = eig(1) %v: principal moments of inertia, d directional cosines for axes of inertia 11 12 plot3([0,1],[0,0], [0,0], 'k', 'LineWidth', 1.5) 13 hold on 14 plot3([0,0], [0,1],[0,0], 'k', 'LineWidth', 1.5) 15 plot3([0,0], [0,0],[0,1], 'k', 'LineWidth', 1.5) 16 xlabel 'x' 17 ylabel 'y' 18 zlabel 'z' 19 222222 20 21 23 24 grid 25 v = [0.1819, -0.1587, -0.9704; 0.8156, -0.5269, 0.2391; 0.5492, 0.8350, -0.0336] cosines = acosd (v) %angles between the principal axes and x,y,z plot3([0,v(1,1)], [0,v(2,1)],[0,v(3,1)], 'LineWidth',1.5) plot3([0,v(1,2)], [0, v(2,2)], [0,v(3,2)], 'LineWidth',1.5) plot3([0,v(1,3)], [0,v(2,3)], [0,v(3,3)], 'LineWidth', 1.5)