For a given area the moments of inertia with respect to two rectangular centroidal x and y axes are I x 640 in 4 and I y 280 in 4 , respectively Knowing that after rotating the x and y axes about the centroid 60 clockwise the product of inertia relative to the rotated axes is 180 in 4 , use Mohrs c...

Lave x y 640 in 280 in 460 in x Iy 640 in 280 in 180 in xy 180 in 20 120 Ix ...

For a given area the moments of inertia with respect to two rectangular centroidal x and y

Question:

For a given area the moments of inertia with respect to two rectangular centroidal x and y axes are I_x = 640 in⁴ and I_y = 280 in⁴, respectively. Knowing that after rotating the x and y axes about the centroid 60° clockwise the product of inertia relative to the rotated axes is −180 in⁴, use Mohr’s circle to determine

(a) The orientation of the principal axes,

(b) The centroidal principal moments of inertia.