Find the centroid of the shape shwon x 445in y 6in x 475i

Find the centroid of the shape shwon: x = 4.45in, y = 6in x = 4.75in, y = 6in x = 4.92in; y = 6in x = 5.22in, y = 6in

Solution

Rcm = (m1r1 + m2r2 + m3r3) / (m1 + m2 + m3)

for Xcm ,

Xcm = [ 2(rho x 13 x 2 x (13/2)) + ( 8 x 3 x rho x (3/2)) ] / (2(rho x 13 x 2 ) + ( 8 x 3 x rho))

= 4.92 in

for Ycm,

Ycm = [ (rho x 13 x 2 x 1) + (rho x 13 x 2 x 11) + ( 8 x 3 x rho x (2+4)) ] / (2(rho x 13 x 2 ) + ( 8 x 3 x rho))

= 6 in