Question

Determine the centroid of the area shown. Make clear where y you've taken the centroid relative to. If a homogeneous wire is bent about the perimeter of this shape, where is the centroid of the wire? nm r = 65 mm 125 mm 125 mm

Answer 1

First find the centroid of the semi Circular Ring - AY Toral mass of wire am 0 RCOSO As the wire is uniform, the mass per unit length of the wire is M. The mass of the element is therefore UR TR dm = M J CR dd) = A do the coordinates of centroid are x= 4 Sedm oth (iRcaso) (4) de = 0 and Y = + Syam (Reine) (N) do > Coro)" lj - 2R from the Base

now find the Centroid of whole section as ý = Aly, I A2Y2 A1-A2 ă= Aurit A2X2 ALL A2 now To AIF 125 (210) = 26, 250 mm A2 = I2 = I x 65% = 6636.6445 mm 83.62 mm X = 20 = 66- 2(65) = 28*62 mm - 125 125 X = 125 = 125+85 = 105 mm Yo = 125 mm y = ATX - A2Y) Al-A2 = 26,250 (125 )- 6636-6145(83-62) 26250 - 6636.6145 a = 55.8535mm] y = ALYI - A242 = 26250 (105) - 6636.6145 (125) Al-A2 26250 - 6636.6145 y = 98.2328 mm in arrangement the i given centroid Co-ordinate of given system is 55.3535mm, 98.2326mm/
thank you..