Question

Four very thin rods, each 8.3 m long, are joined to form a square. The center of mass of the square is located at the coordinate origin. The rod on the right is then removed. What are the x- and y-coordinates of the center of mass of the remaining three-rod system?

I have no idea how to approach this.

Answer 1

The center of mass of the upper rod is at (x1,y1) =(0, 4.15)
The center of mass of the left rod is at (x2,y2) =(- 4.15, 0)
The center of mass of the lower rod is at (x3,y3) =(0, - 4.15)
L = 8.3 m

Coordinates of the center of mass of the 3-rod-system are
x =(x1•L +x2•L+x3•L)/3•L =
=(0•L-4.15•L+0•L)/3•L =
= -4.15/3 =1.38 m,
y =(y1•L +y2•L+y3•L)/3•L =
=(4.15•L + 0•L - 4.15•L)/3•L = 0.