# Simple center of mass problem but i cant figure it out

1. Mar 9, 2005

### huk

I feel silly for ask you for help on this simple center of mass problem but i got wrong answers...

Where is the center of mass of a uniform, L-shaped iron rod of sides X = 0.8 m and Y = 0.5 m, respectively? Take the corner to be at (x,y) = (0,0), with the X and Y sides along those axes, respectively. (Assume that the rod is so narrow that the dimensions of the outer bend are the same as those of the inner bend of the L.)

i thought the answer is x = .2667m and y = .1667m perhaps my answers are wrong?

2. Mar 9, 2005

### arildno

Now, the C.O.M of the horizontal leg is (0.4,0), for the vertical leg, (0,0.25)
(Agreed?)
Let $$m_{h}=0.8\rho$$ be the mass of the horizontal leg, and $$m_{v}=0.5\rho$$ the mass of the vertical leg ($$\rho$$ being the density).
Hence, the coordinates of the C.M of the L-shaped object fulfill:
$$(x_{C.M},y_{C.M})=\frac{m_{h}(0.4,0)+m_{v}(0,0.25)}{m_{h}+m_{v}}$$