EXAMPLE 3 Find the moments and center of mass of the system of objects that have masses 4, 3, and 6 at the point (-1, 1), (2, -1), and (3, 2), respectively.
SOLUTION We use the following equations to compute the moments:
My = 4(-1) + 3(2) + 6(3) =
Mx = 4(1) + 3(-1) + 6(2) =
Since m = 4 + 3 + 6 =
, we use these equations to obtain
x = My / m =
y = Mx / m =
Thus the center of mass is (x, y) =
. (See the figure.)
