Question

A square aluminum plate (volume mass ρ = 2700 kg/m^3) has dimension L = 4.8 m and e = 0.9 m. A cylinder of radius R = 1.5 m and at a distance d = 1.2 m from the center of the plate and at 20 deg with the horizontal, is removed from the plate. Find the centre of mass of this plate from the lower left corner. Note the centre of mass about for the z-axis is neglected in the answer, since it is obviously at e/2.

- I found the center of mass for the square aluminum plate before and after a cylinder part of it was removed and subtracted the values but that didn't seem to work.

Answer 1

do MOMENTS not masses

M with center of mass at center, XM, YM, ZM

subtract m with center at xm, ym, zm

now have m' with center x', y', z'
m' = M-m

m x + m' x' = M XM
so
m' x' = M XM - m x