Find the centre of mass of a uniform plate having semicircular inner and outer boundaries of radii R1 and R2 (figure 9-E5).
The x coordinate of centre of mass will be 0.
Let the mass per unit of the plate be m.
Mass of the semi-circular plate having radius R2 = m2 = ϖ(R2)2m
Mass of the semi-circular plate having radius R1 = m1 = ϖ(R1)2m
y-coordinate of centre of mass of semi-circular plate having radius R2 = y2 = 4R2/3ϖ
y-coordinate of centre of mass of semi-circular plate having radius R1 = y1 = 4R1/3ϖ