3.2.3—Centre of mass

A uniform rod, rectangle, circle or sphere has its centre of mass at its geometric centre. Symmetry means equal mass is distributed at equal distances on opposite sides of the symmetry line or plane.

For a composite lamina, split the shape into standard pieces, assign each area as its mass when density and thickness are uniform, and use an area-weighted coordinate average.

A uniform L-shape can be treated as a large rectangle minus a cut-out rectangle; subtract the cut-out’s area moment rather than averaging the two visible arms.

The cut-out is negative area only in the calculation; it is not a negative physical mass, and the uniform-density assumption must be stated.