Centre of mass of uniform bodies — A/L Combined Mathematics

The centre of mass (centre of gravity in a uniform gravitational field) of a rigid body is the unique point at which the entire mass of the body may be considered concentrated for translational dynamics: r_G = (∑ m_i r_i) / (∑ m_i). Symmetry principles dictate that if a uniform body possesses a plane, axis, or centre of geometric symmetry, its centre of mass must lie on that entity: (1) Uniform thin rod: at its geometric midpoint; (2) Uniform rectangular lamina: at the intersection of its diagonals; (3) Uniform circular ring or disc: at the geometric centre; (4) Uniform sphere: at the concentric centre; (5) Triangular lamina: at the centroid (intersection of medians, 2/3 along each median from its vertex).

Check before you answer (A/L Applied Maths Paper 2)

1. Symmetry Argument Justification: Stating the existence of axes or planes of symmetry explicitly to locate coordinates of G without redundant calculations.
2. Centroid of a Triangle: Using the median ratio 2:1 from vertex to base (distance 1/3 h from base along altitude).
3. Tabular Mass-Moment Setup: Structuring discrete particle or element systems into a table listing Component, Mass, Coordinate x, and Moment mx.