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

The centre of mass of a composite body assembled from multiple sub-bodies is determined using the Principle of Moments: M_total X_G = ∑ m_i x_i, where M_total = ∑ m_i. The coordinates of the sub-components are established with respect to a common reference origin. For a 'remainder body' (a parent body from which a portion has been removed or hollowed out), the mass moment equation is formulated as: M_rem X_rem = M_parent X_parent - M_removed X_removed, where M_rem = M_parent - M_removed. Relative masses are expressed in terms of lengths (wires), surface areas (uniform sheets), or volumes (uniform solids).

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

1. Common Axis Origin Alignment: Measuring all component distances from the exact same reference origin or base edge.
2. Subtraction in Remainder Bodies: Accurately subtracting the mass and moment of the removed cavity from the intact parent body.
3. Dimension Proportionality: Substituting mass ratios proportional to areas or volumes when density is uniform, simplifying out constant factors.