Centre of Mass Topic Review summary

Key learning points

• For particles: $\\bar{x}=\\frac{\\sum m_i x_i}{\\sum m_i}$ (similarly $\\bar{y}$).
• Uniform lamina: centre at the geometric centroid (tables for standard shapes).
• Composite body: treat each part’s mass at its own centre, then combine.
• Suspended equilibrium: centre of mass vertically below the pivot.
• Toppling: consider whether the vertical through the CoM falls outside the base.

Worked example 1 — Particles

Masses 2 at $x=0$ and 4 at $x=3$. $\\bar x$?

Working

$\\frac{0+12}{6}$.

Worked example 2 — Composite

Strategy for an L-shape lamina.

Working

Or subtract a cut-out.

Worked example 3 — For particles: \\\x=\\\\\\\sum m_i x_i{\\\

For particles: $\\\\bar{x}=\\\\frac{\\\\sum m_i x_i}{\\\\sum m_i}$ (similarly $\\\\bar{y}$).

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Uniform lamina: centre at the geometric ce

Apply this idea from the Topic Review: Uniform lamina: centre at the geometric centroid (tables for standard shapes).

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.