Statics of a Particle Topic Review summary

Key learning points

• Resolve forces into perpendicular components; $\\sum F_x=0$, $\\sum F_y=0$.
• Friction $F\\le\\mu R$; limiting equilibrium uses $F=\\mu R$.
• Angle of friction / resultant reaction at $\\arctan\\mu$ to the normal.
• Lami’s theorem optional for three concurrent forces in some courses.
• Include weight and any tension/reaction clearly on a diagram.

Worked example 1 — Limiting

On a rough horizontal surface, pull with force $P$ at onset of slip.

Working

$F=\\mu R$ with $R=mg$.

Worked example 2 — Resolve

Why resolve into components?

Working

Choose sensible axes (often along/up the plane).

Worked example 3 — Practice point 1

Resolve forces into perpendicular components; $\\\\sum F_x=0$, $\\\\sum F_y=0$.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Practice point 2

Friction $F\\\\le\\\\mu R$; limiting equilibrium uses $F=\\\\mu R$.

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.