Statics and Equilibrium

This lesson covers statics — the study of bodies in equilibrium — as required by the Edexcel 9MA0 A-Level Mathematics specification. You need to solve problems where forces and moments are in balance.

---

Conditions for Equilibrium

A body is in static equilibrium when:

1. The resultant force is zero (no acceleration).
2. The resultant moment about any point is zero (no rotation).

For a particle (no size, so no rotation):

• Only condition 1 applies.
• Resolve forces in two perpendicular directions and set each component sum to zero.

For a rigid body (has size, can rotate):

• Both conditions apply.
• Resolve forces AND take moments.

---

Resolving Forces

To check equilibrium, resolve all forces into two perpendicular directions (usually horizontal and vertical).

Horizontal equilibrium: ΣFx = 0 Vertical equilibrium: ΣFy = 0

Example: Three forces act on a particle: 10 N horizontally to the right, 6 N at 60° above the horizontal to the left, and a force P vertically downwards.

Horizontal: 10 - 6 cos 60° = 0? → 10 - 3 = 7 ≠ 0.