Conditions of equilibrium for a rigid body in a plane State the necessary conditions that must be satisfied simultaneously for a coplanar force system to be in static equilibrium.

Introduction / Context:
To ensure a rigid body in a plane does not translate or rotate, three independent equilibrium equations are required. These are the foundation of structural analysis, machine design, and statics problem solving.

Given Data / Assumptions:

• Coplanar forces acting on a rigid body.
• Classical statics (no acceleration).
• Any reference point may be chosen for taking moments.

Concept / Approach:

Equilibrium demands zero net translation and zero net rotation. Translational equilibrium in 2D requires ΣH = 0 and ΣV = 0. Rotational equilibrium requires ΣM = 0 about any point (if it is zero about one point and ΣH = ΣV = 0, it is zero about all points).

Step-by-Step Solution:

Verification / Alternative check:

Choosing different moment centers yields consistent results when ΣH = ΣV = 0; otherwise, contradictions appear, revealing imbalance.

Why Other Options Are Wrong:

(a), (b), or (c) alone do not prevent the other type of motion; (e) ignores translational equilibrium.

Common Pitfalls:

Forgetting to include couple moments; assuming ΣM = 0 about one special point is sufficient without verifying forces sum to zero.

Final Answer:

All three: ΣH = 0, ΣV = 0, and ΣM = 0.