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Equilibrium of a Particle

If a single force is acting on a particle, the particle cannot be in equilibrium. But if two forces or three forces or more than three forces are acting on the particle, the particle can be in equilibrium under certain conditions ..

When two forces are acting. If two forces are acting on a particle, the particle will be in equilibrium when the two forces are equal, opposite and collinear.

When three forces are acting. If three forces are acting on a particle, the particle will be in equilibrium when the three forces are concurrent and (i) Resultant force in x and y direction is zero i.e.,

ΣF x = 0 and Σ F y = 0

(ii) The three forces obey Lame’s Theorem* which states that “If a particle (or a body) is in equilibrium under the action of three forces, each force is proportional to the sine of the angle between other two.”

Or

(iii) The three forces form a closed triangle.

When more than three forces are acting. If more than three forces are acting on a particle, the particle will be in equilibrium when the resultant force in x and y directions is zero i.e.

ΣF x = 0 and Σ F y = 0