Systems of coplanar forces (statics) — A/L Combined Mathematics

What must I remember about Systems of coplanar forces (statics)?

• Reduction of a general coplanar force system: Any system of coplanar forces can be reduced to a single resultant force R acting at an arbitrary base point O together with a single couple of moment G.
• Condition for reduction to a single force: If R ≠ 0, shifting base point by perpendicular distance x = G / R reduces the system to a SINGLE force R with zero couple.
• Condition for reduction to a couple: If R = 0 (Rx = 0 and Ry = 0) and G ≠ 0, the system reduces to a pure couple of moment G.
• Complete equilibrium criterion: System reduces to nothing (complete equilibrium) if and only if R = 0 AND G = 0.
• Lami's Theorem: If three coplanar forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces: P / sin α = Q / sin β = R / sin γ.

Test yourself (1 minute)

1. Equation of line of action of resultant

   The line of action of the single resultant force R has Cartesian equation: x*Ry - y*Rx = G (taking origin as reference point where G is sum of moments about origin).

2. Triangle of Forces

   If three coplanar forces acting on a particle are in equilibrium, they can be represented in magnitude and direction by the sides of a closed triangle taken in order.

3. Polygon of Forces

   If n coplanar forces acting on a particle are in equilibrium, the vector polygon formed by drawing the forces head-to-tail must be completely closed.

Practise Systems of coplanar forces (statics) questions today

Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Applied Mathematics, Unit 2

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Year 2 · Term 2