Statics - Parallel coplanar forces — The equilibrium of a system of coplanar forces

About this lesson

This unit covers the equilibrium of a rigid body under the action of a system of coplanar parallel forces. It begins by stating the two necessary and sufficient conditions for equilibrium: the resultant vector of the forces must vanish (R = 0) and the sum of the moments of the forces about a point must vanish (M = 0). It then introduces the use of orthogonal unit vectors (i, j, k) to resolve forces and moments, leading to the algebraic conditions X = 0, Y = 0, and M = 0. The unit provides worked examples and exercises involving uniform rods and boards resting on supports, with weights and boxes, to find reactions and tensions. It also includes problems with ladders resting against smooth or rough walls and floors, and a bar on a rough horizontal plane and a smooth wedge, involving friction and reactions. By the end, a student should be able to apply these equilibrium conditions to solve for unknown forces, reactions, tensions, and positions in various static scenarios.