Explain the conditions of static equilibrium for both coplanar concurrent and non-concurrent force systems.

Static equilibrium refers to a state where a body is at rest or moving at a constant velocity. For a body to be in static equilibrium under the action of forces, two conditions must be satisfied:

1. The vector sum of all forces acting on the body must be zero. This is also known as the equilibrium condition of translational equilibrium. Mathematically, it can be represented as ∑F = 0. This means that the sum of all forces in the x-direction is zero, and the sum of all forces in the y-direction is also zero. This condition ensures that the body does not translate, i.e., it does not move linearly in any direction.

2. The sum of all moments (or torques) about any point must also be zero. This is known as the equilibrium condition of rotational equilibrium. Mathematically, it can be represented as ∑M = 0. This condition ensures that the body does not rotate about any point.

These conditions apply to both coplanar concurrent and non-concurrent force systems.

In a coplanar concurrent force system, all forces act in the same plane and intersect at a common point. In this case, we only need to consider the sum of forces because the sum of moments will automatically be zero as all forces pass through the same point.

In a coplanar non-concurrent force system, forces act in the same plane but do not intersect at a common point. In this case, we need to consider both the sum of forces and the sum of moments. The sum of forces ensures that the body does not translate in the plane, and the sum of moments ensures that the body does not rotate in the plane.