Equilibrium is a crucial concept in physics, enabling us to understand how forces interact with bodies to produce no or constant motion. In two-dimensional equilibrium, force systems can be classified into different categories based on their characteristics.

One of the categories of equilibrium is collinear equilibrium, which involves forces acting along a straight line. This type of equilibrium requires only one force equation in the direction of the forces, as the other equations are automatically satisfied.

Another category is the coplanar concurrent equilibrium, in which all the acting forces meet at a single point in the same plane. In this category, the forces can be resolved into their horizontal and vertical components to determine equilibrium. The vertical and horizontal forces should have an equal magnitude and be directed oppositely to balance each other.

The coplanar non-concurrent equilibrium category involves forces that are parallel but not concurrent to each other. In this type of equilibrium, the moments due to the forces are balanced, resulting in zero net force on the object. For this to happen, the moments generated by the forces should be equal but opposite in direction.

Finally, general equilibrium is the most complicated category, involving any number of forces not necessarily in one plane. This type of equilibrium requires two force equations and a moment equation to obtain a solution.