# Coplanar Forces

Coplanar forces means the forces in a plane. When several forces act on a body, then they are called a force system or a system of forces. In a system in which all the forces lie in the same plane, it is known as coplanar force system. Hence this article deals with a system of forces which are acting in the same plane and the forces are either having a common line of action or intersecting at a common point. If the forces are having common line of action, then they are known as collinear whereas if the forces intersect at a common point, then they are known as concurrent.

A force system may be coplanar or non-coplanar. If in a system all the forces lie in the same plane then the force system is known as coplanar. But if in a system all the forces lie in different planes, then the force system is known as non-coplanar. Hence a force system is classified as shown in Fig. 1.31.

Here we shall discuss only coplanar force system, in which the forces may be :

(i) Collinear

(ii) Concurrent

(iii) Parallel

(iv) Non-concurrent, non-parallel (or General system of forces).

1.9.1. Coplanar Collinear. Fig. 1.32 shows three forces F1 F 2 and F3 acting in a plane. These three forces are in the same line i.e., these three forces are having a common line of action. This system of forces is known as coplanar collinear force system. Hence in coplanar collinear system of forces, all the forces act in the same plane and have a common line of action.

Fig. 1.32. Coplanar collinear forces

1.9.2. Coplanar Concurrent. Fig. 1.33 shows three forces F1 F 2 and F 3 acting in a plane and these forces intersect or meet at a common point 0. This system of forces is known as coplanar concurrent force system. Hence in coplanar concurrent system of forces, all the forces act in the same plane and they intersect at a common point.

Fig. 1.33. Concurrent coplanar forces

1.9.3. Coplanar Parallel. Fig. 1.34 shows three forces F1 F2 and F3 acting in a plane and these forces are parallel. This system of forces is known as coplanar parallel force system. Hence in coplanar parallel system of forces, all the forces act in the same plane and are parallel.

Fig. 1.34. Coplanar parallel forces.

1.9.4. Coplanar Non concurrent Non-parallei. Fig. 1.35 shows four forces F1, F2 , F3 and F4 acting in a plane. The lines of action of these forces lie in the same plane but they are neither parallel nor meet or intersect at a common point. This system of forces is known as coplanar non-concurrent non-parallel force system. Hence in coplanar non-concurrent non-parallel system of forces, all the forces act in the same plane but the forces are neither parallel nor meet at a common point. This force system is also known as general system of forces.

Fig. 1.35. Non-concurrent non-parallel