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Concept
Resultant force
Summary
In physics and engineering, a resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition. The defining feature of a resultant force, or resultant force-torque, is that it has the same effect on the rigid body as the original system of forces. Calculating and visualizing the resultant force on a body is done through computational analysis, or (in the case of sufficiently simple systems) a free body diagram.
The point of application of the resultant force determines its associated torque. The term resultant force should be understood to refer to both the forces and torques acting on a rigid body, which is why some use the term resultant force–torque.
The diagram illustrates simple graphical methods for finding the line of application of the resultant force of simple planar systems.
Lines of application of the actual forces and in the leftmost illustration intersect. After vector addition is performed "at the location of ", the net force obtained is translated so that its line of application passes through the common intersection point. With respect to that point all torques are zero, so the torque of the resultant force is equal to the sum of the torques of the actual forces.
Illustration in the middle of the diagram shows two parallel actual forces. After vector addition "at the location of ", the net force is translated to the appropriate line of application, whereof it becomes the resultant force . The procedure is based on a decomposition of all forces into components for which the lines of application (pale dotted lines) intersect at one point (the so-called pole, arbitrarily set at the right side of the illustration). Then the arguments from the previous case are applied to the forces and their components to demonstrate the torque relationships.
The rightmost illustration shows a couple, two equal but opposite forces for which the amount of the net force is zero, but they produce the net torque where is the distance between their lines of application.
Official source
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