# Net Force - Resultant Force

Resultant Force

Resultant force and torque replaces the effects of a system of forces acting on the movement of a rigid body. An interesting special case is a torque-free resultant which can be found as follows:

1. First, vector addition is used to find the net force;
2. Then use the equation to determine the point of application with zero torque:

where is the net force, locates its application point, and individual forces are with application points . It may be that there is no point of application that yields a torque-free resultant.

The diagram illustrates simple graphical methods for finding the line of application of the resultant force of simple planar systems.

1. Lines of application of the actual forces and on 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.
2. 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, where it becomes the resultant force . The procedure is based on 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.
3. 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. This is "pure" torque, since there is no resultant force.

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The use of force alone is but temporary. It may subdue for a moment; but it does not remove the necessity of subduing again: and a nation is not governed, which is perpetually to be conquered.
Edmund Burke (1729–1797)