Editing Net force (section)

== Resultant force ==
[[File:Rezultanta.JPG|thumb|500px|Graphical placing of the 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:
# Vector addition is used to find the net force;
# Use the equation to determine the point of application with zero torque:
:<math> \mathbf r \times \mathbf F_\mathrm{R} = \sum_{i=1}^N ( \mathbf r_i \times \mathbf F_i ) </math>
where <math> \mathbf F_\mathrm{R} </math> is the net force, <math> \mathbf r</math> locates its application point, and individual forces are <math> \mathbf F_i </math> with application points <math> \mathbf r_i </math>.  It may be that there is no point of application that yields a torque-free resultant.
<!----
  This paragraph confuse[s?] a resultant force and torque with a torque-free resultant:

The above equation may have no solution for <math>\mathbf r</math>. In that case, there is no resultant force, i.e. no single force can replace all actual forces regarding both linear and angular acceleration of the body. And even when <math>\mathbf r</math> can be calculated, it is not unique, because the point of application can move along the line of application without affecting the 
 ---->

The diagram opposite 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 <math>\mathbf F_{1}</math> and <math>\mathbf F_{2}</math> on the leftmost illustration intersect. After vector addition is performed "at the location of <math> \mathbf F_{1}</math>", 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 <math>\mathbf F_\mathrm{R}</math> is equal to the sum of the torques of the actual forces.
# The illustration in the middle of the diagram shows two parallel actual forces. After vector addition "at the location of <math>\mathbf F_{2}</math>", the net force is translated to the appropriate line of application, where it becomes the resultant force <math>\mathbf F_\mathrm{R}</math>. 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.
# The rightmost illustration shows a [[couple (mechanics)|couple]], two equal but opposite forces for which the amount of the net force is zero, but they produce the net torque <math>\tau = Fd </math>&nbsp;&nbsp;&nbsp;where <math>\ d </math>&nbsp; is the distance between their lines of application. Since there is no resultant force, this torque can be [is?] described as "pure" torque.