Resultant of Concurrent Force System:
The resolution of forces helps in finding out the resultant of a number of forces working on a body as it decrease vectorial addition to algebraic addition.
If more than two coplanar, concurrent forces are working on a body, the analytical method of seeking resultant is quicker. Each of the force is resolved out into two mutually perpendicular axes say x and y. All of the components along with the respective axes are added algebraically to obtain the components of the resultant R along x and y axes. Therefore, we obtain
tan θ_{x} = ∑ F_{y} / ∑ F_{x}
where, θ_{x} = angle which the resultant R makes with the x-axis.
In particular case of non-coplanar forces, the given force is resolved out into three mutually perpendicular axes system, for example. x, y and z axes. Therefore, we obtain
cos θ_{x} = ∑ F_{x} / R, cos θ _{y }=∑ Fy / R, cos θ_{z }= ∑ Fz/ R
where ∑ F_{x} , ∑ F_{y } and ∑ F_{z} are the algebraic sums of the components of all of the forces along with x, y and z axes, respectively. The angles θ_{x}, θ_{y }and θ_{z} are the angles which the resultant R makes along with x, y and z axes, respectively.
The measure of the property of a force through virtue of which it tends to rotate the body on which it behaves is called the moment of a force.
A couple is a force system contains two equal, coplanar, parallel forces working in opposite direction.