Wednesday, 20 October 2010

Coplanar Forces and their Rectangular Components

Coplanar forces: a set of forces is coplanar if they all lie in the same geometric plane.  In the diagram below forces F1, F2 and F3 are coplanar because the all lie in the x-y plane.  Refer to the image below.

Coplanar forces can be resolved into components along the x and y axes.  These component forces are called rectangular components.  Rectangular components can be represented in two ways:

  1. Scalar notation

  2. Cartesian vector notation

Scalar Notation: When using the scalar notation the rectangular components of force F is written Fx and Fy.

  • Fx represents the component in the x-axis

  • Fy represents the component in the y-axis

Refer to the image below.






Cartesian Vector Notation: When using the Cartesian vector notation, the rectangular components are represented in terms of unit vectors i and j.  Unit vectors are vectors that have a magnitude of one and they are used to represent direction.  In this case:

  • i represents direction in x-axis

  • j represents direction in y-axis

Refer to the image below.



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