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Statics: Offset Forces

When solving a statics problem, there can be times when the force applied may be at an angle to the coordinate system. Typically when solving a statics problem you would want to solve for forces that are purely in the x, y, and z directions. To solve a problem like this you would have to either reorient your coordinate system, or you would have solve for the amount of force that is in the particular directions that are affected.

When you have a force that is at an angle it can be represented in to different ways. First, that angle of orientation could be stated. But, in some cases there would be a right angle triangle with different number values along the legs and hypotenuse of the triangle. Those values state the contribution of the force in each direction. Refer to the figure below.

Different methods on how to deal with a force that is offset from the main coordinate system of a statics problem

Magnitude and Angle

In addition to being able to calculate the forces in the x, y, and z directions, sometimes you may want to calculate the magnitude of all of those forces combined and the angle that the force is offset from the coordinate system. To calculate the magnitude equation 1 would be used. To calculate the orientation based off of the x-axis for a 2 dimensional problem equation 2 would be used.

How to calculate the magnitude for forces going in different directions (1)

How to calculate the angle of a force offset from the main coordinate system (2)

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