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Resultant of Concurrent Forces in 3D
Add concurrent forces in space component by component and find the magnitude and direction angles of the resultant.
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Problem
Forces Along the Axes
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Resultant of Coplanar Forces by Rectangular Components
Add any number of coplanar forces by summing x and y components, and find an unknown force from a known resultant.
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Cartesian Vectors in 3D: Components and Direction Angles
Describe a force in 3D with i, j, k components, its magnitude, coordinate direction angles and unit vector.
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Adding Forces: Parallelogram Law and Triangle Rule
Find the resultant of two or more forces with the parallelogram law, the triangle rule and the laws of sines and cosines.
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5
Force Vector Directed Along a Line Using Position Vectors
Write a cable or rope force as a Cartesian vector from the coordinates of two points, using position and unit vectors.
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Dot Product: Angle Between Vectors and Projection of a Force
Use the dot product to find the angle between two lines and the parallel and perpendicular components of a force.
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Rectangular Components of a Force in 2D
Write a force by its x and y components, in scalar and Cartesian vector form, and get its magnitude and direction back.
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8
What Is Mechanics
Learn what mechanics studies, how it splits into statics, dynamics and other branches, and why statics comes first.
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Scalars and Vectors in Statics
What makes force a vector, how vectors are drawn and written, and how free, sliding and fixed vectors differ.
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Resolving a Force into Components Along Two Axes
Split a force into components along any two given directions, and see why oblique components are not projections.
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