GNG 1105 Lecture 6: Rigid Bodies part 2

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3. 8 rectangular components of the moment of a force. Resolving r and f into rectangular x, y, and z components simplifies the determination of a force in space (when we aren"t provided a known reference point). In 2d problems, assume f lies on the xy plane, meaning set z=0 and using the determinant form: Two forces f and -f having the same magnitude, parallel lines of action, and opposite sense are said to form a couple. The sum of the two forces in any direction is 0, however, the sum of the moments of the two forces about a given point is not zero. these forces rotate the rigid body, but don"t translate it. If ra and rb are the position vectors of the points of application of f and -f, then the sum of the moments of the two moments about o is: To simplify, we can set , and so the sum of the two moments of.

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