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Lecture 4 part II - PART II CONTENTS VECTOR REPRESENTATION...

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15 PART II CONTENTS: VECTOR REPRESENTATION OF A MOMENT MOMENT OF A FORCE ABOUT A LINE (AXIS) COUPLES
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16 VECTOR REPRESENTATION OF A MOMENT In Fig. 4-1, the moment of the force F about point O can be represented by the expression O = × M r F (9) where r is a position vector from point O to a point A on the line of action of the force F . The sign × means the cross product of two vectors, and is defined as sin sin O α α = × = = M r F r F e F r e Disp where α is the angle (0 180 ) α ° ° between the two vectors r and F , e is a unit vector perpendicular to the plane determined by vectors r and F as shown in Fig. 4-3 a . It can be seen that the term | | sin α r denotes the perpendicular distance d from the moment center O to the line of action. The distance d is independent of the position A along the line of action of the force since A 3 A 2 A 1
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