Lecture04_Vectors_Review

Lecture04_Vectors_Review - Typical applications MOMENT OF A...

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27 Typical applications ± MOMENT OF A FORCE In mechanics the moment m of a force F about a point Q is defined as the product m = ⎪⎢ F d d = r ⎢⎢ sin θ r F d r F m r r r × = = ˆ sin m is called the moment vector or vector moment of F about Q where d is the (perpendicular) distance between Q and the line of action L on F . Q d = r s i n If r is the vector from Q to any point A on L , then
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28 •Torque T = r x F • Force on a moving charge due to a magnetic field due to F B v q F = q v x B • Velocity of a rotating body v = w x r ω = angular speed |w| = ω and directed along axis of rotation w r v ω o More Applications
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29 ¾ Two non-zero vectors A and B are parallel if & if : 0 B A = × r r j k i i j k k i j j i k i k j k j i ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ = × = × = × = × = × = × • Circular Mnemonic : • More Cross Product Properties: ¾ Cross product is not commutative: A B B A A B B A r r r r r r r r × = × × × ¾
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Lecture04_Vectors_Review - Typical applications MOMENT OF A...

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