Chapter_11 - Ch 11: Cross Product Focus: Intro to Ch 11:...

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Ch 11: Cross Product Focus: Intro to Ch 11: Cross Product and Torque in 3 Dimensions Key idea: r rotates out of paper about ω axis. Example: Velocity due to rotation of the position vector r ω θ 1 θ 2 x y r ) sin( 1 2 θ ω = = r r v Speed: Direction: out of paper along z ) cos sin cos (sin 2 1 1 2 = r v z Tip of r makes circle of radius r 2 1 2 1 cos sin sin cos r r v z = ω x y ω y x x y v y x z = Cross Product B A C × = x y z ω y x y z ω x v along + z (out) v along -z (in)
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ω acts like a vector along the rotation axis (of magnitude ω ) Direction : Right-hand-rule Rotate A into B with fingers (closest way), thumb points along C AB θ sin B A C = Magnitude: B A C × = Vector Define Cross Product A B C A B C - × = x y y x z B A B A C = Can show from cross products of unit vectors: x y v y x z ω = Compare to velocity: 21 sin r r v = = Speed: * = ω Try right-hand-rule on previous slide!
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This note was uploaded on 05/13/2010 for the course PHYSICS 53L taught by Professor Mueller during the Fall '07 term at Duke.

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Chapter_11 - Ch 11: Cross Product Focus: Intro to Ch 11:...

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