Chapter_3 - Ch 3: Vectors Focus: Vectors A, Independent...

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Ch 3: Vectors Focus: Vectors A, Independent Components Scalar: Mass- magnitude only Vector: Magnitude and direction, e.g., velocity, force R Specify by Components: R x R y o x y θ sin cos R R R R y x = = 2 2 y x R R R + = = R Magnitude: = x y R R tan Arc Angle:
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Ch 3: Vectors Vector Algebra A B Equality: A = B A x = B x , A y = B y , A z =B z o x y Key idea: Independent components Addition: C = A + B C x = A x +B x , C y = A y +B y , C z = A z +B z A -B C C = A + B C C = A - B = A + (-B) o x y Subtraction: “Head-to-tail method”
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Ch 3: Vectors Unit Vectors: A = k ˆ , j ˆ , i ˆ = Directions of x,y,z i ˆ A x j ˆ + A y k ˆ +A z A o x y Just Vector Addition o x y A j ˆ A y i ˆ A x x 1 y A = A x1 1 i ˆ Which is correct? Both! 2 1 2 2 x y x A A A = + = A Magnitude is a scalar :
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Rate of Change of Vectors: A(t) k j i A ˆ A ˆ A ˆ A z y x + + = A k j i A ˆ A ˆ A ˆ A z y x t t t t + + = Rate of change of
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Chapter_3 - Ch 3: Vectors Focus: Vectors A, Independent...

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