lecture03_Jan19

lecture03_Jan19 - Vectors 2-D Kinematics Relative Velocity...

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Page ± Vectors ± 2-D Kinematics ± Relative Velocity Vectors Vectors z Vectors have both magnitude and direction Displacement vector velocity vector force vector acceleration vector vectors in circular motion Vectors are denoted by an arrow on the symbol: A (or bold letters A )
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Page Addition of Vectors Addition of Vectors (geometric method) (geometric method) Click here for head to tail parallelogram Addition of Vectors Addition of Vectors (geometric method) (geometric method) Addition of 3 vectors What about subtraction of two vectors?
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Page Vectors by Components Vectors by Components z A vector can be specified in different ways Í by length and direction (A and θ ), or Í by components: A = (A x , A y ) Í a coordinate system is needed: angle relative to +x axis. z The two ways are equivalent Click here for components θ sin cos A A A A y x = = x y y x A A A A A = + = tan 2 2 Unit Vectors Unit Vectors j A i A A A A y x y x ˆ ˆ ) , ( + = = r k A j A i A A A A A z y x z y x ˆ ˆ ˆ ) , , ( + + = = r Notations: 3-dimensional ˆ , ˆ , ˆ of instead , ˆ , ˆ , ˆ as denoted are rs unit vecto Cartesian 3 the Sometimes k j i z y x
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Page Addition of Vectors Addition of Vectors (components method) (components method) Given ) , ( ˆ ) ( ˆ ) ( y y x x y y x x B A B A j B A i B A B A R + + = + + + = + = r r r Then Example: What is the sum of two vectors (5,3) and (-2,1)? Answer: (5-2,3+1) = (3,4)
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lecture03_Jan19 - Vectors 2-D Kinematics Relative Velocity...

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