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Phys 0174 Fall 2008 - Chapter 04, 4 slides

Phys 0174 Fall 2008 - Chapter 04, 4 slides - Chapter 4...

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1 Chapter 4 Motion in Two and Three Dimensions ¾ Displacement ¾ Average and instantaneous velocity ¾ Average and instantaneous acceleration ¾ Projectile motion ¾ Uniform circular motion 2 Position Vector The position vector of a particle is defined as a vector whose tail is at a reference point (usually the origin O) and its tip is at the particle at point P. The position vecto Exampl r in t e: he f r G igure is: ˆ ˆ ˆ x y z = + + r i j k G ( ) ˆ ˆ ˆ 3 2 5 m = − + + r i j k G P 3 t 2 t 1 Displacement Vector 1 2 For a particle that changes postion vector from to we define the displacement vector as follows: r r r G G G = 2 1 r r r G G G The position vectors and are written in terms of components as: 1 2 r r G G 1 1 1 1 ˆ ˆ ˆ x y z = + + r i j k G 2 2 2 ˆ ˆ ˆ x y z = + + 2 r i j k G ( ) ( ) ( ) 2 1 2 1 2 1 ˆ ˆ ˆ ˆ ˆ ˆ x x y y z z x y z = + + = ∆ + ∆ + ∆ r i j k i j k G 2 1 x x x = 2 1 y y y = 2 1 z z z = The displacement can then be written as: r G 4 t t + t Average and Instantaneous Velocity Following the same approach as in chapter 2 we define the average velocity as: displacement average velocity = time interval ˆ ˆ ˆ ˆ ˆ ˆ avg x y z x y z t t t t t + ∆ + ∆ = = = + + r i j k v i j k G G Instantaneous velocity: lim 0 d t dt t = = ∆ → r r v G G G ( ) ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ x y z d dx dy dz x y z dt dt dt dt v v v = + + = + + = + + v i j k i j k v i j k G G x dx v dt = y dy v dt = z dz v dt =

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Phys 0174 Fall 2008 - Chapter 04, 4 slides - Chapter 4...

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