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: ˆˆ ˆ xyz =++ ri j k G () ˆ 325 m =− + + j k G P 3 t 2 t 1 Displacement Vector 12 For a particle that changes postion vector from to we define the displacement vector as follows: rr r GG G ∆=− 21 rr r GGG The position vectors and are written in terms of components as: G G 11 1 1 ˆ rijk G 222 ˆ 2 G ( ) ( ) ( ) ˆ ˆ xx yy zz x y z ∆ = + + =∆ +∆ +∆ i j k G xx x ∆= − yy y zz 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 avg xyz x y z ttt t t ∆∆ + + ∆ ∆ ∆ ∆ == = + + ∆∆∆ rij k vi j k G G Instantaneous velocity: lim 0 d td t t ∆ → v G ˆ ˆ ˆ dd x d y d z dt dt dt dt vvv =+ + = + + j k i j k vijk G G x dx v dt = y dy v dt = z dz v dt =
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5 Average and Instantaneous Acceleration The average acceleration is defined as: change in velocity average acceleration = time interval 21 avg tt == ∆∆ vv v a GG G G Instantaneous acceleration: () ˆˆ ˆ ˆ ˆ lim 0 y xz x yz xyz dv dv dv dd vvv aaa td t d t d t t = ++ = + + =++ ∆→ ai j k i j k i i k G
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Phys 0174 Fall 2008 - Chapter 04, 4 slides - Chapter 4...

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