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Lecture 4 - Trajectories

Lecture 4 - Trajectories - Trajectories r r r lim r t t r t...

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Trajectories
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( 29 ( 29 ( 29 lim 0 ˆ ˆ ˆ r t t r t dr v t t t dt dr dx dy dz i j k dt dt dt dt + ∆ - = = ∆ → = + + r r r r r
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( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 ˆ ˆ cos sin ˆ ˆ sin cos ˆ ˆ cos sin ˆ t r i r j r v i r j r a i r j r r v r r ϖ θ θ ϖ θ ϖ θ ϖ θ ϖ θ ϖ = + = - + = - - = - = - ] r r r r
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( 29 2 2 Uniform circular motion constant also does uniform circular motion a is antiparallel to circumference -circle 2 period r v r v r v v r v v a v t v a r r ϖ π ϖ ϖ = = = = = = = r r r r r
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( 29 ( 29 ˆ ˆ cos sin Uniform circular motion constant constant in radiants/second 2 r i r j r r t T θ θ θ ϖ ϖ π ϖ = + = = = = r r
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4 4
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