Dynamics+Eqtn+Sheet_S10+Exam+2 - = = = = Conservation of...

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ES 2120 Exam 2 Equation Sheet Name:____________________________ Cartesian Coordinates k z j y i x dt v d k a j a i a a k z j y i x dt r d k v j v i v v k z j y i x r z y x z y x ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ + + = = + + = + + = = + + = + + = Normal & Tangential Motion n t n n t t t t u v u dt dv u a u a a u dt ds u v v ˆ ˆ ˆ ˆ ˆ ˆ 2 + = + = = = ρ Radius of curvature, ρ + = 2 2 2 3 2 1 dx y d dx dy ρ Work-Energy 2 1 2 2 1 2 1 2 1 2 1 mv T T T d M s d F U = = + = θ Section:_____________________ Polar Coordinates (2-D) ω α θ θ ω θ θ θ θ θ θ θ θ r r r r a r dr dv v r r a u a u a a u r u r u v u v v u r r r r r r r r r r r 2 2 with ˆ ˆ ˆ ˆ ˆ ˆ ˆ 2 2 + = + = = = + = + = + = = Equivalent Acceleration Expressions θ ω ω ω α d d dt d ds dv v dx dv v dt dv a = = = = = Uniform Accelerated Motion Expressions ) ( 2 ; ; 2 1 2 2 2 o o o o o s s a v v at v v at t v s s + = + = + + = Relative Position, Velocity, Acceleration Expressions for Planar Motion A B A B A B A B A B A B A B A B A B A B A B r r x a a a a r x v v v v x x x / 2 / / / / / / / with with
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Unformatted text preview: + = = + = + = Conservation of Mechanical Energy 2 2 2 1 1 1 V T s d F V T ve conservati non + = ⋅ + + ∫ − in out s P P v F dt dU P k s k mgy V = ⋅ = = ∆ = ε spring) (torsional 2 1 spring) (linear ) ( 2 1 (gravity) 2 2 Impulse-momentum ( ) ( ) ( ) ( ) 1 1 2 2 2 2 1 1 with : particles ) ( ) ( B A A B m p o o o o f t t i v v v v e v xm r dm v x r H H dt M H v m dt F v m f i − − = = = = ∑ + = + ∫ ∫ ∑ ∑ ∫ ∑ v A v B...
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