l18anno - TAM 212 First Midterm Exam Room Schedule Building...

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TAM 212 First Midterm Exam Room Schedule Building and Room Discussion Section CA 112 (Chem Annex) L, M MSEB 100 D, I, K, N LMS 141 (Loomis Lab) B, G, H, J NOYES 100 (Noyes Lab) A, C, E, F, O
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Define Constraint Equations Pulley problems: Rope length is constant Relations between and Relations between and e.g. () OA x r OB y r OA r OB r || A BO B O A = rr r
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Cylindrical Coordinates () cos ( () ) s in ) () s ) cos ) r tt t t    ei j j Time dependent basis vectors i j rt t t e r t e () () OP r tr t t z t re k x y P
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“The Formula” 2 () [] [ 2 )) ] (( OP r Pr tr t rz tz t rr r r    re k ee ak vk 
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Tangential and Normal Coordinates s=s(t) is the distance traveled () (() ) OP OP OP OP ts t s t = = = r r rr o Color change denotes different function (of time vs. arc length)
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“The Formula” 2 || () (() ) OP OP P P Pt P n d ts t dt ρ + = = = vv e v av e r e r
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2 F 2 m 21 f 12 f 1 m 1 F 2 a 1 a 3 m 31 f 13 f 3 a 3 F 32 f 23 f 1 1 1 12 13 2 2 21 23 3 3 3 31 32 11 2 2 3 3 1 3 2 2 () ( ) ii i mt t t t t m t m t t t t m t t t t t t t =+ ++= + + + + + = ∑∑ aF f f f f f f aaa F F F System of particles When summed the internal forces cancel ij ji = ff
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Mass Center 11 2 2 3 123 3 Total mass OC ii i i i i i mm m m m m ++ = = = RR R r R 2 m 1 m 3 m O 1 e 2 e 3 R 1 R 2 R OC r C
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Friction: Coulomb s law Two possibilities Stick: Slip x 0 | F f |   | N | P x y Negative friction power (+ve Maximum friction force F f x 0 | F f |   | N | F f , x as drawn) x W N P f F 1. constitutive relation 2. motion (velocity) force F f x 0 | F f |   | N |
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l18anno - TAM 212 First Midterm Exam Room Schedule Building...

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