exam2a_solns - TAM 212 Spring 2004 Exam 2a solutions 1...

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Unformatted text preview: TAM 212, Spring, 2004, Exam 2a solutions 1. Using R O B F O B R F R ' / ' / / r v v v × + + = ω v , with i v v F R − = / ; ( ) ( ) j i v + = 2 2 / / B R B R v ; / ' = F O v ; k B B ω ω = v , and ( ) j i r + = d P O ' , ( ) ( ) ( ) ( )( ) ( ) i j j i j i k j i i − + + = + × + + = − ⇒ d v d v v B B R B B R ω ω 2 2 2 2 / / i-direction: ( ) d v v B B R ω − = − 2 2 / ; j-direction: ( ) ( ) d v d v B B R B B R ω ω − = ⇒ + = 2 2 2 2 / / , so k d v d v d d v B B B B 2 / 2 / = ⇒ = ⇒ − − = − ω ω ω ω v ; ( ) ( ) ( ) j i v + − = ⇒ − = ⇒ 2 / 2 / 2 2 / / v v v B R B R Using ( ) R O B R O B F O B R B B R F R ' 2 ' / ' / / / 2 r r a v a a ω − × α + + × ω + = v , with / = F R a ; ( )( ) j i a + = 2 2 / / B R B R a ; / ' = F O a ; k B B α α = v , ( ) j i r + = d P O ' , and d v B 2 / = ω ( ) ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) j i j i k j i k j i + − + × + + + − × + + = ⇒ 2 / 2 / 2 / 2 / 2 2 2 d v d v d v a B B R α ( ) ( ) ( )( ) ( ) ( ) ( )...
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