# hw31 - B ˆ i 4 α B ˆ j = a P S ˆ i 036 ˆ i 036 ˆ j 1...

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TAM212 Introductory Dynamics Spring 2005 S. Balachandar Homework 31 (3.158, 3.161) 3.158 a P / F = ± ± ±* 0 a P / B + a P 0 / F + 2 ω × v P / B = ± ± ± * 0 a O / F + α ˆ k × r OP - ω 2 r OP + 2 ω × v P / B = 4 ˆ k × ( r OP cos30 ˆ i + r OP sin30 ˆ j ) - 2 2 ( r OP cos30 ˆ i + r OP sin30 ˆ j ) + 2(2) ˆ k × 3 ( cos30 ˆ i + sin30 ˆ j ) = - 4 r OP cos30 ˆ j + 4 r OP sin30 ˆ i - 4 r OP cos30 ˆ i - 4 r OP sin30 ˆ j + 12cos30 ˆ j - 12sin30 ˆ i = - 1 . 4641 r OP ˆ i - 5 . 4641 r OP ˆ j - 6 ˆ i + 10 . 3923 ˆ j f t / sec 2 3.161 a C = - r I ± C α C ˆ i + v 2 C r OC ˆ j = - 0 . 3(0 . 02) ˆ i + 0 . 06 2 0 . 6 - 0 . 3 = - 0 . 006 ˆ i + 0 . 012 ˆ j a E = a C + α C × r CE - ω 2 C r CE = - 0 . 006 ˆ i + 0 . 012 ˆ j + 0 . 02 ˆ k × 0 . 2 ˆ i - 0 . 2 2 (0 . 2) ˆ i = - 0 . 014 ˆ i + 0 . 016 ˆ j a P = a E + α B × r EP - ω 2 B r EP = - 0 . 014 ˆ i + 0 . 016 ˆ j + α B ˆ k × (0 . 4 ˆ i + 0 . 3 ˆ j ) - ( - 0 . 4) 2 (0 . 4 ˆ i + 0 . 3 ˆ j ) = - 0 . 014 ˆ i + 0 . 016 ˆ j - 0 . 3 α B ˆ i + 0 . 4 α B ˆ j - 0 . 064 ˆ i - 0 . 048 ˆ j = - 0 . 078 ˆ i - 0 . 032 ˆ j - 0 . 3 α B ˆ i + 0 . 4 α B ˆ j a P / F = a P / S + a P 0 / F + 2 ω S / F ˆ k × v P / S = a P / S ˆ i - r O 0 P ω 2 S ˆ i + 2 ω S / F ˆ k × v P / S - 0 . 078 ˆ i - 0 . 032 ˆ j - 0 . 3 α B ˆ i + 0 . 4 α B ˆ j = a P / S ˆ i - ( - 0 . 4)(0 . 3) 2 ˆ i + 2(0 . 3) ˆ k × 0 . 06 ˆ i - 0 . 078 ˆ i - 0 . 032 ˆ j - 0 . 3 α

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Unformatted text preview: B ˆ i + . 4 α B ˆ j = a P / S ˆ i + . 036 ˆ i + . 036 ˆ j 1 ˆ j :-. 032 + . 4 α B = . 036 α B = . 17 k rad / s 2 α B = . 17 ˆ k rad / s 2 ˆ i :-. 078-. 3 α B = a P / S + . 036 a P / S =-. 165 m / sec 2 a P / S =-. 165 ˆ i m / sec 2 2...
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## This note was uploaded on 04/14/2010 for the course TAM 212 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw31 - B ˆ i 4 α B ˆ j = a P S ˆ i 036 ˆ i 036 ˆ j 1...

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