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# hw22 - ˆ k × r AP-ω 2 2 r AP =-9 ˆ i-12 ˆ j 3 α 2 ˆ...

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TAM212 Introductory Dynamics Spring 2005 S. Balachandar Homework 22 (3.59, 3.71) 3.59 v B = 10 in/sec a B = 5 in/sec 2 O A B 17 in 5 in i j sqrt(189) ρ Since the normals to v A and v B don’t intersect, so ω ρ = 0 and v A = v B = 10 ˆ i . (See Page 155 in textbook) v A = v O + ω ˆ k × 5 ˆ j 10 ˆ i = 0 - 5 ω ˆ i ω = - 2 ω = - 2 ˆ k rad / sec a A = a B + α ρ ˆ k × r BA - ω 2 ρ r BA = - 5 ˆ j + α ρ ˆ k × - 189 ˆ i + 10 ˆ j - 0 = - 5 ˆ j - 189 α ρ ˆ j - 10 α ρ ˆ i Also, a A = a O + α ˆ k × r OA - ω 2 r OA = α × ( 5 ˆ j ) - ( - 2) 2 5 ˆ j = - 5 α ˆ i - 20 ˆ j 1

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ˆ i coefficients: - 5 - 10 α ρ = - 5 α ˆ j coefficients: - 189 α ρ = - 20 which gives, α ρ = 1 . 45 ˆ k rad / sec 2 α = 3 . 91 ˆ k rad / sec 2 3.71 A P C D 3in 3in 4in v A = - r 1 × ω 1 ˆ i = - 3(2) ˆ i = - 6 ˆ i in / sec So I of β 2 is at P. Hence ω 2 = - 6 / 3 ˆ k = - 2 ˆ k rad / sec ω 3 = 0 rad / sec ω 1 = 2 ˆ k rad / sec a A = a O + α 1 ˆ k × r OA - ω 2 1 r OA = 0 + 3 ˆ k × 3 ˆ j - 2 2 (3)
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Unformatted text preview: ˆ k × r AP-ω 2 2 r AP =-9 ˆ i-12 ˆ j + 3 α 2 ˆ i-(-2) 2 3 ˆ j =-9 ˆ i + 3 α 2 ˆ i-24 ˆ j a P = a C + α 3 ˆ k × r CP-ω 2 3 r CP = + α 3 ˆ k (-4 ˆ i + 3 ˆ j ) + =-3 α 3 ˆ i-4 α 3 ˆ j ˆ j coefFcients,-24 = 4 α 3 α 3 =-6 rad / sec 2 α 3 =-6 ˆ k rad / sec 2 ˆ i coefFcients,-9 + 3 α 2 = 3 α 3 α 2 =-3 ˆ k rad / sec 2 So, a P =-9 ˆ i + 3(-3) ˆ i-24 ˆ j =-18 ˆ i-24 ˆ j in / sec 2 3...
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