691_Dynamics 11ed Manual

691_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 20 ⎛ 0 ⎞ ⎛ α x ⎞ ⎛ b ⎞ ⎛ ωx ⎞ ⎡⎛ ωx ⎞ ⎛ b ⎞⎤ ⎛ aA ⎞ ⎜ ⎟⎜⎟ ⎜ ⎟ ⎢⎜ ⎟ ⎥⎜⎟ 0 ⎟ + ⎜ α y ⎟ × ⎜ −r ⎟ + ⎜ ωy ⎟ × ⎢⎜ ωy ⎟ × ⎜ −r ⎟⎥ = ⎜ 0 ⎟ ⎜ ⎜⎟ ⎜⎟ ⎜ 2 ⎟ ⎜ α ⎟ ⎝ −r ⎠ ⎜ ω ⎟ ⎢⎜ ω ⎟ ⎝ −r ⎠⎥ ⎜ 0 ⎟ −ω r ⎠ ⎝ z ⎠ ⎝ ⎝ z ⎠ ⎣⎝ z ⎠ ⎦⎝⎠ ⎛ ωx ⎞ ⎜⎟ ⎜ ωy ⎟ ⎜ω ⎟ ⎜ z⎟ ⎜ αx ⎟ ⎜ ⎟ = Find ( ωx , ωy , ωz , α x , α y , α z , vA , aA) ⎜ αy ⎟ ⎜α ⎟ ⎜ z⎟ ⎜ vA ⎟ ⎜⎟ ⎝ aA ⎠ ⎛ ωx ⎞ ⎛ 0.182 ⎞ ⎜⎟⎜ ⎟ rad ⎜ ωy ⎟ = ⎜ −0.061 ⎟ ⎜ ω ⎟ ⎝ 0.606 ⎠ s ⎝ z⎠ vA = 0.667 ft s aA = −0.148 ⎛ α x ⎞ ⎛ −0.364 ⎞ ⎜⎟⎜ ⎟ rad ⎜ α y ⎟ = ⎜ −1.077 ⎟ 2 ⎜ α ⎟ ⎝ −0.013 ⎠ s ⎝ z⎠ Problem 20-23 Rod AB is attached to a disk and a collar by ball and-socket joints. If the disk is rotating with an angular acceleration α, and at the instant shown has an angular velocity ω, determine the velocity and acceleration of the collar at A at the instant shown. Given: ω=2 rad s r = 1 ft α=4 rad b = 3 ft 2 s Solution: Guesses ωx = 1 rad s ωy = 1 rad s ωz = 1 rad s vA = 1 ft s 689 ft 2 s ...
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.

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