692_Dynamics 11ed Manual

692_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics αx = 1 rad 2 αy = 1 s αz = 1 rad 2 s Chapter 20 rad 2 s aA = 1 ft 2 s Given ⎛ 0 ⎞ ⎛ ωx ⎞ ⎛ b ⎞ ⎛ vA ⎟ ⎜⎟ ⎜⎞ ⎜ −ω r ⎟ + ⎜ ωy ⎟ × ⎜ −r ⎟ = ⎜ 0 ⎟ ⎜⎟ ⎜ ⎟ ⎝ 0 ⎠ ⎜ ωz ⎟ ⎝ −r ⎠ ⎜ 0 ⎟ ⎝⎠ ⎝⎠ ⎛ ωx ⎞ ⎛ b ⎞ ⎜ ⎟⎜ ⎟ ⎜ ωy ⎟ ⎜ −r ⎟ = 0 ⎜ ω ⎟ ⎝ −r ⎠ ⎝ z⎠ ⎛ αx ⎞⎛ b ⎞ ⎜ ⎟⎜ ⎟ ⎜ α y ⎟ ⎜ −r ⎟ = 0 ⎜ α ⎟ ⎝ −r ⎠ ⎝ z⎠ ⎛ 0 ⎞ ⎛ α x ⎞ ⎛ b ⎞ ⎛ ωx ⎞ ⎡⎛ ωx ⎞ ⎛ b ⎞⎤ ⎛ aA ⎞ ⎜ ⎟⎜⎟ ⎜ ⎟ ⎢⎜ ⎟ ⎥⎜⎟ −α r ⎟ + ⎜ 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 = 1.185 ft 2 s ⎛ α x ⎞ ⎛ −3.636 × 10− 7 ⎞ ⎜⎟⎜ ⎟ rad ⎜ α y ⎟ = ⎜ −1.199 ⎟2 ⎜α ⎟ ⎜ ⎟s 1.199 ⎠ ⎝ z⎠ ⎝ *Problem 20-24 The rod BC is attached to collars at its ends by ball-and-socket joints. If disk A has angular velocity ωA, determine the angular velocity of the rod and the velocity of collar B at the instant shown. Assume the angular velocity of the rod is directed perpendicular to the rod. Given: a = 200 mm 690 ...
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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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