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702_Dynamics 11ed Manual

# 702_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 20 ⎞ ⎛ 0 ⎞ ⎛ ω1 ⎟ ⎛ 0 ⎞ ⎜ ⎟⎜ ⎜⎟ vC = vB + ⎜ vCB ⎟ + ⎜ 0 ⎟ × b ⎜⎟ ⎜ 0 ⎟ ⎜ω ⎟ ⎝0⎠ ⎝ ⎠ ⎝ 2⎠ ⎛ −1.00 ⎞ ⎜ ⎟m vC = 5.00 ⎜ ⎟s ⎝ 0.80 ⎠ ⎞ ⎞ ⎞ ⎛ 0 ⎞ ⎡⎛ ω'1 ⎞ ⎛ ω1 ⎟ ⎛ ω1 ⎟⎤ ⎛ 0 ⎞ ⎛ ω1 ⎟ ⎡⎛ ω1 ⎟ ⎛ 0 ⎞⎤ ⎜ ⎟ ⎢⎜ ⎟ ⎜ ⎞ ⎜ ⎥ ⎜⎟ ⎜ ⎢⎜ ⎜ ⎟⎥ aC = aB + ⎜ aCB ⎟ + ⎢⎜ 0 ⎟ + ⎜ 0 ⎟ × ⎜ 0 ⎟⎥ × b + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × b ⎥ ... ⎜⎟ ⎜⎟ ⎜ 0 ⎟ ⎢⎜ ω' ⎟ ⎜ 0 ⎟ ⎜ ω ⎟⎥ ⎝ 0 ⎠ ⎜ ω ⎟ ⎢⎜ ω ⎟ ⎝ 0 ⎠⎥ ⎝ ⎠ ⎣⎝ 2 ⎠ ⎝ ⎠ ⎝ 2 ⎠⎦ ⎝ 2 ⎠ ⎣⎝ 2 ⎠ ⎦ ω1 ⎞ ⎛ 0 ⎞ ⎛ ⎜ ⎟⎜ ⎟ + 2⎜ 0 ⎟ × ⎜ vCB ⎟ ⎜ω ⎟ ⎜ 0 ⎟ ⎠ ⎝ 2⎠ ⎝ ⎛ −28.8 ⎞ ⎜ ⎟m aC = −5.45 ⎜ ⎟2 ⎝ 32.3 ⎠ s Problem 20-33 At a given instant, rod BD is rotating about the y axis with angular velocity ωBD and angular acceleration ω'BD. Also, when θ = θ1 , link AC is rotating downward such that θ' = ω2 and θ'' = α2. Determine the velocity and acceleration of point A on the link at this instant. Given: ωBD = 2 rad s θ 1 = 60 deg ω'BD = 5 rad ω2 = 2 rad s α2 = 8 rad 2 s L = 3 ft 2 s Solution: ⎛ −ω2 ⎞ ⎜ ⎟ ω = ⎜ −ωBD ⎟ ⎜ ⎟ ⎝0⎠ ⎛ −α 2 ⎞ ⎛ 0 ⎞ ⎜ ⎟⎜ ⎟ α = ⎜ −ω'BD ⎟ + ⎜ −ωBD ⎟ × ω ⎜ ⎟⎜ ⎟ ⎝0⎠⎝0⎠ 700 0 ⎛ ⎞ ⎜ ⎟ rA = ⎜ L cos ( θ 1 ) ⎟ ⎜ −L sin ( θ ) ⎟ 1⎠ ⎝ ...
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