711_Dynamics 11ed Manual

711_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 20 Solution: ⎛ ω2 ⎞ ⎜⎟ ω=⎜0⎟ ⎜ω ⎟ ⎝ 1⎠ vrel ⎛0⎟ ⎜⎞ α = ⎜ 0 ⎟×ω ⎜ ω1 ⎟ ⎝⎠ ⎛0⎞ ⎜ ⎟ = v cos ( θ ) ⎜ ⎟ ⎝ v sin ( θ ) ⎠ arel ⎛0⎞ ⎜ ⎟ rP = r cos ( θ ) ⎜ ⎟ ⎝ r sin ( θ ) ⎠ ⎛0⎞ ⎜ ⎟ = a cos ( θ ) ⎜ ⎟ ⎝ a sin ( θ ) ⎠ vP = vrel + ω × rP aP = arel + α × rP + ω × ( ω × rP) + 2ω × vrel ⎛ −25.5 ⎞ ⎜ ⎟ ft vP = −13.4 ⎜ ⎟s ⎝ 20.5 ⎠ ⎛ 161.2 ⎞ ⎜ ⎟ ft aP = −243.2 ⎜ ⎟2 ⎝ −33.9 ⎠ s Problem 20-43 At the given instant, the rod is spinning about the z axis with an angular velocity ω1 and angular acceleration ω'1. At this same instant, the disk is spinning, with ω2 and ω'2 both measured relative to the rod. Determine the velocity and acceleration of point P on the disk at this instant. Given: ω1 = 3 ω'1 = 4 rad s rad 2 s rad ω2 = 2 s rad ω'2 = 1 2 s a = 2 ft b = 3 ft c = 4 ft r = 0.5 ft Solution: ⎞ ⎛ 0 ⎟ ⎛ b ⎞ ⎛ ω2 ⎟ ⎛ 0 ⎞ ⎜ ⎞ ⎜⎟ ⎜ ⎜⎟ vP = ⎜ 0 ⎟ × c + ⎜ 0 ⎟ × − r ⎜⎟ ⎜⎟ ⎜ ω1 ⎟ ⎝ 0 ⎠ ⎜ ω ⎟ ⎝ 0 ⎠ ⎝⎠ ⎝ 1⎠ ⎛ −10.50 ⎞ ⎜ 9.00 ⎟ ft vP = ⎜ ⎟s ⎝ −1.00 ⎠ 709 ...
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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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