503_Dynamics 11ed Manual

503_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 16 Solution: 0 0 ⎞ ⎛ 0 ⎞ ⎛ a cos ( θ ) ⎞ ⎛ ⎜ ⎟⎜ ⎟⎛⎞ ⎟+⎜ ⎜ −r ⎟ 0 vC = ⎜ 0 ⎟ × a sin ( θ ) ⎟×⎜ ⎟ ⎜ ⎟⎜ ⎜ ωAB ⎟ ⎝ 0 ⎠ ⎜ ωAB − ω' ⎟ ⎝ 0 ⎠ ⎝ ⎠ ⎝ ⎠ ⎛ −7.00 ⎞ ft vC = ⎜ 17.32 ⎟ ⎜ ⎟s ⎝ 0.00 ⎠ ⎤ ⎡⎛ 0 ⎞ ⎛ a cos ( θ ) ⎞ ⎛ 0 ⎞ ⎡⎛ 0 ⎞ ⎛ a cos ( θ ) ⎞⎥⎤ ⎢⎜ ⎟⎜ ⎟ + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × ⎜ a sin ( θ ) ⎟ ⎥ ... aC = ⎢⎜ 0 ⎟ × a sin ( θ ) ⎟ ⎢⎜ ⎟⎜ ⎜ ⎟⎜ ⎟⎥⎥ ⎢⎜ α AB ⎟ ⎝ 0 ⎠ ⎜ ωAB ⎟ ⎢⎜ ωAB ⎟ ⎝ 0 ⎠⎥⎥ ⎣⎝ ⎠ ⎝ ⎠ ⎣⎝ ⎠ ⎦⎦ 0 0 0 ⎞ ⎛0⎞ ⎛ ⎞ ⎡⎛ ⎞ ⎛ 0 ⎞⎤ ⎛ ⎜ ⎟⎜⎟⎜ ⎟ ⎢⎜ ⎟ ⎜ ⎟⎥ 0 0 0 +⎜ ⎟ × ⎜ −r ⎟ + ⎜ ⎟ × ⎢⎜ ⎟ × ⎜ −r ⎟⎥ ⎜ α AB − α' ⎟ ⎝ 0 ⎠ ⎜ ωAB − ω' ⎟ ⎢⎜ ωAB − ω' ⎟ ⎝ 0 ⎠⎥ ⎝ ⎠ ⎝ ⎠ ⎣⎝ ⎠ ⎦ ⎛ −38.84 ⎞ ft aC = ⎜ −6.84 ⎟ ⎜ ⎟ s2 ⎝ 0.00 ⎠ Problem 16-149 The cars on the amusement-park ride rotate around the axle at A with constant angular velocity ωAf measured relative to the frame AB. At the same time the frame rotates around the main axle support at B with constant angular velocity ωf .Determine the velocity and acceleration of the passenger at C at the instant shown. Given: rad ωAf = 2 ωf = 1 s rad s a = 15 ft b = 8 ft θ = 30 deg 501 ...
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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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