470_Dynamics 11ed Manual

470_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 16 Given: vC = 4 aC = 3 ft s ft 2 rAB = 0.5 ft rBC = 0.5 ft s θ = 90 deg φ = 45 deg Solution: Guesses ωAB = 1 rad α AB = 1 rad s 2 s ωBC = 1 rad α BC = 1 rad s 2 s Given ⎞ ⎞⎜ ⎛ 0 ⎞ ⎛ 0 ⎟ ⎛ 0 ⎟ ⎛ rBC sin ( θ ) ⎟ ⎛ −vC cos ( φ ) ⎞ ⎞⎜ ⎜ ⎟⎜ ⎜ ⎟ ⎜ 0 ⎟ × ⎜ rAB ⎟ + ⎜ 0 ⎟ × ⎜ −rBC cos ( θ ) ⎟ = ⎜ vC sin ( φ ) ⎟ ⎜ ωAB ⎟ ⎜ 0 ⎟ ⎜ ωBC ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎝ ⎠⎝ 0 0 ⎠⎝ ⎠ ⎛ 0 ⎞ ⎛ 0 ⎟ ⎛ 0 ⎞ ⎡⎛ 0 ⎞ ⎛ 0 ⎟⎤ ⎞⎜ ⎞⎥ ⎜ ⎟⎜ ⎟ ⎢⎜ ⎟⎜ ⎜ 0 ⎟ × ⎜ rAB ⎟ + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × ⎜ rAB ⎟⎥ ... ⎜ α AB ⎟ ⎜ 0 ⎟ ⎜ ωAB ⎟ ⎢⎜ ωAB ⎟ ⎜ 0 ⎟⎥ ⎝ ⎠⎝ ⎠⎝ ⎠ ⎣⎝ ⎠⎝ ⎠⎦ 0 ⎞ ⎛ rBC sin ( θ ) ⎞ ⎛ 0 ⎞ ⎡⎛ 0 ⎞ ⎛ rBC sin ( θ ) ⎞⎤ ⎛ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎢⎜ ⎟⎜ ⎟⎥ + ⎜ 0 ⎟ × ⎜ −rBC cos ( θ ) ⎟ + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × ⎜ −rBC cos ( θ ) ⎟⎥ ⎜ α BC ⎟ ⎜ ⎟ ⎜ ωBC ⎟ ⎢⎜ ωBC ⎟ ⎜ ⎟⎥ ⎝ ⎠⎝ 0 ⎠ ⎣⎝ ⎠⎝ 0 ⎠⎝ ⎠⎦ ⎛ ωAB ⎞ ⎜ ⎟ ⎜ ωBC ⎟ ⎜ ⎟ = Find ( ωAB , ωBC , α AB , α BC) ⎜ α AB ⎟ ⎜ α BC ⎟ ⎝ ⎠ ⎛ aC cos ( φ ) ⎞ ⎜ ⎟ = ⎜ −aC sin ( φ ) ⎟ ⎜ ⎟ 0 ⎝ ⎠ ⎛ ωAB ⎞ ⎛ 5.66 ⎞ rad ⎜ ⎟=⎜ ⎟ ⎝ ωBC ⎠ ⎝ 5.66 ⎠ s α BC = 27.8 rad 2 s α AB = −36.2 rad 2 s Problem 16-111 The flywheel rotates with angular velocity ω and angular acceleration α. Determine the angular acceleration of links AB and BC at the instant shown. 468 ...
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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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