475_Dynamics 11ed Manual

475_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics ⎛ −4.33 ⎞ m aB = ⎜ 4.45 ⎟ ⎜ ⎟2 ⎝ 0.00 ⎠ s Chapter 16 aB = 6.21 m 2 s ⎞ ⎟ ⎜ −a + α r sin ( φ ) − ω2 r cos ( φ ) ⎟ ⎝0 ⎠ ⎛ α r cos ( φ ) + ω r sin ( φ ) 2 θ = atan ⎜ θ = −45.8 deg θ = 45.8 deg Problem 16-117 The disk rotates with angular velocity ω and angular acceleration α. Determine the angular acceleration of link CB at this instant. Given: ω=5 α=6 rad s rad 2 a = 2 ft b = 1.5 ft s r = 0.5 ft θ = 30 deg Solution: ⎛0⎞ r1 = ⎜ −r ⎟ ⎜⎟ ⎝0⎠ ⎛ a cos ( θ ) ⎞ r2 = ⎜ a sin ( θ ) ⎟ ⎜ ⎟ ⎝0⎠ ⎛0⎞ r3 = ⎜ b ⎟ ⎜⎟ ⎝0⎠ ⎛0⎞ k = ⎜0⎟ ⎜⎟ ⎝1⎠ Guesses Given ωAB = 1 rad s ωBC = 1 rad α AB = 1 s rad α BC = 1 2 s rad 2 s ωk × r1 + ωABk × r2 + ωBCk × r3 = 0 α k × r1 + ωk × ( ωk × r1 ) + α ABk × r2 + ωABk × ( ωABk × r2 ) ... = 0 + α BC k × r3 + ωBCk × ( ωBC k × r3 ) ⎛ ωAB ⎞ ⎜ ⎟ ⎜ ωBC ⎟ ⎜ ⎟ = Find ( ωAB , ωBC , α AB , α BC) ⎜ α AB ⎟ ⎜ α BC ⎟ ⎝ ⎠ ⎛ ωAB ⎞ ⎛ 0.00 ⎞ rad ⎜ ⎟=⎜ ⎟ ⎝ ωBC ⎠ ⎝ 1.67 ⎠ s α AB = −4.81 rad 2 s 473 α BC = 5.21 rad 2 s ...
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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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