673_Dynamics 11ed Manual

673_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Guesses ω2 = 1 rad s Chapter 20 α2 = 1 rad 2 ay = 1 s m 2 az = 1 s m 2 s Given Enforce the no-slip constraint 0 ⎛ ⎞ ⎜ ⎟ (θ ) ⎟ × r = 0 ω2 cos ⎜ ⎜ ω + ω sin ( θ ) ⎟ 2 ⎝1 ⎠ 0 0 ⎡⎛ ⎞ ⎛0⎞ ⎛ ⎞⎤ ⎢⎜ ⎟⎜ ⎟⎜ ⎟⎥ ( θ ) ⎟ + ⎜ 0 ⎟ × ⎜ ω2 cos (θ ) ⎟⎥ × r = α 2 cos ⎢⎜ ⎢⎜ α + α sin ( θ ) ⎟ ⎜ ω1 ⎟ ⎜ ω + ω sin ( θ ) ⎟⎥ 2 2 ⎣⎝ 1 ⎠ ⎝ ⎠⎝1 ⎠⎦ ⎛ ω2 ⎟ ⎜⎞ ⎜ α2 ⎟ ⎜ ⎟ = Find ( ω2 , α 2 , ay , az) ⎜ ay ⎟ ⎜ az ⎟ ⎝⎠ ⎛ ay ⎞ ⎛ 0 ⎞ m ⎜ ⎟=⎜ ⎟ ⎝ az ⎠ ⎝ 26.3 ⎠ s2 ⎛0⎞ ⎜⎟ ⎜ ay ⎟ ⎜ az ⎟ ⎝⎠ ω2 = −8.77 rad s α 2 = −5.85 rad 2 s Now construct the angular velocity and angular acceleration. 0 ⎛ ⎞ ⎜ ⎟ ω = ⎜ ω2 cos ( θ ) ⎟ ⎜ ω + ω sin ( θ ) ⎟ 2 ⎝1 ⎠ ⎛ 0.00 ⎞ ⎜ ⎟ rad ω = −8.24 ⎜ ⎟s ⎝ 0.00 ⎠ 0 0 ⎛ ⎞ ⎛0⎞ ⎛ ⎞ ⎜ ⎟⎜ ⎟⎜ ⎟ α = ⎜ α 2 cos ( θ ) ⎟ + ⎜ 0 ⎟ × ⎜ ω2 cos ( θ ) ⎟ ⎜ α + α sin ( θ ) ⎟ ⎜ ω1 ⎟ ⎜ ω + ω sin ( θ ) ⎟ 2 2 ⎝1 ⎠ ⎝ ⎠⎝1 ⎠ ⎛ 24.73 ⎞ ⎜ ⎟ rad α = −5.49 ⎜ ⎟2 ⎝ 0.00 ⎠ s Problem 20-7 At a given instant, the antenna has an angular motion ω1 and ω'1 about the z axis. At the same instant θ = θ1, the angular motion about the x axis is ω2 and ω'2. Determine the velocity and acceleration of the signal horn A at this instant. The distance from O to A is d. 671 ...
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