772_Dynamics 11ed Manual

# 772_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics ⎛α ⎞ ⎜⎟ ⎜ β ⎟ = acos ( u) ⎜γ ⎟ ⎝⎠ Chapter 21 ⎛ α ⎞ ⎛ 69.3 ⎞ ⎜⎟⎜ ⎟ ⎜ β ⎟ = ⎜ 127.8 ⎟ deg ⎜ γ ⎟ ⎝ 45.0 ⎠ ⎝⎠ The last rotation (ψ) does not affect the result because the rod just spins around its own axis. The order of application of the rotations does affect the final result since rotational position is not a vector quantity. Problem 21-63 The turbine on a ship has mass M and is mounted on bearings A and B as shown. Its center of mass is at G, its radius of gyration is kz, and kx = ky. If it is spinning at angular velocity ω, determine the vertical reactions at the bearings when the ship undergoes each of the following motions: (a) rolling ω1, (b) turning ω2, (c) pitching ω3. Units Used: kN = 1000 N Given: M = 400 kg kx = 0.5 m ω = 200 rad s kz = 0.3 m ω1 = 0.2 rad s a = 0.8 m ω2 = 0.8 rad s ω3 = 1.4 rad s b = 1.3 m Solution: ⎛ kx2 0 0 ⎞ ⎜ ⎟ ⎜ ⎟ IG = M 0 kx2 0 ⎜ ⎟ ⎜ 2⎟ ⎝ 0 0 kz ⎠ Guesses Ax = 1 N Ay = 1 N Bx = 1 N By = 1 N 770 ...
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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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