774_Dynamics 11ed Manual

774_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 21 ⎞ ⎡ ⎞⎤ ⎛ 0 ⎟ ⎛ ω3 ⎞ ⎢ ⎛ ω3 ⎟⎥ ⎞ ⎛ 0 ⎞ ⎛ Ax ⎞ ⎛ 0 ⎞ ⎛ Bx ⎟ ⎜ ⎟⎜⎟⎜ ⎜ 0 ⎟ × A + 0 × B = I ⎜ −ω ω + ⎜ ⎟ × I ⎜ 3 ⎟ ⎜ 0 ⎟ ⎢ G⎜ 0 ⎟⎥ ⎜ ⎟ ⎜ y ⎟ ⎜ ⎟ ⎜ y ⎟ G⎜ ⎜ 0 ⎟ ⎝ −a ⎠ ⎜ 0 ⎟ ⎜ 0 ⎟ ⎜ ω ⎟ ⎢ ⎜ ω ⎟⎥ ⎝b⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ ⎝ ⎠⎦ ⎝⎠ ⎛ Ax ⎞ ⎜⎟ ⎜ Ay ⎟ = Find ( A , A , B , B ) xyxy ⎜ Bx ⎟ ⎜⎟ ⎝ By ⎠ ⎛ Ax ⎞ ⎛ −4.80 ⎞ ⎜ ⎟=⎜ ⎟ kN ⎝ Bx ⎠ ⎝ 4.80 ⎠ ⎛ Ay ⎞ ⎛ 1.50 ⎞ ⎜ ⎟=⎜ ⎟ kN ⎝ By ⎠ ⎝ 2.43 ⎠ *Problem 21-64 An airplane descends at a steep angle and then levels off horizontally to land. If the propeller is turning clockwise when observed from the rear of the plane, determine the direction in which the plane tends to turn as caused by the gyroscopic effect as it levels off. Solution: As noted on the diagram Mx represents the effect of the plane on the propeller. The opposite effect occurs on the plane. Hence, the plane tends to turn to the right when viewed from above. Problem 21-65 The propeller on a single-engine airplane has a mass M and a centroidal radius of gyration kG computed about the axis of spin. When viewed from the front of the airplane, the propeller is turning clockwise at ωs about the spin axis. If the airplane enters a vertical curve having a radius ρ and is traveling at speed v, determine the gyroscopic bending moment which the propeller exerts on the bearings of the engine when the airplane is in its lowest position. 772 ...
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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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