773_Dynamics 11ed Manual

773_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics (a) Rolling Chapter 21 Given ⎛ Ax ⎞ ⎛ Bx ⎞ ⎛ 0 ⎞ ⎛ 0 ⎞ ⎜⎟⎜⎟⎜ ⎟ ⎜⎟ ⎜ A y ⎟ + ⎜ B y ⎟ + ⎜ −M g ⎟ = ⎜ 0 ⎟ N ⎜ 0 ⎟ ⎜ 0 ⎟ ⎝ 0 ⎠ ⎝0⎠ ⎝⎠⎝⎠ ⎞ ⎛ 0 ⎞ ⎛ Ax ⎞ ⎛ 0 ⎞ ⎛ Bx ⎟ ⎛0⎞ ⎛ 0 ⎞ ⎡ ⎛ 0 ⎞⎤ ⎜ ⎟⎜⎟⎜ rad ⎜ ⎟ ⎢ ⎜ ⎟⎥ ⎜0⎟ × A + 0 × B = I ⎜0⎟ + 0 ×I 0 ⎜ ⎟ ⎜ y ⎟ ⎜ ⎟ ⎜ y ⎟ G⎜ ⎟ s2 ⎜ ⎟ ⎢ G⎜ ⎟⎥ ⎜ 0 ⎟ ⎝ −a ⎠ ⎜ 0 ⎟ ⎝b⎠ ⎝ ⎠ ⎝0⎠ ⎝ ω ⎠ ⎣ ⎝ ω ⎠⎦ ⎝⎠ ⎛ Ax ⎞ ⎜⎟ ⎜ Ay ⎟ = Find ( A , A , B , B ) xyxy ⎜ Bx ⎟ ⎜⎟ ⎝ By ⎠ (b) Turning ⎛ Ax ⎞ ⎛ 0.00 ⎞ ⎜ ⎟=⎜ ⎟ kN ⎝ Bx ⎠ ⎝ 0.00 ⎠ ⎛ Ay ⎞ ⎛ 1.50 ⎞ ⎜ ⎟=⎜ ⎟ kN ⎝ By ⎠ ⎝ 2.43 ⎠ Given ⎛ Ax ⎞ ⎛ Bx ⎞ ⎛ 0 ⎞ ⎛ 0 ⎞ ⎜⎟⎜⎟⎜ ⎟ ⎜⎟ ⎜ A y ⎟ + ⎜ B y ⎟ + ⎜ −M g ⎟ = ⎜ 0 ⎟ N ⎜ 0 ⎟ ⎜ 0 ⎟ ⎝ 0 ⎠ ⎝0⎠ ⎝⎠⎝⎠ ⎞ ⎛ ω ω2 ⎞ ⎛ 0 ⎞ ⎢ ⎛ 0 ⎟⎥ ⎛ 0 ⎞ ⎛ Ax ⎞ ⎛ 0 ⎞ ⎛ Bx ⎟ ⎜ ⎟⎜⎟⎜ ⎟ ⎜ ⎟ ⎡ ⎜ ⎞⎤ ⎜0⎟ × A + 0 × B = I ⎜ + ω ×I ω ⎜ ⎟ ⎜ y ⎟ ⎜ ⎟ ⎜ y ⎟ G⎜ 0 ⎟ ⎜ 2 ⎟ ⎢ G⎜ 2 ⎟⎥ ⎜ 0 ⎟ ⎜ ω ⎟ ⎢ ⎜ ω ⎟⎥ ⎝ b ⎠ ⎜ 0 ⎟ ⎝ −a ⎠ ⎜ 0 ⎟ ⎝ ⎠ ⎝ ⎠ ⎣ ⎝ ⎠⎦ ⎝⎠ ⎝⎠ ⎛ Ax ⎞ ⎜⎟ ⎜ Ay ⎟ = Find ( A , A , B , B ) xyxy ⎜ Bx ⎟ ⎜⎟ ⎝ By ⎠ (c) Pitching ⎛ Ax ⎞ ⎛ 0.00 ⎞ ⎜ ⎟=⎜ ⎟ kN Bx ⎠ ⎝ 0.00 ⎠ ⎝ Given ⎛ Ax ⎞ ⎛ Bx ⎞ ⎛ 0 ⎞ ⎛ 0 ⎞ ⎜⎟⎜⎟⎜ ⎟ ⎜⎟ ⎜ A y ⎟ + ⎜ B y ⎟ + ⎜ −M g ⎟ = ⎜ 0 ⎟ N ⎜ 0 ⎟ ⎜ 0 ⎟ ⎝ 0 ⎠ ⎝0⎠ ⎝⎠⎝⎠ 771 ⎛ Ay ⎞ ⎛ −1.25 ⎞ ⎜ ⎟=⎜ ⎟ kN By ⎠ ⎝ 5.17 ⎠ ⎝ ...
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