728_Dynamics 11ed Manual

728_Dynamics 11ed Manual - 12 cos 2 W r r B r A 2 ⎛ ⎝...

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Engineering Mechanics - Dynamics Chapter 21 Problem 21-19 The assembly consists of a plate A of weight W A , plate B of weight W B , and four rods each of weight W r . Determine the moments of inertia of the assembly with respect to the principal x, y , z axes. Given: W A 15 lb = W B 40 lb = W r 7lb = r A 1f t = r B 4f t = h 4f t = Solution: Lr B r A () 2 h 2 + = L 5.00 ft = θ asin h L = θ 53.13 deg = I x 2 W r L 2 3 sin θ () 2 2 W r L 2 12 W r h 2 2 r A r B + 2 2 + + + W B r B 2 4 + W A r A 2 4 W A h 2 + + ... = I y I x = by symmetry I z 4 W r
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Unformatted text preview: 12 cos ( ) 2 W r r B r A + 2 ⎛ ⎝ ⎞ ⎠ 2 + ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ W A r A 2 2 ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ + W B r B 2 2 ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ + = I x I y I z ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ 20.2 20.2 16.3 ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ slug ft 2 ⋅ = *Problem 21-20 The thin plate has a weight W p and each of the four rods has weight W r . Determine the moment of 726...
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