Analytical Mech Homework Solutions 123

Analytical Mech Homework Solutions 123 - 9.3 (a) From...

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9.3 (a) From equation 9.2.13, 2 tan 2 xy xx yy I I I θ = From Prob. 9.1, 2 3 xx ma I = , 2 4 3 yy ma I = , 2 2 xy ma I =− tan 2 1 = 2 45 22.5 θθ == DD The 1-axis makes an angle of with the x-axis. 22.5 D (b) From symmetry, the principal axes are parallel to the sides of the lamina and perpendicular to the lamina, respectively. 9.4 (a) From symmetry, the coordinate axes are principal axes. From Table 8.3.1: ω G z x ()() 22 2 1 13 23 12 12 m I aa m  =+ =  a () 2 2 10 3 12 12 m I m =+= a 2 3 5 2 12 12 m I m a y 123 ˆˆˆ 14 eee + G From equation 9.2.5, 2 11 3 1 0 4 5 9 21 2 1 4 1 2 1 4 1 2 1 4 Tm a m a m a 2 ωω = +⋅  7 24 ma = (b) From equation 9.2.4, 13 10 2 5 3 12 12 12 14 14 14 L e ma e ma e ma 2  =⋅   G 2 12 13 20 15 12 14
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