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Analytical Mech Homework Solutions 121

Analytical Mech Homework Solutions 121 - CHAPTER 9 MOTION...

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CHAPTER 9 MOTION OF RIGID BODIES IN THREE DIMENSIONS 9.1 (a) ( ) 2 2 xx I y z dm = + dm dxdy ρ = and m a 2 2 ρ = z ( ) 2 2 0 0 0 y a x a xx y x I y dx ρ = = = = = + dy 2a a x = 2 0 2 a a y dy ρ 2 4 2 3 3 xx ma I a ρ = = y ( ) 2 2 2 2 0 0 y a x a yy y x I x z dm x dxd ρ = = = = = + = y 3 0 8 3 a a dy ρ = 4 2 8 4 3 3 yy a m I ρ = = a From the perpendicular axis theorem: 2 5 3 zz xx yy ma I I I = + + 2 0 0 y a x a xy yx y x I I xydm xy dx ρ = = = = = = − = − dy 2 0 4 2 a a ydy ρ = − 2 4 2 xy yx ma I I a ρ = = − = − 0 xz zx yz zy I I xzdm I = = − = = = I (b) 2 5 α = cos , 1 cos 5 β = , cos 0 γ = From equation 9.1.10 … 2 2 2 4 4 1 2 1 2 3 5 3 5 2 5 5 ma ma ma I
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