263_Problem CHAPTER 9

263_Problem CHAPTER 9 - PROBLEM 9.181 The homogeneous...

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PROBLEM 9.181 The homogeneous circular cylinder shown has a mass m , and the diameter OB of its top surface forms 45 D angles with the x and z axes. ( a ) Determine the principal moments of inertia of the cylinder at the origin O . ( b ) Compute the angles that the principal axes of inertia at O form with the coordinate axes. ( c ) Sketch the cylinder, and show the orientation of the principal axes of inertia relative to the x , y , and z axes. SOLUTION ( a ) First compute the moments of inertia using Figure 9.28 and the parallel-axis theorem. () 2 2 22 2 2 11 3 3 12 2 12 2 13 xz y aa I Im a a m m a a m a m a     == + + + =    =+= Next observe that the centroidal products of inertia are zero because of symmetry. Then 2 1 2 2 xy x y I x y m m a ′′  =+ = = 2 1 2 2 yz y z I y z m m a = = 2 1 2 zx z x I z x m m a = = Substituting into Equation (9.56) 32 2 13 3 13 12 2 12 Km a K −+ + 2 2 2 13 3 3 13 13 13 1 1 1 12 2 2 12 12 12 2 ma K + × + ×+×−
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This note was uploaded on 07/11/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.

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