239_Problem CHAPTER 9

239_Problem CHAPTER 9 - PROBLEM 9.166 The homogeneous...

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PROBLEM 9.166 The homogeneous circular cone shown has a mass m . Determine the moment of inertia of the cone with respect to the line joining the origin O and point A . SOLUTION First note that ()( ) 2 22 39 33 OA da a a a  =+ + =   Then () 13 1 2 2 9 23 2 OA aaa a =− + = + ijk i j k λ For a rectangular coordinate system with origin at point A and axes aligned with the given , , xyz axes, have (using Figure 9.28) 2 31 3 3 54 1 0 xz y I Im aa I m a  == + = 
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