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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 2 2 3 9 3 3 2 2 OA d a a a a = + + = Then ( ) 1 3 1 3 3 2 2 9 2 3 2 OA a a a a = + = + i j k i j k λ For a rectangular coordinate system with origin at point A and axes aligned with the given , , x y z axes, have (using Figure 9.28) ( ) 2 2 2 3 1 3 3 5 4 10 x z y I I m a a I ma = = + =
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