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238_Problem CHAPTER 9

# 238_Problem CHAPTER 9 - PROBLEM 9.165 The homogeneous...

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PROBLEM 9.165 The homogeneous circular cylinder shown has a mass m . Determine the moment of inertia of the cylinder with respect to the line joining the origin O and point A which is located on the perimeter of the top surface of the cylinder. SOLUTION From Figure 9.28 2 1 2 y I ma = and using the parallel-axis theorem ( ) ( ) 2 2 2 2 2 1 1 3 3 4 12 2 12 x z h I I m a h m m a h = = + + = + Symmetry implies 0 xy yz zx I I I = = = For convenience, let point A lie in the yz plane. Then ( ) 2 2 1 OA h a h a = + + j k λ With the mass products of inertia equal to zero, Equation (9.46) reduces
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