148_Problem CHAPTER 9

148_Problem CHAPTER 9 - PROBLEM 9.121 The parabolic...

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PROBLEM 9.121 The parabolic spandrel shown is revolved about the x axis to form a homogeneous solid of revolution of mass m . Using direct integration, express the moment of inertia of the solid with respect to the x axis in terms of m and b . SOLUTION At 2 2 , : or b xa yb bk a k a == = = Then 2 2 b yx a = Now ( ) 2 dm r dx ρπ = 2 2 2 b x dx a πρ  =   Then 2 4 4 0 a b mx d x a = 2 5 4 0 1 5 a b x a = 2 2 15 or 5 m ab ab Now 22 2 11
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