150_Problem CHAPTER 9

150_Problem CHAPTER 9 - PROBLEM 9.123 The area shown is...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PROBLEM 9.123 The area shown is revolved about the x axis to form a homogeneous solid of revolution of mass m . Determine by direct integration the moment of inertia of the solid with respect to ( a ) the x axis, ( b ) the y axis. Express your answers in terms of m and a . SOLUTION At () 3 2 1 2 2 2 or 4 xa a k a k a == = Then 3 2 1 4 yx a = Now ( ) 2 dm r dx = ρπ 2 36 24 1 41 6 x dx x dx aa    πρ Then 2 6 4 16 a a mx d x a = () ( ) 2 77 73 44 11 2 7 2 71 1 2 16 112 a a x a  =   or 3 112 127 m a = ( a ) Now 2 23 6 6 61 2 43 4 1 1 1 22 6 1 2 7 32 127 16
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online