240_Problem CHAPTER 9

240_Problem CHAPTER 9 - PROBLEM 9.167 Shown is the machine...

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PROBLEM 9.167 Shown is the machine element of Problem 9.143. Determine its moment of inertia with respect to the line joining the origin O and point A . SOLUTION First compute the mass of each component Have () 3 23 2 0.284 lb/in 0.008819 lb s /ft in 32.2 ft/s sT mV V V ρ == = Then 2 2 1 0.008819 lb s /ft in 4 in. 2 in. 0.88667 lb s /ft m π  =⋅ =  2 2 2 0.008819 lb s /ft in 1in. 3 in. 0.083125 lb s /ft m ( ) 2 2 3 0.008819 lb s /ft in 2 in. 0.055417 lb s /ft m Symmetry implies ( ) 1 00 yz zx xy II I = and ( ) ( ) 0 xy ′′ = = Now ( ) 222 333 xy x y I Im x y m x y m x y + = ( ) 2 2 2 1ft 0.083125 lb s /ft 2 in. 1.5 in.
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