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164_Problem CHAPTER 9

164_Problem CHAPTER 9 - PROBLEM 9.130 Shown is the cross...

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PROBLEM 9.130 Shown is the cross section of an idler roller. Determine its moment of inertia and its radius of gyration with respect to the axis . AA (The density of bronze is 8580 kg/m 3 ; of aluminum, 2770 kg/m 3 ; and of neoprene, 1250 kg/m 3 .) SOLUTION First note for the cylindrical ring shown that ( ) ( ) 2 2 2 2 2 1 2 1 4 4 m V t d d t d d π π ρ ρ ρ = = × = and, using Figure 9.28, that 2 2 2 1 2 1 1 1 2 2 2 2 AA d d I m m = 2 2 2 2 2 2 1 1 1 8 4 4 t d d t d d π π ρ ρ = × × ( ) 4 4 2 1 1 8 4 t d d π ρ = ( )( ) 2 2 2 2 2 1 2 1 1 8 4 t d d d d π ρ = + ( ) 2 2 1 2 1 8 m d d = + Now treat the roller as three concentric rings and, working from the
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