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201_Problem CHAPTER 9

201_Problem CHAPTER 9 - PROBLEM 9.147 Determine the moment...

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PROBLEM 9.147 Determine the moment of inertia of the steel machine element shown with respect to ( a ) the x axis, ( b ) the y axis, ( c ) the z axis. (The specific weight of steel is 490 lb/ft 3 .) SOLUTION Have ST ST mV V g δ ρ == Then () 3 3 3 1 2 490 lb/f 1ft 314 i n 12 in. 32.2 ft/s t m  × × ×   32 105.676 10 lb s /ft 3 3 33 2 2 2 490 lb/ft 1.5 1 2 in 26.419 10 lb s /ft 12 in. 32.2 ft/s m × × × = × 3 3 2 2 3 2 490 lb/ft 0.5 1.5 in 5.1874 10 lb s /ft 21 2 i n . 32.2 ft/s m π  × × = ×   3 3 2 3 4 2 490 lb/ft 1.4 0.4 in 2 i n . 32.2 ft/s m × × 10.8491 10 lb s /ft ( a ) Using Fig. 9.28 for components 1 and 2 and the equations derived above for components 3 and 4, have ( ) ( ) ( ) 1234 x xx xx I IIII =++− where () ( ) 2 22 2 1 11 4 1 f t 105.676 10 lb s /ft 1 4 in 12 2 2 12 in.
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