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Moment of inertia bar variable density 
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#1
Mar1911, 06:20 PM

P: 13

1. The problem statement, all variables and given/known data
I think I solved this correctly, but im not sure. Find the moment of inertia of a bar with density d=kx^2, where x is the distance from the center of the bar(find the moment of inertia at the center) THe length of the bar is L 2. Relevant equations d=kx^2 Moment of inertia=sum of mx^2 3. The attempt at a solution FInd K. Well, the integral of density over a bar is the mass, so from the center, integrate kx^2 to half of the distance L, gives kx^3/(8*3)= M/2 k= 12M/(L^3) To find the moment of inertia, sum m1x1^2+m2x2^2...mnxn^2= integral x^2dm density =kx^2, so dm=kx^2dx Integrate 2k *x^4(over L/2)which equals 2k* L^5/(32*5) sub in k Moment of inertia of the bar equals 3/20 L^2 Is this right? It seems low 


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