# Moment of inertia bar variable density

by chrisandmiss
Tags: density, inertia, moment, variable
 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

 Related Discussions Calculus & Beyond Homework 2 Introductory Physics Homework 1 Advanced Physics Homework 2 Introductory Physics Homework 6