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Moment of inertia from Lambda= 2+1X^3. Its a review for a physics exam. I think I integrate the function but don't know what to do next.?
A rod of length 1.00 m has a mass per unit length given by lambda = 2.00 + 1.00x^{2} , where lambda is in kg/m. The rod is placed on the x axis going from x = 0.00 m to x = 1.00 m. What is the moment of inertia of the rod in kgm2 about the y axis?
1 Answer
- Andrew SmithLv 75 years agoFavorite Answer
I = sum( m * x^2 )
= sum( (2+ x^2) * x^2 ) dx
= sum(2x^2)dx + sum(x^4) dx
= 2/3 x^3 + x^5/5 (+c) evaluated from x = 0 to x = 1
= 2/3 + 1/5 = 13/15 kg m^2
