Find Moment of Inertia of Horizontal Rod - Help with Integral Setup

fredrick08
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Homework Statement


find I of a horizontal rod, with radius a and length L, with axis through the centre in the z direction

The Attempt at a Solution


ok can someone please help me set up the integral for this?

i got rho=m/v=m/2pi*a^2*L, I=int(rho*r^2)dV, i used r=rho for cylindrical=L/2

I=(m/2pi)int from -a to a, 0 to 2pi, 0 to L/2(rho^2/a^2*L)drho dtheta dz, that gave me (mL^2)/12, which apparently is the answer for a thin rod, of infinite thinness... according to wiki... but my answer is supposed to be m((L^2/12)+(a^2/4))... can anyone help me understand this better... because I am getting confused with my dimensions.
 
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sorry, what i did was wrong in the first place...
 

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