(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have a drum that comprises of basically a cylinder and rotated line in the form y=mx+c

http://img22.imageshack.us/img22/6108/druma.jpg [Broken]

2. Relevant equations

[tex]I=\int r^2 dm[/tex]

3. The attempt at a solution

I found the MOI for the cylinder as 1/2M(a^{2}+b^{2}) where a and b are the inner and outer radii respectively.

I am getting trouble forming the MOI for the line. I am supposed to consider an elemental section, but I am not sure if I should consider a disc or some other shape.

Disc: (Width dx and radius 'y')

dI=1/2(dm)y^{2}

dm=ρ dV = ρ(πy^{2}dx)

dI=1/2ρπ y^{4}dx

[tex]I_{line}= \frac{1}{2} \rho \pi \int_{x_1} ^{x_2} y^4 dx[/tex]

Since I have two lines, the inertia would be

[tex]I = \frac{1}{2} \rho \pi \int_{x_1} ^{x_2} (y_2^4 -y_1^4) dx[/tex]

I can appropriately select x_{2}and x_{1}based on height of the cylinder and the height of the total drum. I can find the ρ for the material. But I'd need to calculate the equations for y_{2}and y_{1}.

So my MOI would be

[tex]I = \frac{1}{2} M(a^2+b^2)+ \frac{1}{2} \rho \pi \int_{x_1} ^{x_2} (y_2^4 -y_1^4) dx[/tex]

Is this correct or did I make a mistake in my element or in the algebra?

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# Homework Help: Moment of inertia of a rotated line

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