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Homework Statement
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]
Homework Equations
[tex]I=\int r^2 dm[/tex]
The Attempt at a Solution
I found the MOI for the cylinder as 1/2M(a2+b2) 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)y2
dm=ρ dV = ρ(πy2dx)
dI=1/2ρπ y4 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 x2 and x1 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 y2 and y1.
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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