(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Moment of inertia of a rotated line

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**