# A tricky intigration for rotational inertia

1. Jun 10, 2010

### blahman

1. The problem statement, all variables and given/known data
alright, so i'm trying to find the rotational inertia of a urethane longboard wheel, and i need to integrate a section of it that looks like a truncated annular cylinder that looks something like this if you cut it in half

2. Relevant equations
just to be sure that i don't plagiarize or anything, i was hoping for more of a hint instead of a straight up answer if possible... question mark

3. The attempt at a solution
i first derived the equation for the rotational inertia of an annular cylinder (I=(1/2)M(R1^2+R2^2), then i used M=(density)V to find the mass, but i can't find the density unless i dump the wheel into a wet measure filled with water, and i really don't wanna do that.

any ideas?

#### Attached Files:

• ###### wheel.jpg
File size:
18.8 KB
Views:
82
2. Jun 10, 2010

### rock.freak667

Your drawings look like you have a cylinder and then you removed a cone from it, so you can get the inertia like that.

3. Jun 10, 2010

### blahman

actually i figured it out, it just turned out that i needed to dunk the wheel in water no matter what. eh, all in the name of physics i guess

4. Jun 12, 2010

### Ben Niehoff

Why not just put it on a scale and weigh it to find the mass?