Center of mass and Moment of Intertia

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Homework Help Overview

The discussion revolves around calculating the moment of inertia and the center of mass for a specific object with given dimensions and density. The object is described as having a thickness of 2 cm, a density of 7800, an angle of pi/6, and a radius of 0.75 meters, with rotation around the origin.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about finding the center of mass, mentioning integration and referencing a classmate's use of triple integration. They also attempt to relate the moment of inertia to that of a cylinder, using a formula and a reasoning based on angles.
  • Some participants suggest using a different approach to integration for the center of mass, proposing to use "r" instead of Cartesian coordinates.
  • There is a question regarding the validity of the moment of inertia calculation, with a participant prompting a reconsideration of the mass distribution in relation to the cylinder.

Discussion Status

The discussion is ongoing, with participants exploring different methods and questioning assumptions about the calculations. Some guidance has been offered regarding the integration approach for the center of mass, but there remains a lack of consensus on the moment of inertia calculation. The original poster has requested further clarification on these concepts.

Contextual Notes

There is a mention of missing information regarding the integration process and the meaning of "dm," which has not been defined in the discussion. The original poster also indicates a lack of familiarity with certain mathematical concepts, which may affect their understanding of the problem.

sally21
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Homework Statement


The thickness of the object is 2 cm. The density of the material (pronounced row) is 7800. The angle (theta) is pi/6. The radius is .75 meters. What is the moment of inertia and
the center of mass?

Here is what the object looks like:

http://www13.zippyshare.com/v/36721619/file.html

The object is rotating around the origin.


Homework Equations


None given

The Attempt at a Solution


Okay, so I have no idea how to find the center of mass for this object. I know you have to use integration, but the other kid in my class was using triple integration (which is something I don't know and I don't know if he was right any way). So I have no idea how to find the center of mass for this object.

As for the moment of inertia, I think that the moment of inertia will be 1/12 of the moment of inertia of a cylinder. I figure this because pi/6 = 30 degrees. 360/30=12. So I think that the moment of inertia will be:

I= 1/2m[(r1^2)+(r2^2)] * 1/12

this is just the moment of inertia formula for a hollow cylinder and I multiplied it by 1/12.

Thank you very much for helping me in any way!
 
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sally21 said:
Okay, so I have no idea how to find the center of mass for this object. I know you have to use integration, but the other kid in my class was using triple integration (which is something I don't know and I don't know if he was right any way). So I have no idea how to find the center of mass for this object.

You don't need triple integration. Instead of using x,y,z coordinates, use "r" instead. You can integrate dm*r, then divide the result by the mass to get the r coordinate of the center of mass.

As for the moment of inertia, I think that the moment of inertia will be 1/12 of the moment of inertia of a cylinder. I figure this because pi/6 = 30 degrees. 360/30=12. So I think that the moment of inertia will be:

I= 1/2m[(r1^2)+(r2^2)] * 1/12

this is just the moment of inertia formula for a hollow cylinder and I multiplied it by 1/12.

That's not right. Think about it this way: if we fill in the missing 11/12 of the cylinder, the cylinder's mass would be 12m.
 
Oh thank you!

But, I don't really understand how to find the moment of inertia and now I don't know how to find the center of mass. Can you show me how to find it for this problem? I have no idea what dm is.
 
bumb

anyone know how to solve this?
 

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