Radius of Gyration and moment of inertia

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Homework Help Overview

The discussion revolves around the concepts of radius of gyration and moment of inertia, particularly in relation to a circular shape. Participants explore the relationship between area and moment of inertia in their calculations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formula for radius of gyration and attempt to calculate moment of inertia. There is an exploration of finding the centroid and using the parallel axis theorem to adjust for different axes of rotation.

Discussion Status

The conversation includes various attempts to calculate the moment of inertia, with some participants suggesting alternative approaches. There is acknowledgment of a better method involving the subtraction of inner and outer moments of inertia, and guidance is provided regarding the application of the parallel axis theorem.

Contextual Notes

Participants mention specific values for area and mass, as well as the need to ensure calculations are centered about a specific point. There is an indication of a potential misunderstanding regarding the positioning of the inner disc in relation to the axis of rotation.

SteelDirigibl
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Homework Statement


Screenshot2011-04-22at53716PM.png



Homework Equations


i guess its r=sqrt(I/A)
where A is the area of the circle thing and I is the moment of intertia.

The Attempt at a Solution



I guess I'm just having trouble getting I. A is 33pi
 
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what have you tried?
 
finding the centroid of the shape.
 
were you able to find that? I think there is a better approach: I = I_outer - I_inner . (be careful that everything is calculated about O).
 
how do I find I_inner ?
 
The moment of inertia of a uniform disk around its center is 1/2MR^2. However, the inner disc (the empty region) is not centered on O, but on C. You have to use the parallel axis theorem to account for this.
 
so according to that...

1/2*49pi*7^2 [I_outer] - (1/2*16pi*4^2+16*1)[I_inner]=3319

3319/(33pi)=32

sqrt(32)=5.66

And that was right...
thanks guys. I understand it a little better now..
 

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