Radius of Gyration and moment of inertia

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SUMMARY

The discussion focuses on calculating the radius of gyration and moment of inertia for a composite shape consisting of an outer and inner disk. The formula used is r = sqrt(I/A), where A is the area (33π) and I is the moment of inertia. The moment of inertia is determined using the equation I = I_outer - I_inner, applying the parallel axis theorem for the inner disk. The final result for the radius of gyration is 5.66.

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  • Understanding of moment of inertia and its calculation
  • Familiarity with the parallel axis theorem
  • Knowledge of geometric properties of circles
  • Basic algebra for manipulating equations
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  • Study the parallel axis theorem in detail
  • Learn about calculating moment of inertia for various shapes
  • Explore applications of radius of gyration in engineering
  • Investigate the properties of composite shapes in mechanics
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Students in physics or engineering, particularly those studying mechanics, as well as professionals involved in structural analysis and design.

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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