Finding the moment of inertia for a specific figure (illustrated)

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SUMMARY

The discussion focuses on calculating the moment of inertia for a specific geometric figure, utilizing the principles of symmetry and similar triangles. The solution involves integrating the figure's dimensions, specifically using the height fraction h/2 to account for symmetry. Participants clarify that the base of the smaller triangle can be derived from the larger triangle's base, denoted as b. This understanding is crucial for accurately applying the moment of inertia formula presented in the referenced image.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with integral calculus
  • Knowledge of geometric properties of triangles
  • Ability to interpret and manipulate mathematical equations
NEXT STEPS
  • Study the derivation of the moment of inertia formula for various shapes
  • Learn about the application of integral calculus in physics
  • Explore the properties of similar triangles in geometric calculations
  • Practice solving problems involving symmetry in physical figures
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Students in physics or engineering courses, educators teaching mechanics, and anyone interested in understanding the application of calculus to physical properties of shapes.

PhyIsOhSoHard
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Homework Statement


http://img577.imageshack.us/img577/2069/inertia.gif

The following figure with these known lengths are given. I need to find the moment of inertia.

Homework Equations


According to my book's facit, this is the solution:
http://img845.imageshack.us/img845/6725/inertiaformula.png

The Attempt at a Solution


This is what I understand so far...
The fraction h/2 refers to half the figure (when cut from horizontal). So you start from the middle of the figure, and then move up to the end in which case you have traveled the vertical length h/2. Then by multiplying the entire integral with 2, you take the bottom half of the figure into account as well (since it's symmetrical).

I have no idea about the fraction. I've tried, but I have no idea how they came up with that. All I know is that "y" is the vertical axis for the figure...
 
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Welcome to PF!

Hi PhyIsOhSoHard! Welcome to PF! :smile:
PhyIsOhSoHard said:
I have no idea about the fraction. I've tried, but I have no idea how they came up with that. All I know is that "y" is the vertical axis for the figure...

it's similar triangles …

you want the base of the smaller triangle, and you know that the base of the larger triangle is b :wink:
 

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