How to Calculate Moment of Inertia for Polygons in a 2D System?

  • Context: Undergrad 
  • Thread starter Thread starter Aidman
  • Start date Start date
  • Tags Tags
    Inertia Polygon
Click For Summary
SUMMARY

The calculation of the moment of inertia for polygons in a 2D system can be achieved without triangulation, using a double integral approach. The moment of inertia is calculated relative to the polygon's centroid, assuming a constant density across the polygon. The formula for the moment of inertia is expressed in terms of the position vectors of the vertices, incorporating the polygon's total mass. For complex polygons, the inertia can be derived by dissecting the polygon into simpler shapes, such as triangles, and applying the parallel axis theorem as necessary.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with double integrals in calculus
  • Knowledge of centroid calculations for polygons
  • Basic principles of polygon triangulation
NEXT STEPS
  • Research the application of the parallel axis theorem in moment of inertia calculations
  • Learn about triangulation methods for complex polygons
  • Study the derivation of moment of inertia formulas for various geometric shapes
  • Explore computational methods for calculating inertia using programming languages like Python or MATLAB
USEFUL FOR

Engineers, physicists, and mathematicians involved in structural analysis, CAD modeling, or any field requiring precise calculations of rotational dynamics for polygonal shapes.

  • #31
GINGERBEER said:
Sorry to comment on an old thread but i was just wondering why the ||\vec{P}_{n+1}\times\vec{P}_{n}|| is not canceled out in the equation seeing as it is in the numerator and denominator.

You can only cancel common factors in the numerator and denominator.

Just because a given term in the numerator happens to include a factor that is identical to a term in the numerator does not make this into a common factor.
 

Similar threads

Undergrad How do you find the moment of inertia of a polygon?
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad Moment of inertia of a polygon
  • · Replies 3 ·
Replies
3
Views
11K
Undergrad Finding the moment of inertia of a 2D polygon.
  • · Replies 2 ·
Replies
2
Views
15K
Graduate How to derive the formula for moment of inertia of polygon?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Similar Polygon Comparison for School Project
  • · Replies 9 ·
Replies
9
Views
2K
Calculating Moment of Inertia for Hollow Cylinder w/ Water
  • · Replies 40 ·
2
Replies
40
Views
6K
Moment of inertia for Concave Polygon
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Axial angular momentum calculation
  • · Replies 30 ·
2
Replies
30
Views
4K
Graduate Ordering Line Segments to form a 2D Polygon after slicing a 3D Tri Map
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad How find moment of inertia for car in turn?
  • · Replies 49 ·
2
Replies
49
Views
5K