Inertia Moment of Two Rectangles

Inertia Moment of Two Rectangles
Loading the math board and drawing, please wait…
2019-08-21 08:29
This example demonstrates the area moment of inertia of two rectangles. Key mathematical concepts include the geometric properties of rectangles and the calculation of their moment of inertia. Using GeoGebra commands such as Line, Intersect, Point, Polygon, Centroid, etc., rectangles are constructed and their moment of inertia is calculated. Suitable for high school physics and engineering courses.

GeoGebra Commands & Parameters

  1. Line(AA, xAxis) → g
  2. Line(AA, yAxis) → h
  3. Line(AA, zAxis) → i
  4. Intersect(xAxis, yAxis) → A
  5. Point(xAxis) → B
  6. Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
  7. Centroid(poly1) → Cent
  8. Translate(A, v) → A'
  9. Translate(B, v) → B'
  10. Translate(C, v) → C'
  11. Translate(D, v) → D'
  12. Translate(E, v) → E'
  13. Polygon(A', B', C', D', E') → poly1', a', b', c', d', e'
  14. Rotate(A, (-α), g) → A'_1
  15. Rotate(B, (-α), g) → B'_1
  16. Rotate(C, (-α), g) → C'_1
  17. Rotate(D, (-α), g) → D'_1
  18. Rotate(E, (-α), g) → E'_1
  19. Polygon(A'_1, B'_1, C'_1, D'_1, E'_1) → poly1'_1, a'_1, b'_1, c'_1, d'_1, e'_1
  20. Rotate(poly1', (-α), g) → poly1''
  21. Rotate(A, α, h) → A'_2
  22. Rotate(B, α, h) → B'_2
  23. Rotate(C, α, h) → C'_2
  24. Rotate(D, α, h) → D'_2
  25. Rotate(E, α, h) → E'_2
  26. Polygon(A'_2, B'_2, C'_2, D'_2, E'_2) → poly1'_2, a'_2, b'_2, c'_2, d'_2, e'_2
  27. Rotate(poly1', α, h) → poly1''_1
  28. Rotate(A, α, i) → A'_3
  29. Rotate(B, α, i) → B'_3
  30. Rotate(C, α, i) → C'_3
  31. Rotate(D, α, i) → D'_3
  32. Rotate(E, α, i) → E'_3
  33. Polygon(A'_3, B'_3, C'_3, D'_3, E'_3) → poly1'_3, a'_3, b'_3, c'_3, d'_3, e'_3
  34. Rotate(poly1', α, i) → poly1''_2

AI Drawing Prompt Reference

Draw two rectangles and calculate their moments of inertia by rotating them around the x-axis, y-axis, and z-axis. Start by drawing a rectangle on the x-axis, then rotate it around the x-axis. Repeat this process for the y-axis and z-axis. Finally, calculate the moment of inertia for each rotated rectangle.
The prompt above was compiled from the original drawing commands and is for reference only.