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Earth's Rotational Linear Speed Calculator

Earth's Rotational Linear Speed Calculator
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2017-10-06 23:18
VectorTrigonometryCoordinate GeometryGeometric Construction
In collections Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster
This example demonstrates the variation of linear speed at different latitudes as Earth rotates about its axis. Key math concepts include circular motion, trigonometry, vector operations, and analytical geometry. Construction highlights involve GeoGebra commands such as IntersectPath, Rotate, Dilate, Segment, Angle, Polygon, Line, Textfield, Vector, and Translate. Suitable for high school and above students to understand Earth's rotation and linear speed relationships, fostering spatial reasoning skills.

GeoGebra Commands & Parameters

  1. IntersectPath(z = 0, a) → c
  2. Plane((0, 0, 0), (1, 0, 0), (2, 0, 1)) → d
  3. Rotate(A, (b * π / 180), (0, 0, 0), d) → A'
  4. IntersectPath(f, a) → g
  5. Dilate(B, If[0 < h ≤ 1, 1 - h, 0], A') → B'
  6. Segment(B, B') → i
  7. Angle(A, B, A') → α
  8. Dilate(A', If[1 < h ≤ 2, 2 - h, 0], C) → A''
  9. Segment(A', A'') → j
  10. Dilate(C, If[2 < h ≤ 3, 3 - h, 0], B) → C'
  11. Segment(C, C') → k
  12. Angle(A', C, B) → β
  13. Polygon(B, C, A') → t1, a', b_1, c_1
  14. Line(B, (1, 0, 0)) → l
  15. Line(B, (0, 0, 1)) → m
  16. Line(B, (0, 1, 0)) → n
  17. Rotate(C, o, B, z = 0) → C'_1
  18. Polygon(B, C'_1, E) → t2, e_1, b_2, c'_1
  19. Segment(B, E) → p
  20. Segment(E, C'_1) → q
  21. Segment(C'_1, B) → r
  22. Angle(C'_1, B, E) → γ
  23. Angle(B, C'_1, E) → δ
  24. Textfield(b) → InputBox1
  25. Dilate(B, If[0 < t ≤ 1, 1 - t, 0], F) → B'_1
  26. Vector(B, B'_1) → u
  27. Translate(C, u) → C'_2
  28. Translate(C', u) → C''
  29. Segment(C'_2, C'') → k'