Moment About the Origin

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2015-12-04 14:13

Vector Function Calculus

This example demonstrates how to calculate the moment. It shows the moment in action through two different equations. Commands used include Point, Vector, Translate, Segment, Angle, OrthogonalLine, Rotate, Intersect, and Integral. Suitable for high school and above students learning the concept of moment in calculus.

GeoGebra Commands & Parameters

Point(Moment) → A
Vector(B, C) → u
Translate(A, u) → A'
Vector(D, E) → v_1
Translate(A', v_1) → A''
Segment(A'', A) → b
Segment(A'', A') → c
Segment(A, A') → d
Vector(F, G) → w
Translate(A, w) → A'_1
Vector(A, A'_1) → m
Vector(A'', A'_1) → g
Point(b) → I
Segment(H, I) → h
Segment(H, J) → i
Angle(J, H, I) → α
Point(Moment) → K
Point(Moment) → L
Segment(K, L) → j
Point(Moment) → M
Point(j) → P
Segment(P, M) → l_1
Point(Circle[P, 7.3]) → Q
Point(j) → R
Vector(P, A) → l
Point(l) → O
Segment(P, O) → q
Angle(j, q) → β
OrthogonalLine(S, j) → v
Point(v) → T
Rotate(T, 180°, S) → T'
Segment(T, T') → k
Angle(j, k) → γ
Angle(b, h) → δ
Intersect(Moment, b, (1.6000000000000005, 4.748376421329871)) → U
Point(m) → V
Segment(U, V) → pm
Angle(b, pm) → ε
Point(l) → W
Integral(f, 0, 50) → m_r
Integral(Moment, -25, 25) → m_x

AI Drawing Prompt Reference

Draw a moment about the origin. Start by creating point A and vector u, then translate A to get A'. Next, create vector v1, translate A' to get A'', and connect A'', A, and A' to form segments b, c, and d. Then, create vector w, translate A to get A'_1, and get vectors m and g. Next, create point I, line segment h, i, and angle α. Then, create points K, L, M, line segments j, l1, and points Q, R. Next, create vector l, point O, line segment q, and angle β. Then, create perpendicular line v, points T, T', line segment k, and angles γ and δ. Finally, create points U, V, line segment pm, and angle ε.

The prompt above was compiled from the original drawing commands and is for reference only.