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Areal velocity is the rate at which area is swept by the position vector of a point which moves along a curve. Areal velocity is the magnitude of the areal velocity vector, which is parallel (but not necessarily proportional in magnitude) to the angular velocity vector. Jump to: navigation, search This article is about velocity in physics. ...
This article explains the meaning of area as a physical quantity. ...
The word vector means carrier in Latin; it is derived from the Latin verb vehere, which means to carry. ...
In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ...
Areal velocity depends on a reference point: the origin of the coordinate system of the position vector, which is a function of time. The origin of something (from the Latin origo, beginning) is where it came from, in the sense of a physical location or a metaphysical source. ...
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 Figure 1. Areal velocity is the area (shown in yellow) swept per unit time by a particle moving along a curve (shown in blue). Figure 1 shows a regular curve in blue. At time t a moving particle is located at point B, and at time t + Δt the same particle has moved to point C. Jump to: navigation, search Image File history File links ArealVelocity. ...
Jump to: navigation, search Image File history File links ArealVelocity. ...
The area swept (or transcribed) during time period Δt by the particle is nearly equal to the area of triangle ABC. As Δt approaches zero this near equality becomes exact as a limit. Jump to: navigation, search In mathematics, the limit of a function is a fundamental concept in mathematical analysis. ...
Meanwhile, vectors AB and AC add up by the parallelogram method to vector AD, so that point D is the fourth corner of parallelogram ABDC shown in Figure 1.
The area of triangle ABC (in yellow) is half the area of parallelogram ABDC, and the area of ABDC is equal to the magnitude of the cross product of vectors AB and AC, so that In mathematics, the cross product is a binary operation on vectors in a three dimensional vector space. ...
The areal velocity vector is -
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But r′(t) is the linear velocity vector v(t), so that Kepler's second law of planetary motion is a statement of conservation of areal velocity of the orbiting planet with respect to the Sun. Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ...
Notice that twice the areal velocity times mass equals angular momentum, just as linear velocity times mass is linear momentum, i.e. In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the direction in which, the object rotates about the reference point. ...
- linear velocity : linear momentum :: (double) areal velocity : angular momentum.
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