What is areal velocity?

Answer 1

The areal velocity of a particle is the rate at which area is swept out as the particle travels along a curve. The area is swept out by a vector (starting at the origin.)

In words:

Imagine an empty space with a single point in it. That point doesn't move; it represents the the origin. Now image a particle flying around in that space. An arrow always points from the origin to that particle (and touches the particle). As the particle moves, that arrow moves, possibly getting longer or shorter depending on where the particle is. Instead of just moving though, it creates a "path" of area. Everywhere that arrow touches in the space, it "paints" that space, so as it moves, more and more space gets "painted". This "painted space" is the area. The rate at which the amount of this "painted space" changes is the areal velocity of that particle.

As equations:

dA/dt=r x v/2

dA/dt=L/(2m)

Notice that the areal velocity is a vector.

Answer 2

Areal velocity is the rate at which a two-dimensional area is swept out by a moving particle. It is calculated as the cross product of the position vector and the velocity vector of the particle. Areal velocity is important in the study of angular momentum and orbital mechanics.