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What is meant by the areal velocity is constant?

(1970) [1914]. An Introduction to Celestial Mechanics. Dover. ISBN 978-0-486-64687-9 . Goldstein, H.

Why is areal velocity constant in central force motion?

Constant areal velocity The magnitude of h also equals twice the areal velocity, which is the rate at which area is being swept out by the particle relative to the center. Thus, the areal velocity is constant for a particle acted upon by any type of central force; this is Kepler’s second law.

Is areal velocity directly proportional to velocity?

The areal velocity vector is always perpendicular to the conical surface and is proportional to the angular momentum of the particle. In some problems, the magnitude of the areal velocity is constant while its direction changes. In others, only a component of the areal velocity vector is constant.

What is areal velocity of the planet explain its significance?

Areal velocity of a planet is area traversed/sec by the line joining the centre of planet to the centre of the sun. According to kepler’s second law, the aeal velocity of a plant around the sun remains aleways a constsnt.

What is areal velocity Class 11?

System of Particles and Rotational Motion. The area swept by position vector of a particle in one second is known as the areal velocity.

What is the areal velocity of the particle in a central force field?

3. The particle moves in such a way that the position vector (from the point O) sweeps out equal areas in equal times. In other words, the time rate of change in area is constant. This is referred to as the Law of Areas.

What are the unit of areal velocity?

The SI unit of areal velocity is meter per second (m/s). Explanation: In classical mechanics, areal velocity (also called sector velocity or sectorial velocity) is the rate at which area is swept out by a particle as it moves along a curve.

What is the areal velocity in physics?

Areal velocity. Areal velocity is the area swept out per unit time by a particle moving along a curve (shown in blue). In classical mechanics, areal velocity (also called sector velocity or sectorial velocity) is the rate at which area is swept out by a particle as it moves along a curve.

Why does the areal velocity of a planet change with distance?

The planet moves faster near the Sun, so the same area is swept out in a given time as at larger distances, where the planet moves more slowly. The concept of areal velocity is closely linked historically with the concept of angular momentum. Kepler’s second law states that the areal velocity of a planet, with the sun taken as origin, is constant.

How do you calculate areal velocity from angular momentum?

The areal velocity is simply the rate of change of area with time, so we have areal velocity = ΔA Δt = L 2m. areal velocity = Δ A Δ t = L 2 m. Since the angular momentum is constant, the areal velocity must also be constant. This is exactly Kepler’s second law.

What is sector velocity in physics?

In classical mechanics, areal velocity (also called sector velocity or sectorial velocity) is a pseudovector whose length equals the rate of change at which area is swept out by a particle as it moves along a curve. In the adjoining figure, suppose that a particle moves along the blue curve.