“angular momentum”的概念、定义、翻译、参考文献-科学参考

angular momentum

Physics

Symbol L. The product of the angular velocity of a body and its moment of inertia about the axis of rotation, i.e. L=Iω‎.

Mathematics

Suppose that the particle P of mass m has position vector r and is moving with velocity v. Then the angular momentum L of P about the point A with position vector r_A is the vector defined by L=(r−r_A) ×mv. It is the moment of the linear momentum about the point A. See also conservation of angular momentum.

Consider a rigid body rotating with angular velocity ω‎ about a fixed axis, and let L be the angular momentum of the rigid body about a point on the fixed axis. Then L = Iω‎, where I is the moment of inertia of the rigid body about the fixed axis.

To consider the general case, let ω‎ and L be column vectors representing the angular velocity and the angular momentum of a rigid body about a fixed point (or the centre of mass). Then L = Iω‎, where I is a 3 × 3 matrix, called the inertia matrix, whose elements involve the moments of inertia and the products of inertia of the rigid body relative to axes through the fixed point (or centre of mass).

The rotational motion of a rigid body depends on the angular momentum of the rigid body. In particular, the rate of change of the angular momentum about a fixed point (or centre of mass) equals the sum of the moments of the forces acting on the rigid body about the fixed point (or centre of mass).

Astronomy

The momentum a body has by virtue of its rotation. A body such as a planet has two types of angular momentum: one type results from its motion in orbit around the Sun, and the other from its spin on its own axis. Angular momentum in orbit is given by the body’s mass multiplied by its orbital angular velocity and by its distance from the Sun. Angular momentum of spin depends on the mass of the body’s individual parts and their distances from its centre (the moment of inertia) multiplied by its angular velocity of spin. As a consequence of conservation of angular momentum, a body spins faster as it gets smaller, such as when a gas cloud shrinks to become a star.

Chemistry

A property of a rotating body. In the case of a rigid rotating body the angular momentum is given by Iω‎, where I is the moment of inertia of the body and ω‎ is its angular velocity. The quantum theory of angular momentum is closely associated with the rotation group and has important applications in the electronic structure of atoms and diatomic molecules and rotational spectroscopy of molecules. Electron spin is a type of angular momentum.

Chemical Engineering

A measure of the momentum of a body caused by its circular motion around an axis of rotation. It is the vector product of the position vector and the tangential component of velocity of an object moving about a centre of rotation. The angular momentum of a mass m of fluid is mv_θr where v_θ is the tangential velocity.

Geology and Earth Sciences

The momentum of a body rotating in a plane around a point. It is formally the product of the mass of the body, the radius of the orbit, and the square of the angular velocity (mrω‎²). Because of its rotation about its axis, the Earth has rotational angular momentum, and orbital angular momentum on account of its annual revolution around the Sun. The angular momentum of the Earth–Moon system (3.45 × 10³⁴ rad/kg/m²/s) is the sum of the rotational angular momentum of the Earth and the Moon’s orbital angular momentum, and is high compared to that of the other terrestrial planets.

Geography

The momentum of a body taking a curved path; for a rotating planet, angular momentum is defined as the moment of the linear momentum of a particle about a point, thus:
$M = \underset{r}{\to} x m \underset{V}{\to}$
where M is the angular momentum about a point 0, $\underset{r}{\to}$ the position vector from 0 to the particle, m the mass of the particle, and $\underset{V}{\to}$ the velocity. As Rossby (1940) Q. J. Royal Met. Soc. 66, 68 explains, the Earth’s angular momentum can easily be visualized by taking a marble on the end of a string and rotating it on a smooth table. If the string is shortened the rate increases; if lengthened it slows. The speed is inversely proportional to radius. Thus, part of the atmospheric envelope, rotating with the Earth at the equator, moves polewards, it will tend to speed up; see conservation of angular momentum.

单词	angular momentum
释义	angular momentum Physics Symbol L. The product of the angular velocity of a body and its moment of inertia about the axis of rotation, i.e. L=Iω‎. Mathematics Suppose that the particle P of mass m has position vector r and is moving with velocity v. Then the angular momentum L of P about the point A with position vector r_A is the vector defined by L=(r−r_A) ×mv. It is the moment of the linear momentum about the point A. See also conservation of angular momentum. Consider a rigid body rotating with angular velocity ω‎ about a fixed axis, and let L be the angular momentum of the rigid body about a point on the fixed axis. Then L = Iω‎, where I is the moment of inertia of the rigid body about the fixed axis. To consider the general case, let ω‎ and L be column vectors representing the angular velocity and the angular momentum of a rigid body about a fixed point (or the centre of mass). Then L = Iω‎, where I is a 3 × 3 matrix, called the inertia matrix, whose elements involve the moments of inertia and the products of inertia of the rigid body relative to axes through the fixed point (or centre of mass). The rotational motion of a rigid body depends on the angular momentum of the rigid body. In particular, the rate of change of the angular momentum about a fixed point (or centre of mass) equals the sum of the moments of the forces acting on the rigid body about the fixed point (or centre of mass). Astronomy The momentum a body has by virtue of its rotation. A body such as a planet has two types of angular momentum: one type results from its motion in orbit around the Sun, and the other from its spin on its own axis. Angular momentum in orbit is given by the body’s mass multiplied by its orbital angular velocity and by its distance from the Sun. Angular momentum of spin depends on the mass of the body’s individual parts and their distances from its centre (the moment of inertia) multiplied by its angular velocity of spin. As a consequence of conservation of angular momentum, a body spins faster as it gets smaller, such as when a gas cloud shrinks to become a star. Chemistry A property of a rotating body. In the case of a rigid rotating body the angular momentum is given by Iω‎, where I is the moment of inertia of the body and ω‎ is its angular velocity. The quantum theory of angular momentum is closely associated with the rotation group and has important applications in the electronic structure of atoms and diatomic molecules and rotational spectroscopy of molecules. Electron spin is a type of angular momentum. Chemical Engineering A measure of the momentum of a body caused by its circular motion around an axis of rotation. It is the vector product of the position vector and the tangential component of velocity of an object moving about a centre of rotation. The angular momentum of a mass m of fluid is mv_θr where v_θ is the tangential velocity. Geology and Earth Sciences The momentum of a body rotating in a plane around a point. It is formally the product of the mass of the body, the radius of the orbit, and the square of the angular velocity (mrω‎²). Because of its rotation about its axis, the Earth has rotational angular momentum, and orbital angular momentum on account of its annual revolution around the Sun. The angular momentum of the Earth–Moon system (3.45 × 10³⁴ rad/kg/m²/s) is the sum of the rotational angular momentum of the Earth and the Moon’s orbital angular momentum, and is high compared to that of the other terrestrial planets. Geography The momentum of a body taking a curved path; for a rotating planet, angular momentum is defined as the moment of the linear momentum of a particle about a point, thus: $M = \underset{r}{\to} x m \underset{V}{\to}$ where M is the angular momentum about a point 0, $\underset{r}{\to}$ the position vector from 0 to the particle, m the mass of the particle, and $\underset{V}{\to}$ the velocity. As Rossby (1940) Q. J. Royal Met. Soc. 66, 68 explains, the Earth’s angular momentum can easily be visualized by taking a marble on the end of a string and rotating it on a smooth table. If the string is shortened the rate increases; if lengthened it slows. The speed is inversely proportional to radius. Thus, part of the atmospheric envelope, rotating with the Earth at the equator, moves polewards, it will tend to speed up; see conservation of angular momentum.
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