angular momentum (redirected from Rotational angular momentum)

angular momentum: see momentum.

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angular momentum

Property that describes the rotary inertia of a system in motion about an axis. It is a vector quantity, having both magnitude and direction. The magnitude of the angular momentum of an object is the product of its linear momentum (mass m × velocity v) and the perpendicular distance r from the centre of rotation, or mvr. The direction is that of the axis of rotation. The angular momentum of an isolated system is constant. This means that a rigid spinning object continues to spin at a constant rate unless acted upon by an external torque. A spinning gyroscope in an airplane remains fixed in its orientation, independent of the airplane's motion, because of the conservation of direction as well as magnitude.

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angular momentum [′aŋ·gyə·lər mə′ment·əm]

(mechanics)

The cross product of a vector from a specified reference point to a particle, with the particle's linear momentum. Also known as moment of momentum.

For a system of particles, the vector sum of the angular momenta (first definition) of the particles.

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Angular momentum

In classical physics, the moment of linear momentum about an axis. A point particle with mass m and velocity v has linear momentum p = m v . Let r be an instantaneous position vector that locates the particle from an origin on a specified axis. The angular momentum L can be written as the vector cross-product in Eq. (1). (1)  See Momentum

The time rate of change of the angular momentum is equal to the torque N . A rigid body satisfies two independent equations of motion (the dynamical equations) given by

(2) 

(3) 

Eqs. (2) and (3), where d/dt denotes the rate of change, the derivative with respect to time t. Only Eq. (2) is required for a point particle. Equation (2) indicates that a rigid body acts as a point particle located at its center of mass. The motion of the center of mass depends upon the net force F , which is the vector sum of all applied forces. Equation (3) gives the angular motion about the center of mass. The case of statics occurs when the net force and net torque both vanish. See Kinetics (classical mechanics), Statics, Torque

A symmetry is a transformation that leaves a physical system unchanged. A physical quantity is called invariant under a transformation if it remains the same after being transformed. For example, the solutions to Eqs. (2) and (3) are invariant under change of the coordinate origin or orientation of the i , j , and k axes. The freedom to choose any orientation of coordinate axes is called rotational invariance, because one choice of axes can be rotated into another. In physics, the rotational invariance follows from the isotropy and homogeneity of space that has been experimentally established to high accuracy.

The study of symmetry shows that one of the deepest relations in physics is that between dynamics and conservation. A physical quantity is conserved if it is constant in time, although it may vary in space. Noether's theorem states that if a physical system is invariant under a continuous symmetry, a conservation law exists, provided that the observable in question decreases rapidly enough at infinity. Thus, when the force is zero everywhere (the system is invariant under translation in space), the linear momentum is conserved. If the torque is zero everywhere (the system is invariant under rotation), the angular momentum is conserved. If the system is invariant under translations in time, the total energy is conserved. See Conservation laws (physics), Conservation of energy, Conservation of momentum

Quantum mechanics has a richer and more complicated structure than classical physics. Because of this, the relationship between symmetry and conservation is even more useful.