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The trivial case of the angular momentum of a body in an orbit is given by = where is the mass of the orbiting object, is the orbit's frequency and is the orbit's radius.. The angular momentum of a uniform rigid sphere rotating around its axis, instead, is given by = where is the sphere's mass, is the frequency of rotation and is the sphere's radius.
Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]
The torque acting on a point-like particle is defined as the derivative of the angular momentum tensor given above with respect to proper time: [8] [9] = = or in tensor components: = where F is the 4d force acting on the particle at the event X. As with angular momentum, torque is additive, so for an extended object one sums or integrates over ...
Quantum orbital motion involves the quantum mechanical motion of rigid particles (such as electrons) about some other mass, or about themselves.In classical mechanics, an object's orbital motion is characterized by its orbital angular momentum (the angular momentum about the axis of rotation) and spin angular momentum, which is the object's angular momentum about its own center of mass.
A diagram of angular momentum. Showing angular velocity (Scalar) and radius. In physics, angular mechanics is a field of mechanics which studies rotational movement. It studies things such as angular momentum, angular velocity, and torque. It also studies more advanced things such as Coriolis force [1] and Angular aerodynamics.
When Newton's laws are applied to rotating extended bodies, they lead to new quantities that are analogous to those invoked in the original laws. The analogue of mass is the moment of inertia, the counterpart of momentum is angular momentum, and the counterpart of force is torque. Angular momentum is calculated with respect to a reference point ...
where is the mass of the rigid body; ¯ is the velocity of the center of mass of the rigid body, as viewed by an observer fixed in an inertial frame N; ¯ is the angular momentum of the rigid body about the center of mass, also taken in the inertial frame N; and is the angular velocity of the rigid body R relative to the inertial frame N. [3]
Left: intrinsic "spin" angular momentum S is really orbital angular momentum of the object at every point, right: extrinsic orbital angular momentum L about an axis, top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω) [6] bottom: momentum p and its radial position r from the axis. The total angular ...