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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.
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. [1] [2]: 183–184 Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory.
A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry. All celestial objects – planets, stars , galaxies, black holes – spin. [1] [2] [3] The boundaries of a Kerr black hole relevant to astrophysics. Note that there are no physical "surfaces" as such.
When planets spin, they generate angular momentum. This does things such as cause the planet to be slightly oval-shaped, and cause deformities [6] in the planet. Another example of angular mechanics in planetary motion is orbiting around a star. Because of the speed of the orbit, they do not go plummeting into their star.
For reference and background, two closely related forms of angular momentum are given. In classical mechanics, the orbital angular momentum of a particle with instantaneous three-dimensional position vector x = (x, y, z) and momentum vector p = (p x, p y, p z), is defined as the axial vector = which has three components, that are systematically given by cyclic permutations of Cartesian ...
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 total angular momentum of light consists of two components, both of which act in a different way on a massive colloidal particle inserted into the beam. The spin component causes the particle to spin around its axis, while the other component, known as orbital angular momentum (OAM), causes the particle to rotate around the axis of the beam.
The quantity S is the density of spin angular momentum (spin in this case is not only for a point-like particle, but also for an extended body), and M is the density of orbital angular momentum. The total angular momentum is always the sum of spin and orbital contributions. The relation: gives the torque density showing the rate of conversion ...