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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.
Total energy is the sum of rest energy = and relativistic kinetic energy: = = + Invariant mass is mass measured in a center-of-momentum frame. For bodies or systems with zero momentum, it simplifies to the mass–energy equation E 0 = m 0 c 2 {\displaystyle E_{0}=m_{0}c^{2}} , where total energy in this case is equal to rest energy.
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 ...
Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation , the following dependence on the object's moment of inertia is observed: [ 1 ] E rotational = 1 2 I ω 2 {\displaystyle E_{\text ...
In celestial mechanics, the specific relative angular momentum (often denoted or ) of a body is the angular momentum of that body divided by its mass. [1] In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum , divided by the mass of the body in question.
The greater the angular momentum of the spinning object such as a top, the greater its tendency to continue to spin. The angular momentum of a rotating body is proportional to its mass and to how rapidly it is turning. In addition, the angular momentum depends on how the mass is distributed relative to the axis of rotation: the further away the ...
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.
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]