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The moment of force, or torque, is a first moment: =, or, more generally, .; Similarly, angular momentum is the 1st moment of momentum: =.Momentum itself is not a moment.; The electric dipole moment is also a 1st moment: = for two opposite point charges or () for a distributed charge with charge density ().
In other words, a couple, unlike any more general moments, is a "free vector". (This fact is called Varignon's Second Moment Theorem.) [2] The proof of this claim is as follows: Suppose there are a set of force vectors F 1, F 2, etc. that form a couple, with position vectors (about some origin P), r 1, r 2, etc., respectively. The moment about P is
If the angular momentum is exactly aligned with a principal axes, the torus degenerates into a single loop. If exactly two moments of inertia are equal (a so-called symmetric body), then in addition to tori there will be an infinite number of loops, and if all three moments of inertia are equal, there will be loops but no tori.
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 ...
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.
A warning has been issued to travelers over the spread of three diseases, including the Marburg virus. It’s a close cousin of Ebola that’s been dubbed the “bleeding eye” virus due to one ...
Eggs are one of the cheapest sources of protein. And they offer a delicious and easy avenue for getting veggies, like in this frittata. Using frozen vegetables saves prep time, too.
A similar definition holds for θ 2, the angle of the second particle. If the path of the first particle is described in the form r = g(θ 1), the path of the second particle is given by the function r = g(θ 2 /k), since θ 2 = k θ 1. For example, let the path of the first particle be an ellipse