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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
In an inertial frame of reference (subscripted "in"), Euler's second law states that the time derivative of the angular momentum L equals the applied torque: = For point particles such that the internal forces are central forces, this may be derived using Newton's second law.
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.
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 ...
Hyundai and Kia are recalling over 208,000 electric vehicles to fix a pesky problem that can cause loss of drive power, increasing the risk of a crash. The recalls cover more than 145,000 Hyundai ...
Dr. Jeremy London, shown above, is a cardiovascular surgeon in Savannah, Georgia. He shared some strong thoughts about red wine and the heart.
Organic eggs sold at Costco are being recalled due to the risk that they may expose consumers to salmonella, a type of bacteria that can be deadly for certain populations.