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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
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 the magnetic pole model, the magnetic dipole moment is due to two equal and opposite magnetic charges that are separated by a distance, d. In this model, m is similar to the electric dipole moment p due to electrical charges: =, where q m is the ‘magnetic charge’. The direction of the magnetic dipole moment points from the negative south ...
The moment tensor solution is displayed graphically using a so-called beachball diagram. The pattern of energy radiated during an earthquake with a single direction of motion on a single fault plane may be modelled as a double couple, which is described mathematically as a special case of a second order tensor (similar to those for stress and strain) known as the moment tensor.
Peanut Butter Blossoms. As the story goes, a woman by the name of Mrs. Freda F. Smith from Ohio developed the original recipe for these for The Grand National Pillsbury Bake-Off competition in 1957.
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.
Euler angles are one way to represent orientations. There are others, and it is possible to change to and from other conventions. Three parameters are always required to describe orientations in a 3-dimensional Euclidean space. They can be given in several ways, Euler angles being one of them; see charts on SO(3) for others.
President-elect Trump's adviser on government efficiency, Elon Musk, called for eliminating the Consumer Financial Protection Bureau.