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This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.
The final column lists some special properties that some of the quantities have, such as their scaling behavior (i.e. whether the quantity is intensive or extensive), their transformation properties (i.e. whether the quantity is a scalar, vector, matrix or tensor), and whether the quantity is conserved.
A free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector. Aside from the notion of units and support, physical vector quantities may also differ from Euclidean vectors in terms of metric.
Position, when thought of as a displacement from an origin point, is a vector: a quantity with both magnitude and direction. [9]: 1 Velocity and acceleration are vector quantities as well. The mathematical tools of vector algebra provide the means to describe motion in two, three or more dimensions.
In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [ 1 ] [ 2 ] It is typically formulated as the product of a unit of measurement and a vector numerical value ( unitless ), often a Euclidean vector with magnitude and direction .
A cylindrical joint requires that a line, or axis, in the moving body remain co-linear with a line in the fixed body. It is a combination of a revolute joint and a sliding joint. This joint has two degrees of freedom. The position of the moving body is defined by both the rotation about and slide along the axis.
A physical quantity (or simply quantity) [1] [a] is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value , which is the algebraic multiplication of a numerical value and a unit of measurement .
Another useful result is Poisson's theorem, which states that if two quantities and are constants of motion, so is their Poisson bracket {,}. A system with n degrees of freedom, and n constants of motion, such that the Poisson bracket of any pair of constants of motion vanishes, is known as a completely integrable system .