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Dimensions (mechanics)

Length, mass, time, or combinations of these quantities serving as an indication of the nature of a physical quantity. Quantities with the same dimensions can be expressed in the same units. For example, although speed can be expressed in various units such as miles/hour, feet/second, and meters/second, all these speed units involve the ratio of a length unit to a time unit; hence, the dimensions of speed are the ratio of length L to time T, usually stated as LT-1. The dimensions of all mechanical quantities can be expressed in terms of L, T, and mass M. The validity of algebraic equations involving physical quantities can be tested by a process called dimensional analysis; the terms on the two sides of any valid equation must have the same dimensions. See Dimensional analysis, Units of measurement



The dimensions of a physical quantity show by what factor the unit of the physical quantity is changed when the units of the quantities adopted as fundamental in the given system are altered. The dimensions are expressed by a monomial consisting of the product of various powers of the fundamental units, which are represented by generalized symbols; the exponents may be positive or negative integers or fractions. Thus, the dimensions of velocity are LT-1, where T represents the dimension of time and L the dimension of length. These symbols denote the units of time and length regardless of the specific size of the units. The units may be, for example, a second, minute, or hour and a meter or centimeter. In many cases, the dimensions permit the relations between corresponding quantities to be established.


The product of powers of fundamental quantities (or of convenient derived quantities) which are used to define a physical quantity; the fundamental quantities are often mass, length, and time.
References in periodicals archive ?
Programmatic use of processes promoting focused conversation around mutual problem-solving, shared visioning, collaborative learning, collegial coaching, and shared work do appear to facilitate the development of teacher thinking across the dimensions of dialogue identified in the analysis.
In the late 1970s, mathematicians used Delsarte's methods to figure out the kissing numbers in dimensions 8 and 24.
In this article we use the integral model to illustrate how dimensions of spiritual wellness (drawn from the authors cited above) can be part of a school guidance program.
If the counselor and retiree find that the potential career environment does not support older workers, the counselor and retiree might decide that the environment dimensions do not adequately correspond with the retiree's individual dimensions.
Having adopted the term science to comprehend this particular domain of scientific knowledge and activity, we now need to be clear whether we are only concerned with its epistemological dimension dealing with knowledge content or only with its ethical dimension dealing with applications of that knowledge, or with both.
Dislocation lines in icosahedral quasicrystals arise from a four-dimensional defect surface in six dimensions.
The Mayo Clinic experience using a structured paper medical record system gives a glimpse of what could be accomplished at every center after achievement of the Z dimension of CIS.
This allowed the molder to see shot-to-shot variations in process parameters, and correlate them with shot-to-shot variations in part dimensions.
Of the five dimensions hypothesized by Schornmer's (1990) model, on which the scenario was based, only omniscient authority did not appear as its own factor in the analysis.
In this new hypothesis of so-called large extra dimensions resides a possible solution to a long-standing puzzle: Why is gravity so much weaker than the other forces?
The relation between the second and third dimensions may also have interesting implications.