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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 classic literature ?
But some philosophical people have been asking why THREE dimensions particularly--why not another direction at right angles to the other three?
By giving the balloon these cubic dimensions, and filling it with hydrogen gas, instead of common air--the former being fourteen and a half times lighter and weighing therefore only two hundred and seventy-six pounds--a difference of three thousand seven hundred and twenty-four pounds in equilibrium is produced; and it is this difference between the weight of the gas contained in the balloon and the weight of the surrounding atmosphere that constitutes the ascensional force of the former.
Their method of communication Perry has likened to the pro-jection of a sixth sense into a fourth dimension, where it becomes cognizable to the sixth sense of their audience.
Pete's air of distinguished valor had grown upon him until it threatened stupendous dimensions.
This distinguished scientist has expounded his views in a book entitled "Verschwinden und Seine Theorie," which has attracted some attention, "particularly," says one writer, "among the followers of Hegel, and mathematicians who hold to the actual existence of a so- called non-Euclidean space--that is to say, of space which has more dimensions than length, breadth, and thickness--space in which it would be possible to tie a knot in an endless cord and to turn a rubber ball inside out without 'a solution of its continuity,' or in other words, without breaking or cracking it.
Nevertheless, after mature consideration, it has appeared to me that the question of the projectile must take precedence of that of the cannon, and that the dimensions of the latter must necessarily depend on those of the former.
There is the "Sea of Serenity," over which the young girl bends; "The Lake of Dreams," reflecting a joyous future; "The Sea of Nectar," with its waves of tenderness and breezes of love; "The Sea of Fruitfulness;" "The Sea of Crises;" then the "Sea of Vapors," whose dimensions are perhaps a little too confined; and lastly, that vast "Sea of Tranquillity," in which every false passion, every useless dream, every unsatisfied desire is at length absorbed, and whose waves emerge peacefully into the "Lake of Death
When looking down from the highest crest of the Cordillera, the mind, undisturbed by minute details, was filled with the stupendous dimensions of the surrounding masses.
And the more he worked in this cause, the more incontestable it seemed to him that it was a cause destined to assume vast dimensions, to create an epoch.
It was not badly named in one respect, being in truth a particularly little Bethel--a Bethel of the smallest dimensions-- with a small number of small pews, and a small pulpit, in which a small gentleman (by trade a Shoemaker, and by calling a Divine) was delivering in a by no means small voice, a by no means small sermon, judging of its dimensions by the condition of his audience, which, if their gross amount were but small, comprised a still smaller number of hearers, as the majority were slumbering.
Or if this postulate is as untenable as all the others, still I am very glad that I did not then lose any fact of the majesty, and beauty, and pathos of the great certain measures for the sake of that fourth dimension of the poem which is not yet made palpable or visible.
Among themselves they communicate by means of what Perry says must be a sixth sense which is cognizant of a fourth dimension.