What's the difference between dimension and unit? Dimension Definition: n. Measure in a single line, as length, breadth, height, thickness, or circumference; extension; measurement; -- usually, in the plural, measure in length and breadth, or in length, breadth, and thickness; extent; size; as, the dimensions of a room, or of a ship; the dimensions of a farm, of a kingdom.
Extent; reach; scope; importance; as, a project of large dimensions. The degree of manifoldness of a quantity; as, time is quantity having one dimension; volume has three dimensions, relative to extension. A literal factor, as numbered in characterizing a term. The term dimensions forms with the cardinal numbers a phrase equivalent to degree with the ordinal; thus, a2b2c is a term of five dimensions, or of the fifth degree. The manifoldness with which the fundamental units of time, length, and mass are involved in determining the units of other physical quantities.
Example Sentences: 1 There was a linear increase in the dimensions of these zones after the chewing. Usually the quantity to be measured influences the choice of units to be employed, that is, meters or feet to measure the length of the book rather than kilometers or miles. Units are artificial constructs that allow people to express a dimension as a number. This allows physicians to use arithmetic calculations to predict an experimental result.
Very powerful invention. And a dimension is an arbitrarily chosen physical property. In English, a number can be also called a "quantity"; hence, a "physical quantity" is a number of physical units. For example: "this ball will fall for a quite short span of time" can be more precisely expressed as "this ball will fall 3 seconds".
Note that in both cases dimension is time, but only in the latter case it could be computed. Alas your book maybe Elements of Physics judging from a cursory Google Books search uses different definitions. It assumes a base of fundamental quantities. Say [mass, length, time].
In such base a unit of an area can be described as [0, 2, 0] and unit of acceleration as [0, 1, -2]. They don't call the fundamental quantities "dimensions". They don't call these vectors of exponents "dimensions". Dimension is defined as a single exponent that comprises that vector. Just one small number. Confusing, isn't it? As you see, with such definition, "dimensions are powers".
To obtain a unit of area, you need to assign a dimension of 2 to a unit of length. So one of dimensions is literally 2 and other dimensions are zero. Personally, I think such definition of "dimension" is utter crap, especially when talking to mathematicians.
Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Difference between units and dimensions Ask Question. Asked 4 years, 5 months ago. Active 2 years, 7 months ago. Viewed 6k times. There was a line in my book which stated Mass, length, time, thermodynamic temperature, electric current, amount of substance, luminous intensity are the seven fundamental quantities and are often called the seven dimensions of the world.
Winter But they all measure the same thing and each can be converted to the others, so they are the same dimension: length. Add a comment. Active Oldest Votes. I would also disagree that the distinction can be quite useful, e.
I've also found the distinction important when implementing units or dimensions in a programming language. As for dimensionless units they are as units regarded just a dimensionless constant ie real number. The point is that you can get the same work done using unit analysis instead - there are details in the procedure that may differ, but basically the approach is equivalent.
Show 1 more comment. Winter M. A My height is a length; B My height is meters. Which one? A Speed is distance over time; B Speed is inches over seconds. Plus, inches are not SI :. Simone Simone 2 2 bronze badges. Example: The Becquerel is a unit of radioactivity, referring to an average of 1 decay per second. I think this distinction matters even more in physics, as Randall Munroe pointed out in an excellent and fun way here: what-if. I have copied and pasted it from somewhere but with the hope that it helps.
Thank you. The "dimensions are powers" confusion Alas your book maybe Elements of Physics judging from a cursory Google Books search uses different definitions.
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