Dimensions of a physical quantity

Dimensions of a physical quantity are the powers to which the fundamental quantities must be raised.

In mathematics and physics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it (for example, to locate a point on the surface of a sphere you need both its latitude and its longitude). The inside of a cube, a cylinder or a sphere is three-dimensional because three co-ordinates are needed to locate a point within these spaces.

The concept of dimension is not restricted to physical objects. High-dimensional spaces occur in mathematics and the sciences for many reasons, frequently as configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in. Some physical theories are also high-dimensional, such as the 4-dimensional general relativity and higher-dimensional string theories. Indeed, the state-space of quantum mechanics is an infinite-dimensional function space.

We know that velocity = displacement / time =[L]/[T] = [MoL¹T^-1] where [M], [L] and [T] are the dimensions of the fundamental quantities mass, length and time respectively. Therefore velocity has zero dimension in mass, one dimension in length and -1 dimension in time. Thus the dimensional formula for velocity is [MoL¹T^-1] or simply [LT^-1].The dimensions of fundamental quantities are given below Dimensions of fundamental quantities