Dimension of Physical Quantities
All the derived physical quantities can be expressed in terms of some combination of the seven fundamental or base quantities. These base quantities are known as dimensions of the physical world, and are denoted with square bracket [ ]. The three dimensions in mechanics are [L] for length, [m] for mass and [T] for time. In electricity, [A] is the dimension of electric current. In thermodynamics, [K] is the dimension for the temperature. In optics [cd] or [Φ] is the dimension for luminous intensity. The dimension of amount of substance is [mol].
The dimensions of a physical quantity are the powers to which the units of base quantities are raised to represent a derived unit of that quantity.
Hence the dimensions of velocity are 0 in mass, 1 in length and -1 in time.
Dimensional formula is an expression which shows how and which of the fundamental units are required to represent the unit of a physical quantity.
For example, [M0LT−2] is the dimensional formula of acceleration.
When the dimensional formula of a physical quantity is expressed in the form of an equation, such an equation is known as the dimensional equation.
Example, acceleration = [M0LT−2]. The dimensional formula of various physical quantities are tabulated in Table 1.11.