1.7 Dimensions of Physical Quantities

1.7 Dimensions of Physical Quantities

Any physical quantity can be described by certain familiar properties such as length, mass, time, temperature, electric current, etc. These measurable properties are called dimensions.

Dimensions deal with the qualitative nature of a physical quantity in terms of fundamental quantities. The quantities such as length, depth, height, diameter, light year are all measured in metre and denoted by the same dimension, basically known as length given by symbol $L$ written within square brackets $[L]$.

Similarly, the other fundamental quantities, mass, time, electric current and temperature are denoted by specific symbols:

• Mass: $[M]$
• Time: $[T]$
• Electric current: $[A]$
• Temperature: $[\theta]$

These five dimensions have been chosen as being basic because they are easy to measure in experiments.

The dimensions of other quantities indicate how they are related to the basic quantities and are combination of fundamental dimensions.

For example, speed $v$ is measured in metres per second, so it has the dimensions of length $[L]$ divided by time $[T]$:

As the acceleration $a = \Delta v/\Delta t$

Dimensions of acceleration are:

Also, dimensions of force can be written as:

By the use of dimensionality, we can check the homogeneity (correctness) of a physical equation, and also, we can derive formula for a physical quantity.