Units and Dimensions - Quantities
Advertisements
Description:
Concept of Dimensions
All physical quantities are said to be described by its dimensions.
There are 7 (seven) fundamental quantities, hence, 7 (seven) fundamental dimensions.
| Base Quantity | Unit Name | Dimensions |
|---|---|---|
| Length | Meter (m) | [L] |
| Mass | Kilogram (kg) | [M] |
| Time | Second (s) | [T] |
| Electric Current | Ampere (A) | [I] |
| Temperature | Kelvin (K) | [θ] |
| Amount of Substance | Mole (mol) | [N] |
| Luminous Intensity | Candela (cd) | [J] |
| Plane and Solid Angle | Radian and Steradian | [1] (Dimensionless) |
Dimensions of derived quantities
All the derived quantities possess dimensions obtained by multiplication and division of fundamental dimensions.
For example, to calculate the dimensions of Kinetic Energy (a derived quantity), we do the following −
Write the equation/formula of the derived quantity.
K.E = 12 mv2
For each variable substitute the dimensions of that physical quantity.
m ≡ [M]
v ≡ [L][T]-1
All pure numbers have the dimension of 1 (one), hence, they should be ignored.
Calculate the dimensions −
[K.E] = [M]([L][T]-1)2
[K.E] = [M][L]2[T]-2
Dimensions of few derived quantities
| Derived Quantity | Unit Name | Dimensions |
|---|---|---|
| Velocity | m/s | [L][T]-1 |
| Acceleration | m/s2 | [L][T]-2 |
| Force | N or kg m/s2 | [M][L][T]-2 |
| Momentum | kg m/s | [M][L][T]-1 |
| Area | m2 | [L]2 |
| Volume | m3 | [L]3 |
| Energy | kg m2/s2 | [J] |
Advertisements