Evolution of Units

Historically, different systems were used:

  • CGS: centimetre, gram, second
  • FPS: foot, pound, second
  • MKS: metre, kilogram, second

The need for standardization led to the adoption of the SI system in 1971 by the General Conference on Weights and Measures.

The SI System

The International System of Units (Système International d'Unités or SI) is a globally accepted standard for measurement.

Seven Base SI Units:

  1. Length – metre (m)
  2. Mass – kilogram (kg)
  3. Time – second (s)
  4. Electric current – ampere (A)
  5. Thermodynamic temperature – kelvin (K)
  6. Amount of substance – mole (mol)
  7. Luminous intensity – candela (cd)

Definitions of Base Units (simplified)

  • Metre (m): Based on the speed of light.
  • Kilogram (kg): Based on the Planck constant.
  • Second (s): Based on the cesium-133 atom’s radiation frequency.
  • Ampere (A): Defined using the elementary charge e=1.602×10−19 Ce = 1.602\times10^{-19}\ \text{C}.
  • Kelvin (K): Based on the Boltzmann constant.
  • Mole (mol): Fixed value of Avogadro’s number 6.022×10236.022\times10^{23}.
  • Candela (cd): Based on luminous efficacy.

Supplementary Units

  1. Plane angle: radian (rad) — θ=dsr\theta = \frac{ds}{r}
  2. Solid angle: steradian (sr) — Ω=dAr2\Omega = \frac{dA}{r^2}

Derived Units

Quantities like velocity, force, pressure, and energy are expressed using derived units based on the base units:

  • Velocity: m/s
  • Force: newton (N) = kg⋅m/s²
  • Energy: joule (J) = N⋅m = kg⋅m²/s²

SI Prefixes (Examples)

  • 10310^3: kilo (k)
  • 10−310^{-3}: milli (m)
  • 10−610^{-6}: micro (μ)
  • 10610^6: mega (M)

These prefixes help express values in manageable forms.

Example: Convert CGS to SI

The density of a material is 10 g/cm310\ g/cm^3. Express this in SI units.

Solution: We convert:

  • 1 g=10−3 kg1\ g = 10^{-3}\ kg
  • 1 cm3=10−6 m31\ cm^3 = 10^{-6}\ m^3

So, ρ=10×10−310−6=104 kg/m3\rho = 10 \times \frac{10^{-3}}{10^{-6}} = 10^4\ kg/m^3 Thus, the density is 104 kg/m310^4\ kg/m^3 in SI units.