PHYSICS: UNITS AND MEASUREMENTS

Systems of Units

• Measurement: Q = n × u (numerical value × unit).
• CGS: centimetre, gram, second.
• FPS (British): foot, pound, second; 1 lb ≈ 453.59 g.
• MKS: metre, kilogram, second.
• SI: internationally adopted in 1960; 7 base units.

SI Base and Angle Units

Quantity	SI unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Thermodynamic temperature	kelvin	K
Luminous intensity	candela	cd
Amount of substance	mole	mol
Plane angle	radian	rad
Solid angle	steradian	sr

Derived Quantities and Dimensions

Quantity	SI unit	Dimensional formula
Speed / velocity	m/s	[LT⁻¹]
Acceleration	m/s²	[LT⁻²]
Force / weight / thrust	newton (N)	[MLT⁻²]
Work / energy / heat / torque	joule (J)	[ML²T⁻²]
Power	watt (W)	[ML²T⁻³]
Pressure / stress / Young’s modulus	pascal (Pa)	[ML⁻¹T⁻²]
Momentum / impulse	kg·m/s; N·s	[MLT⁻¹]
Coefficient of viscosity (η)	Pa·s	[ML⁻¹T⁻¹]
Surface tension	N/m	[MT⁻²]
Planck’s constant (h)	J·s	[ML²T⁻¹]
Gravitational constant (G)	N·m²/kg²	[M⁻¹L³T⁻²]

• Key relations: v = displacement/time; a = change in velocity/time; F = ma; W = Fd; P = W/t; pressure = force/area; p = mv; impulse = FΔt; E = hν.

Same Dimensions and Dimensionless Quantities

• [ML²T⁻²]: work, energy, heat, torque.
• [MLT⁻¹]: momentum, impulse.
• [ML⁻¹T⁻²]: pressure, stress, Young’s modulus.
• [ML²T⁻¹]: Planck’s constant, angular momentum.
• Dimensionless, no units: strain, relative density/specific gravity, refractive index, Poisson’s ratio, π, e, sin θ.
• Dimensionless but expressed with units: plane angle (radian), solid angle (steradian), angular displacement.