Dimensional Formulae of Physical Quantities

These flashcards cover the dimensional formulae of various physical quantities and their respective relationships.

Area

Length x breadth, dimension: [L²], formula: [M° LT]

Volume

Length x breadth x height, dimension: [L³], formula: [M°L³T°]

Mass density

Mass/volume, dimension: [M]/[L³], formula: [ML³T°]

Frequency

1/time period, dimension: 1/[T], formula: [M°L°T']

Velocity, speed

Displacement/time, dimension: [L]/[T], formula: [M°LT']

Acceleration

Velocity/time, dimension: [LT']/[T], formula: [M°LT²]

Force

Mass acceleration, dimension: [M][LT], formula: [M LT²]

Impulse

Force x time, dimension: [M LT²][T], formula: [M LT¹]

Work, Energy

Force x distance, dimension: [MLT²], formula: [ML² T²]

Power

Work/time, dimension: [ML² T²]/[T], formula: [ML² T³]

Momentum

Mass x velocity, dimension: [M][LT'], formula: [M LT']

Pressure, stress

Force/area, dimension: [M LT²]/[L²], formula: [ML⁻¹ T⁻²]

Strain

Change in dimension/original dimension, dimension: [L]/[L], formula: [M°L°T°]

Modulus of elasticity

Stress/strain, dimension: [ML⁻¹ T⁻²], formula: [ML⁻¹T⁻²]

Surface tension

Force/length, dimension: [MLT⁻²]/[L], formula: [ML° T⁻²]

Surface energy

Energy/area, dimension: [ML² T²]/[L²], formula: [ML°T⁻²]

Velocity gradient

Velocity/distance, dimension: [LT]/[L], formula: [ML°T⁻¹]

Pressure gradient

Pressure/distance, dimension: [MLT²]/[L], formula: [ML²T²]

Pressure energy

Pressure x volume, dimension: [MLT²][L³], formula: [ML² T⁻²]

Coefficient of viscosity

Force/area x velocity gradient, dimension: [MLT⁻²],[MLT⁻¹]

Angle, Angular displacement

Arc/radius, dimension: [L]/[L], formula: [ML°T]

Trigonometric ratio

Length/length, dimension: [L]/[L], formula: [M°LT]

Angular velocity

Angle/time, dimension: [L°]/[T], formula: [ML°T']

Angular acceleration

Angular velocity/time, dimension: [T']/[T], formula: [ML°T]

Radius of gyration

Distance, dimension: [L], formula: [M°LT]

Moment of inertia

Mass (radius of gyration)², dimension: [ML² T°]

Angular momentum

Moment of inertia × angular velocity, dimension: [ML²][T], formula: [ML² T']

Moment of force, moment of couple

Force x distance, dimension: [ML² T²]

Torque

Angular momentum/time, dimension: [ML² T']/[T], formula: [ML² T²]

Angular frequency

2π × Frequency, dimension: [T'], formula: [M'L'T']

Wavelength

Distance, dimension: [L], formula: [M°LT]

Hubble constant

Recession speed/distance, dimension: [LT']/[L], formula: [ML°T']

Intensity of wave

(Energy/time)/area, dimension: [ML² T²/T]/[L²], formula: [MLT³]

Radiation pressure

Intensity of wave/Speed of light, dimension: [MT]/[LT], formula: [MLT²]

Energy density

Energy/volume, dimension: [ML²T²]/[L³], formula: [MLT²]

Critical velocity

Reynold's number x coefficient of viscosity, dimension: [M°LT][ML T⁻³]

Escape velocity

Root of (2 × acceleration due to gravity × earth's radius), dimension: [LT]

Heat energy, internal energy

Work (Force × distance), dimension: [MLT²]

Kinetic energy

(1/2) mass (velocity)², dimension: [ML²T²]

Rotational kinetic energy

Moment of inertia x (angular velocity)², dimension: [ML²T²]

Efficiency

Output work or energy/Input work or energy, dimension: [M L² T²]

Angular impulse

Torque x time, dimension: [ML² T²][T], formula: [ML²'T']

Gravitational constant

Force (mass × mass)/distance², dimension: [MLT⁻²][L²]

Planck constant

Energy/frequency, dimension: [ML² T²]/[T]

Heat capacity, entropy

Heat energy/temperature, dimension: [ML² T²]/[K]

Specific heat capacity

Heat Energy/Mass temperature, dimension: [ML² T²]/[M][K]

Latent heat

Heat energy/mass, dimension: [ML² T²]/[M]

Thermal expansion

Change in dimension/original dimension, dimension: [L]/[L][K]

Thermal conductivity

Heat energy/(thickness x area x temperature x time)