Dimensional Formulas for Physical Quantities | Derived SI units with Special Names | Quantities Have Same Dimensional Formula

Learn the dimensional formulas for various physical quantities, including derived SI units with special names. Explore how different quantities have the same dimensional formula and understand their significance in physics and engineering. Perfect for students and professionals looking to strengthen their knowledge of unit analysis and dimensional consistency

Derived SI units with Special Names

Physical QuantitySI UnitSymbol
FrequencyhertzHz
EnergyjouleJ
ForcenewtonN
PowerwattW
PressurepascalPa
Electric charge or quantity of electricitycoulombC
Electric potential difference and emfvoltV
Electric resistanceohm\(\begin{array}{l}\Omega\end{array} \)
Electric conductancesiemenS
Electric capacitancefaradF
Magnetic fluxweberWb
InductancehenryH
Magnetic flux densityteslaT
IlluminationluxLx
Luminous fluxlumenLm

Dimensional Formulas for Important Physical Quantities

Physical QuantityUnitDimensional Formula
Acceleration or acceleration due to gravityms–2LT–2
Angle (arc/radius)radMoLoTo
Angular displacementradMoloTo
Angular frequency (angular displacement/time)rads–1T–1
Angular impulse (torque x time)NmsML2T–1
Angular momentum (Iω)kgm2s–1ML2T–1
Angular velocity (angle/time)rads–1T–1
Area (length x breadth)m2L2
Boltzmann’s constantJK–1ML2T–2θ–1
Bulk modulus \(\begin{array}{l}\left(\Delta P.\frac{V}{\Delta V} \right)\end{array} \)Nm–2, PaM1L–1T–2
Calorific valueJkg–1L2T–2
Coefficient of linear or areal or volume expansionoC–1 or K–1θ–1
Coefficient of surface tension (force/length)Nm–1 or Jm–2MT–2
Coefficient of thermal conductivityWm–1K–1MLT–3θ–1
Coefficient of viscosity \(\begin{array}{l}\left(F=\eta A\frac{dv}{dx} \right)\end{array} \)poiseML–1T–1
Compressibility (1/bulk modulus)Pa–1, m2N–2M–1LT2
Density (mass/volume)kgm–3ML–3
Displacement, wavelength, focal lengthmL
Electric capacitance (charge/potential)CV–1, faradM–1L–2T4I2
Electric conductance (1/resistance)Ohm–1 or mho or siemenM–1L–2T3I2
Electric conductivity (1/resistivity)siemen/metre or Sm–1M–1L–3T3I2
Electric charge or quantity of electric charge (current x time)coulombIT
Electric currentampereI
Electric dipole moment (charge x distance)CmLTI
Electric field strength or intensity of electric field (force/charge)NC–1, Vm–1MLT–3I–1
Electric resistance \(\begin{array}{l}\left(\frac{potential\ difference}{current} \right)\end{array} \)ohmML2T–3I–2
Emf (or) electric potential (work/charge)voltML2T–3I–1
Energy (capacity to do work)jouleML2T–2
Energy density \(\begin{array}{l}\left(\frac{energy}{volume} \right)\end{array} \)Jm–3ML–1T–2
Entropy \(\begin{array}{l}\left(\Delta S=\Delta Q/T \right)\end{array} \)–1ML2T–2θ–1
Force (mass x acceleration)newton (N)MLT–2
Force constant or spring constant (force/extension)Nm–1MT–2
Frequency (1/period)HzT–1
Gravitational potential (work/mass)Jkg–1L2T–2
Heat (energy)J or calorieML2T–2
Illumination (Illuminance)lux (lumen/metre2)MT–3
Impulse (force x time)Ns or kgms–1MLT–1
Inductance (L) \(\begin{array}{l}\left(energy =\frac{1}{2}L{{I}^{2}} \right)\end{array} \) or coefficient of self-inductionhenry (H)ML2T–2I–2
Intensity of gravitational field (F/m)Nkg–1L1T–2
Intensity of magnetization (I)Am–1L–1I
Joule’s constant or mechanical equivalent of heatJcal–1MoLoTo
Latent heat (Q = mL)Jkg–1MoL2T–2
Linear density (mass per unit length)kgm–1ML–1
Luminous fluxlumen or (Js–1)ML2T–3
Magnetic dipole momentAm2L2I
Magnetic flux (magnetic induction x area)weber (Wb)ML2T–2I–1
Magnetic induction (F = Bil)NI–1m–1 or TMT–2I–1
Magnetic pole strength (unit: ampere–meter)AmLI
Modulus of elasticity (stress/strain)Nm–2, PaML–1T–2
Moment of inertia (mass x radius2)kgm2ML2
Momentum (mass x velocity)kgms–1MLT–1
Permeability of free space \(\begin{array}{l}\left(\mu_o = \frac{4\pi Fd^{2}}{m_1m_2} \right)\end{array} \)Hm–1 or NA–2MLT–2I–2
Permittivity of free space \(\begin{array}{l}\left({{\varepsilon }_{o}}=\frac{{{Q}_{1}}{{Q}_{2}}}{4\pi F{{d}^{2}}} \right)\end{array} \)Fm–1 or C2N–1m–2M–1L–3T4I2
Planck’s constant (energy/frequency)JsML2T–1
Poisson’s ratio (lateral strain/longitudinal strain)––MoLoTo
Power (work/time)Js–1 or watt (W)ML2T–3
Pressure (force/area)Nm–2 or PaML–1T–2
Pressure coefficient or volume coefficientoC–1 or θ–1θ–1
Pressure headmMoLTo
Radioactivitydisintegrations per secondMoLoT–1
Ratio of specific heats––MoLoTo
Refractive index––MoLoTo
Resistivity or specific resistance\(\begin{array}{l}\Omega\end{array} \) –mML3T–3I–2
Specific conductance or conductivity (1/specific resistance)siemen/metre or Sm–1M–1L–3T3I2
Specific entropy (1/entropy)KJ–1M–1L–2T2θ
Specific gravity (density of the substance/density of water)––MoLoTo
Specific heat (Q = mst)Jkg–1θ–1MoL2T–2θ–1
Specific volume (1/density)m3kg–1M–1L3
Speed (distance/time)ms–1LT–1
Stefan’s constant \(\begin{array}{l}\left( \frac{heat\ energy}{area\ x\ time\ x\ temperatur{{e}^{4}}} \right)\end{array} \) .Wm–2θ–4MLoT–3θ–4
Strain (change in dimension/original dimension)––MoLoTo
Stress (restoring force/area)Nm–2 or PaML–1T–2
Surface energy density (energy/area)Jm–2MT–2
TemperatureoC or θMoLoToθ
Temperature gradient \(\begin{array}{l}\left(\frac{change\text{ in temperature}}{\text{distance}} \right)\end{array} \)oCm–1 or θm–1MoL–1Toθ
Thermal capacity (mass x specific heat)–1ML2T–2θ–1
Time periodsecondT
Torque or moment of force (force x distance)NmML2T–2
Universal gas constant (work/temperature)Jmol–1θ–1ML2T–2θ–1
Universal gravitational constant \(\begin{array}{l}\left(F = G.\frac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}} \right)\end{array} \)Nm2kg–2M–1L3T–2
Velocity (displacement/time)ms–1LT–1
Velocity gradient (dv/dx)s–1T–1
Volume (length x breadth x height)m3L3
Water equivalentkgMLoTo
Work (force x displacement)JML2T–2

Quantities Having the Same Dimensional Formula

  1. Impulse and momentum.
  2. Work, torque, the moment of force, energy.
  3. Angular momentum, Planck’s constant, rotational impulse.
  4. Stress, pressure, modulus of elasticity, energy density.
  5. Force constant, surface tension, surface energy.
  6. Angular velocity, frequency, velocity gradient.
  7. Gravitational potential, latent heat.
  8. Thermal capacity, entropy, universal gas constant and Boltzmann’s constant.
  9. Force, thrust.
  10. Power, luminous flux.

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