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Dimensional formula of coefficient of friction

The dimensional formula of coefficient of friction is [M⁰L⁰T⁰].

[M⁰L⁰T⁰]Dimensional formula
[M⁰L⁰T⁰]With every power shown
no unitSI unit
f = μNDefining relation

How to derive it

Start from a formula that defines coefficient of friction, then replace each quantity with its dimensions. M is mass, L is length, T is time.

  1. μ = friction force ÷ normal force = [MLT⁻²] ÷ [MLT⁻²]
  2. So [coefficient of friction] = [M⁰L⁰T⁰].

Same dimensions as coefficient of friction: strain, refractive index. JEE often asks which pairs match.

Dimensional formulas of other quantities

QuantityDimensional formula
velocity[LT⁻¹]
acceleration[LT⁻²]
force[MLT⁻²]
momentum[MLT⁻¹]
impulse[MLT⁻¹]
work[ML²T⁻²]
energy[ML²T⁻²]
power[ML²T⁻³]
pressure[ML⁻¹T⁻²]
stress[ML⁻¹T⁻²]
Young's modulus[ML⁻¹T⁻²]
density[ML⁻³]
torque[ML²T⁻²]
moment of inertia[ML²]
angular momentum[ML²T⁻¹]
angular velocity[T⁻¹]
frequency[T⁻¹]
gravitational constant G[M⁻¹L³T⁻²]
acceleration due to gravity g[LT⁻²]
gravitational potential[L²T⁻²]
surface tension[MT⁻²]
spring constant[MT⁻²]
coefficient of viscosity[ML⁻¹T⁻¹]
Planck's constant h[ML²T⁻¹]
heat[ML²T⁻²]
specific heat capacity[L²T⁻²K⁻¹]
latent heat[L²T⁻²]
entropy[ML²T⁻²K⁻¹]
universal gas constant R[ML²T⁻²K⁻¹mol⁻¹]
Boltzmann constant k[ML²T⁻²K⁻¹]
thermal conductivity[MLT⁻³K⁻¹]
Stefan–Boltzmann constant σ[MT⁻³K⁻⁴]
Wien's constant b[LK]
coefficient of linear expansion[K⁻¹]
electric charge[TA]
electric potential (voltage, EMF)[ML²T⁻³A⁻¹]
resistance[ML²T⁻³A⁻²]
resistivity[ML³T⁻³A⁻²]
conductance[M⁻¹L⁻²T³A²]
capacitance[M⁻¹L⁻²T⁴A²]
electric field[MLT⁻³A⁻¹]
electric flux[ML³T⁻³A⁻¹]
permittivity of free space ε₀[M⁻¹L⁻³T⁴A²]
electric dipole moment[LTA]
magnetic field B[MT⁻²A⁻¹]
magnetic flux[ML²T⁻²A⁻¹]
permeability of free space μ₀[MLT⁻²A⁻²]
inductance[ML²T⁻²A⁻²]
magnetic moment[L²A]
intensity of a wave[MT⁻³]
wave number[L⁻¹]
Rydberg constant[L⁻¹]
power of a lens[L⁻¹]
strain[M⁰L⁰T⁰]
refractive index[M⁰L⁰T⁰]
coefficient of friction[M⁰L⁰T⁰]
time constant RC[T]

The full searchable list, with SI units, is on the dimensional formula page.

Questions students ask

What is the dimensional formula of coefficient of friction?

[M⁰L⁰T⁰], from f = μN. Its SI unit is no unit.

What are the dimensions of coefficient of friction?

Coefficient of friction is dimensionless: it's a ratio of two quantities with the same dimensions.

What is the SI unit of coefficient of friction?

no unit.

Which quantities have the same dimensions as coefficient of friction?

strain, refractive index, all [M⁰L⁰T⁰].

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