Rankwise

Dimensional formula of angular velocity

The dimensional formula of angular velocity is [T⁻¹].

[T⁻¹]Dimensional formula
[M⁰L⁰T⁻¹]With every power shown
rad s⁻¹SI unit
ω = θ ÷ tDefining relation

How to derive it

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

  1. An angle (arc ÷ radius) has no dimensions.
  2. ω = angle ÷ time = 1 ÷ [T]
  3. So [angular velocity] = [T⁻¹], also written [M⁰L⁰T⁻¹].

Same dimensions as angular velocity: frequency. 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 angular velocity?

[T⁻¹] (or [M⁰L⁰T⁻¹]), from ω = θ ÷ t. Its SI unit is rad s⁻¹.

What are the dimensions of angular velocity?

M: 0, L: 0, T: -1.

What is the SI unit of angular velocity?

rad s⁻¹.

Which quantities have the same dimensions as angular velocity?

frequency, all [T⁻¹].

Use these next

Dimensional formulasDimensions and SI units of 57 physical quantities.Physics formula sheetEvery important formula, chapter by chapter, searchable.Physical constantsValues and units of the constants used in physics and chemistry.Formula SprintA daily 60-second game of formulas, units and facts.