Angular wave number ( k ) is constant for a particular wave , which is  closely related to the  wavelength of the wave. In geophysics  we are related to oscillating waveform,  angular frequency and angular wave number. Angular wave number can be defined as the ratio of angular frequency to velocity.

Mathematically,

Angular wave number ( k )  = Angular frequency / Velocity

Dimensional formula of Angular Frequency = M⁰L⁰T^-1
Dimensional formula of Velocity = M⁰L¹T^-1

Putting these values in above equation we get,

Dimensional Formula of Angular wave number ( k ) = M⁰L^-1T⁰
SI Unit of Angular wave number ( k ) is radians per meter

Wave number can be defined as the number of waves per unit length. In other words it is number of waves that occurs across a fixed distance. It is also known as propagation constant.

Wavenumber is reciprocal of Wave length. Unit of Wavenumber are cycles per centimeter or inverse centemeters.

Wave number (k) = 2 π / λ (Wave length)

Dimensional formula of wavelength = M⁰L¹T⁰

So putting this value in the formula we get,

Dimensional Formula of Wave number or Propagation constant  = M⁰L^-1T⁰
SI units of Wave number or Propagation constant is m^-1.

Centripetal acceleration is the acceleration directed towards the centre of curvature of the path of a body which is moving along that path with a constant speed.

Mathematically,
Centripetal acceleration = (Velocity)² / radius.

Dimensional Formula of Velocity = M⁰L¹T^-1
Dimensional Formula of Radius = M⁰L¹T⁰

Putting these values in above equation we get,
Dimensional Formula of Centripetal acceleration = M⁰L¹T^-2
SI unit of Centripetal acceleration is ms^-2

Angular impulse is defined as the product of  torque and time for which it acts.

Mathematically,
Angular impulse = Torque X Time.

Dimensional Formula of Torque = M¹L²T^-2
Dimensional Formula of Time = M⁰L⁰T¹

Putting these values in the given equation we get,

Dimensional Formula of Angular impulse = M¹L²T^-1
SI Unit of Angular impulse is Kg m²s^-1

Efficiency can be  defined as the  ratio of useful output energy to the amount of input energy.

Mathematically,

Efficiency = Useful output energy / Input energy.

Dimensional formula of output energy = M¹L²T^-2
Dimensional formula of input energy = M¹L²T^-2

Putting these values in above equation we get,

Dimensional formula of Efficiency = M⁰L⁰T⁰.
Efficiency has no SI Unit. (As both values are of energy).