Units and Dimensions


Acceleration=V/T=[LT⁻¹/T] = [LT⁻²]
[V=change in velocity and T =Time]

*Force
= mass(a)×acceleration due to gravity (g) 
=[M]×[LT⁻²]
=[MLT⁻²]

* Momentum
=mass×velocity
=M×V
=[M][LT⁻¹]
=[MLT⁻¹]

*Linear momentum
=mass×velocity 
=M×V
 =[M][LT⁻¹]
 =[MLT⁻¹]

*Angular Momentum L=rp [r=radius  and p=momentum]
 =r*mv
 =L*[MLT⁻¹]
 =[ML²T⁻¹]

*Impulse
=Force×Time 
=[MLT⁻²][T]
=[MLT⁻¹]
[ Unit of impulse is Ns]

*Work of Energy
=Force×displacement
=[MLT⁻²][L] 
=ML²T⁻²

*Power
=Work done
   Time taken
=[ML²T⁻²][T⁻¹]
=[ML²T⁻³]

*Pressure or Stress
=Force/Area
=[MLT⁻²][L⁻²]
=[ML⁻¹T⁻²]

*Elastic Modulus(k)
=Stress
  Strain
F/A       
  [M⁰L⁰T⁰] 
=[ML⁻¹T⁻²]

*Frequency=1/T=T⁻¹
 





 

 *Angular Frequency(w)=
                           =2π/T


*Plank's Constant(h)=E/F
  [where E=energy and F=frequency]
 =[ML²T⁻²][T] 
 = [ML²T⁻¹]
  

*E=mc²
  =[M][LT⁻¹]²
  =[M][L²T⁻²]
  =[ML²T⁻²]


 
       


*Moment of Force
=Force×Distance
=[MLT⁻²][L]
=[ML²T⁻²]



 *Surface Energy=W/A
                             =[ML²T⁻²]
                                 [ L²]
                            =[ML⁰T⁻²]



*Surface Tension=Force
                                  length
                  =[MLT⁻² ]         
                         [L]

                  =[ML⁰T⁻²]


*Force Constant

=Force           
  Displacement
=[MLT⁻²]
      [ L]
=[ML⁰T⁻²]

*Radius of Gyration(k)

=Distance=[M⁰LT⁰]

 *Thermal conductivity,For thermal conductivity you can find the dimensional formula using the equation,
ΔQ/Δt =-KA(ΔΤ/Δx)
-K=(ΔQ/Δt)×(Δx/ΔT)×A
therefore the dimension of thermal(K)=(ΔQ/Δt)×(Δx/ΔT)×1/A=

ML²T ⁻³ ×L/k ×1/L²=
[ML²T⁻²]
[TKL]
=[MLT⁻³K⁻¹]

 



















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