# 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]

=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]