Monday, 30 November 2015

DIMENSIONAL FORMULA OF ALL PHYSICS FUNDAMENTAL/DERIVED QUANTITY

Table of Units and Dimensions of Physical quantities.


Units & Dimensions of Physical quantities in S.I system.
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Fundamental Physical Quantities:
S.No Fundamental Physical Quantity Formula Dimensional Formula S.I Unit of physical quantity
1. Mass Amount of matter in the object M kg
2. Length
L meter
3. Time
T sec
4. Electric current
I or A ampere
5. Amount of substance
N mole(mol
6. Luminous intensity
J candela(cd)
7. Temperature
K or \theta Kelvin
Derived Physical Quantities:
S.No Derived Physical Quantity Formula Dimensional Formula S.I Unit of physical quantity
1. Area l\times b [M^0L^2T^o] m^2
2. Volume l\times b\times h [M^0L^3T^o] m^3M^3
3. Density \frac{M}{V} [M^1L^{-3}T^0] kg/m^3
4. Specific Gravity \frac{Density of Substance}{Density of Water} [M^0L^0T^0] No units
5. Frequency \frac{no of vibrations}{Time} [M^0L^0T^{-1}] hertz
6. Angle \frac{Arc}{radius} M^0L^oT^o No units
7. Velocity \frac{Displacement}{time} M^0L^1T^{-1} m/sec
8. Speed \frac{Distance}{time} M^0L^1T^{-1} m/sec
9. Areal velocity \frac{Area}{time} M^0L^2T^{-1} m^2sec^{-1}
10. Acceleration \frac{Change in velocity }{time} M^0L^1T^{-2} m/sec^2
11. Linear momentum M\times V M^1L^1T^{-1} kg m/sec
12. Force mass\times acceleration M^1L^1T^{-2} kg-m/sec^2 or Newton
13. Weight w=mg M^1L^1T^{-2} kg-m/sec^2 or Newton
14. Moment of force/Torque/Couple Force\times arm M^1L^2T^{-2} kgm^2sec^{-2}
15. Impulse Force\times time M^1L^1T^{-1} kg m/sec or Ns
16. Pressure \frac{Force}{Area} M^1L^{-1}T^{-2} N/m^2 or Pa
17. Work Force\times Distance M^1L^2T^{-2} Nm or Joule
18. Kinetic Energy \frac{1}{2} mv^2 M^1L^2T^{-2} joule
19. Potential Energy mgh M^1L^2T^{-2} joule
20. Gravitational constant \frac{Force\times (Length)^2}{(mass)^2} M^{-1}L^3T^{-2} kg^{-1}m^3sec^{-2}
21. Gravitational field strength \frac{Force}{mass} M^0L^1T^{-2} N kg^{-1}
22. Gravitational Potential \frac{Work}{mass} M^0L^2T^{-2} J kg^{-1}
23. Force constant (k) \frac{F}{L} M^1L^0T^{-2} N m^{-1}
24. Power \frac{Work}{time} M^1L^2T^{-3} W or J/sec
25. Moment of Inertia ( I ) Mass\times Distance^2 M^1L^2T^{0} kgm^2
26. Stress \frac{Force}{Area} M^1L^{-1}T^{-2} N/m^2 or Pa
27. Strain \frac{Change in length}{Origional length} M^0L^0T^0 No units
28. Modulus of Elasticity \frac{Stress}{Strain} M^1L^{-1}T^{-2} N/m^2 or Pa
29. Poission’s Ratio σ =\frac{Y}{2n}-1 M^0L^0T^0 No units
30. Velocity gradient \frac{Change in velocity}{Distance} M^0L^0T^{-1} sec^{-1}
31. Coefficient of dynamic viscosity \frac{Tangential stress}{Velocity Gradient} M^1L^{-1}T^{-1} kgm^{-1}sec^{-1}(or) N-sec/$latex  \m^2$ (or)pascal-sec (or)poiseuille
32. Surface Tension \frac{Force}{Length} M^1L^0T^{-2} kg sec^2,N/m
33. Angular displacement (\theta) \frac{Arc}{radius} M^0L^oT^o no Units
34. Angular velocity(ω) \frac{Angular displacement}{Time} M^0L^oT^{-1} rad/sec
35. Angular acceleration(α) \frac{Change in angular velocity}{Time} M^0L^oT^{-2} rad/sec^{-2}
36. Angular momentum Iω ML^2T^{-1} kg-m^2 sec^{-1}
37. Angular Impulse Iω ML^2T^{-1} kg-m^2 sec^{-1}
38. Temperature
\theta or K kelvin or degree Celsius
39. Coefficient of linear expansion(α) \frac{l_2-l_1}{l_1\times Temp(t_2-t_1)} M^0L^0T^0K^{-1} /kelvin
40. Specific heat \frac{Energy}{Mass\times Temp} M^0L^2T^{-2}K^{-1}
41. Latent heat \frac{Energy}{Mass} M^0L^2T^{-2} joule-kg^{-1}
42. Entropy \frac{Q}\theta M^1L^2T^{-2}K^{-1} J K^{-1}
43. Thermal capacity \frac{H}\theta M^1L^2T^{-2}K^{-1} J K^{-1}
44. Gas constant \frac{PV}{m T} M^0L^2T^{-2}K^{-1} joule-K^{-1}
45. coefficient of thermal conductivity \frac{Qd}{A(\theta_2-\Theta_1)t} M^1L^1T^{-3}K^{-1} W m^{-1}K^{-1}
46. Pole strength Ampere\times meter M^0L^1T^0I Am
47. Magnetic Moment
M^0L^2T^0I^1 Amp-m^2
48. Magnetic flux \phi
ML^2T^{-2}I^{-1} weber ;T-m^{2} ;J/Amp
49. Magnetic field,magnetic flux density (B)
MT^{-2}I^{-1} Tesla;J/A-m^{2}
50. Permeability of free space \frac{\mu}{\mu_r} MLT^{-2}I^{-2} NA^{-2}
51. Magnetic susceptibilty also called volumetric or bulk susceptibility χm χm = μr − 1 M^0L^oT^o no units
52. Electric Charge I\times T M^0L^0T^1I^1 Amp sec , coul
53. Electric potential \frac{Work}{Charge} M^1L^2T^{-3}I^{-1} Volt
54. E.M.F \frac{Work}{Charge} M^1L^2T^{-3}I^{-1} Volt
55. Electric Capacity \frac{q}{V} M^{-1}L^{-2}T^4I^2 Farad
56. Electric Resistance \frac{V}{i} M^1L^2T^{-3}I^{-2} Ohm (Ω) or volt/amp
57. Resistivity \rho \frac{R A}{L} M^1L^3T^{-3}I^{-1} Ohm mt (Ω-m)
58. Conductivity \sigma 1/\rho M^{-1}L^{-3}T^3I Siemens/m
59. Permittivity \varepsilon
\varepsilon = \varepsilon_r \varepsilon_0 = (1+\chi)\varepsilon_0
M^{-1}L^{-3}T^4I^2 farad/m
60. Electric conductance \frac{1}{R} M^{-1}L^{-2}T^3I^2 Siemens (or) mhos
61. Electric power V\times I M^1L^2T^{-3}I^{-1} Watt
62. Electrical Impedance(Z) \frac{V}{i} M^1L^2T^{-3}I^{-2} Ohm (Ω) or volt/amp
63. Electrical admittance 1/Z(Reciprocal of electric impedance) M^{-1}L^{-2}T^3I^3 Siemens (or) mhos
64. Self Inductance(L) \displaystyle v=L\frac{di}{dt} ML^2T^{-2}I{-2} weber/amp or Henry
65. Boltzmann’s constant \frac{Energy}{Temp} M^1L^2T^{-2}K^{-1} J/kelvin
66. Stefan’s constant \frac{E}{At \theta^4} M^1L^0T^{-3}K^{-4} W m^{-2}K^{-4}
67. Co-efficient of friction \mu \mu=\frac{F}{N},N=Normal reaction dimension less scalar no units
68. Dielectric constant \varepsilon_r It is also called relative permittivity dimension less no
units
69. Planck’s constant E=h\nu ML^2T^{-1} J.sec (or) eV.sec
70. Refractive index μ M^0L^oT^o no units
71. Focal length(f) Distance between center of the lens(mirror) to its focus L meter
72. Power of a lens (P) The reciprocal of the focal length of a lens in meters is called power of a lens; p=1/f L^{-1} diaptors
73. Wave number No.of waves/distance L^{-1} m^{-1}
74. Wave length Length of a wave L meter
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