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^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 ML^2T^{-1} kg-m^2 sec^{-1}
37. Angular Impulse 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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Important formulas in Physics.

Kinematics :

    • Average Speed = \frac{Totaldistancetraveled}{Total time taken}
    • If the body covers 1st half of distance with a speed x and the second half with a speed y,then the average speed = \frac{2xy}{x+y}
    • If the body covers 1st 1/3rd of a distance with a speed x , and 2nd 1/3 with a speed y , and the 3rd 1/3rd distance with a speed z, then average speed =\frac{3xyz}{xy+yz+zx}
    • Average velocity = \frac{TotalDisplacement}{Total time taken}
    • If a body travels a displacement s_1 in t_1 seconds and a displacement s_2 in t_2 seconds, in the same direction then   Average velocity = \frac{s_1+s_2}{t_1+t_2} .
    • If a body travels a displacement s_1 with velocity v_1 , and displacements_2 with velocity v_2 in the same direction then Average velocity = \frac{( s_1 + s_2) v_1v_2}{s_1v_2+s_2v_1}
    • If a body travels first half of the displacement with a velocity v_1and next half of the displacement with a velocity v_2 in the same direction , then                                                          Average velocity = \frac{2v_1v_2}{v_1+v_2} .
    • If a body travels a time t_1 with velocity v_1 and for a time t_2 with a velocity v_2 in the same direction then Average velocity = \frac{v_1t_2+V_2t_1}{t_1+t_2} .
    • If the body travels 1st half of the time with a velocity v_1 next half of the time with a velocity v_2 in same direction , then  Average velocity = \frac{v_1+v_2}{2}
    • For a body moving with uniform acceleration if the velocity changes from u to v in t seconds, then Average velocity = (u+v)/2 .
  • Equations of motion of a body moving with uniform acceleration along straight line.
  • a) V=u+at    b) S=ut+\frac{1}{2}at^2  c) v^2u^2 =2as
    • Distance traveled  in the nth second    s_n=u+a(n-1/2)
    • Equations of motion for a freely falling body ( Note: we can obtain these equations by substitution of u=0 and a=g in above equations . a) v=gt b) S=1/2 gt^2 c) v^2 = 2gs and the equation for the distance traveled in nth second changes to          s_n=g(n-1/2)
    • Equations of motion of a body projected up vertically :(we will obtain these equations by substitution a=-g in equations of motion)
    • a) v=u-gt  b) S=ut-1/2gt^2  c) v^2-u^2=-2gs and s_n=u-g(n-1/2)
    • Equation for maximum height reached H_{max} = \frac{u^2}{2g} \Rightarrow H_{max} \alpha u^2
    • Time of ascent t_a=\frac{u}{g};     t_a\alpha u
    • Time of descent  t_d =\frac{u}{g}t_d \alpha u
    • Time of flight T=2u/g
    • When a body is thrown up from top of a tower or released from a rising baloon,with velocity u.Displacement traveled before reaching ground              S=-ut+1/2gt^2. (t= time during which the object is in the air and S=h=height of the tower).
    • When a body is dropped from a tower of height h and another body is thrown up vertically with a velocity u then they will meet after t=h/u seconds.
    • When a body is dropped from a tower of height h . Its velocity when it reaches ground v=\sqrt(2gh)
    • If the displacements of a body in m^{th} ,n^{th} seconds of its journey.Then the uniform acceleration of the body a=\frac{s_n-s_m}{n-m}
    • From the above equation we can observe that by substituting n=1,2,3,4,…. we get a=s_2-s_1=s_3-s_2=……….. =s_{n-s}s_{n-1} =a.
    • A body projected up with velocity u from the top  of a tower reaches ground in t_1 seconds.If  it  is thrown down with the same velocity u it reaches ground in t_2 seconds.Then, when it is dropped freely the time taken to reach the ground will be t=\sqrt(t_1t_2)   and h=1/2 gt_1t_2   and t_1 -t_2 =2 \frac{u}{g}.
    • Projectile motion :Let us suppose that a projectile is projected with an initial velocity u making an angle \theta with x axis. a)Horizontal component of velocity u_x = u cos\theta , and u_x =v_x ,which will be constant through out the flight of the projectile as horizontal component of acceleration a_x = 0.  b)Vertical component of velocity of the projectile u_y = u sin\theta. Vertical component of velocity at any time of its journey v_y =u_y-gt or v_y =usin\theta -gt.   c)Magnitude of the resultant velocity V = \sqrt(v_x^2+v_y^2)  and the angle x made by v with the horizontal is given by Tan\alpha= \frac{v_y}{v_x}
    • Time of ascent = \frac{usin\theta}{g}
    • Time of descent = \frac{usin\theta}{g}
    • Time of flight = \frac{2u sin\theta}{g}
    • Maximum height reached  H_{max} =\frac{u^2 sin^2\theta}{2g} ;\frac{H1}{H2} =\frac{sin^2\theta_1}{sin^2\theta_2} when u is same
    • Horizontal Range R= \frac{(u^2sin2\theta)}{g }=\frac{2u^2 sin\theta cos\theta}{g}  a)R is maximum when \theta =45^0  b)R_{max} =\frac{u^2}{g}  c) If T is the time of flight, R=u cos\theta\times t  d)For given velocity of projection R is same for the angles of projections \theta and (90-\Theta)  Ex: 25 and 65 i.e the Range for those two angles will be same whose sum is 90^0)