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Units, Dimension & Measurements Cheat Sheet by

Units, Dimension, Measurements & Practical Physics.

Set of Quantities having same Dimensions

Sr. No.
Quantities
Dimensions
1
strain, refractive index, relative density, angle, solid angle, phase, distance gradient, relative permea­bility, relative permit­tivity, angle of contact, Reynolds number, coeffi­cient of friction, mechanical equivalent of heat, electric suscep­tib­ility, etc.
[M0L0T0]
2
Mass or inertial mass
[M1L0T0]
3
Momentum and impulse
[M1L1T-1]
4
Thrust, Force, weight, tension, energy gradient
[M1L1T-2]
5
Pressure, stress, Young's modulus, bulk modulus, shear modulus, modulus of rigidity, energy density
[M1L-1T-2]
6
Angular momentum and Planck's constant
[M1L2T-1]
7
Accele­ration, g and gravit­ational field intensity
[M0L1T-2]
8
Surface tension, free surface energy (energy per unit area), force gradient, spring constant
[M1L0T-2]
9
Latent heat and gravit­ational potential
[M0L2T-2]
10
Thermal capacity, Boltzmann constant, entropy
[M1L2T-2K-1]
11
Work, Torque, internal energy, potential energy, kinetic energy, moment of force, (q/C2), (LI2), (qV), (V2C), (I2Rt), (VIt), (V2t/R), (PV), (RT), (mL), (mc ΔT)
[M1L2T-2]
12
Frequency, angular frequency, angular velocity, velocity gradient, radioa­cti­vity, (R/L), (1/RC), (1/ (LC)1/2)
[M0L0T-1]
13
(l/g)1/2, (m/k)1/2, (L/R), (RC), (LC)1/2, time
[M0L0T1]
14
(VI), (I2R), (V2/R), Power
[M1L2T-3]

Rules for Counting Signif­icant Figures

For numbers greater than 1
•All non-zero digits are signif­icant
•All zeroes between two non-zero digits are signif­icant. The location of the decimal does not matter.
•If the number is without a decimal point, then the trailing zeroes are not signif­icant.
•Trailing zeroes in the decimal part are signif­icant.

For numbers less than 1
•Any zero to the right of a non-zero digit is signif­icant.
•All zeroes between the decimal point and the first non-zero digit are not signif­icant,

Fundam­ental or Base Quantities

The quantities which do not depend upon other quantities for their complete definition are known as fundam­ental or base quantities.
e.g.: length, mass, time, etc.

Derived Quantities

The quantities which can be expressed in terms of the fundam­ental quantities are known as derived quantities
e.g.: Speed (= distan­ce/­time), Volume, accele­ration, force, pressure, etc.

Units of Physical Quantities

The chosen reference standard of measur­ement in multiples of which, a physical quantity is expressed is called the unit of the quantity.
e.g.: Physcial Quantity = Numerical Value x Unit

Supple­mentary Units

Radian (rad)
for measur­ement of plane angle
Steradian (sr)
for measur­ement of solid angle

Prefixes used for different Powers of 10

Power of 10
Prefix
Synbol
Power of 10
Prefix
Symbol
1018
exa
E
10-1
deci
d
1015
peta
P
10-2
centi
c
1012
tera
T
10-3
milli
m
109
giga
G
10-6
micro
µ
106
mega
M
10-9
nano
n
103
kilo
k
10-12
pico
p
102
hecto
h
10-15
femto
f
101
deca
da
10-18
atto
a

Some Fundam­ental Constants

Constant
Symbol
Value
Gravit­ational Constant
G
6.6*10-11 Nm2kg-2
Speed of Light in Vacuum
c
3*108 ms-1
Permea­bility of vacuum
μ
4π*10-7 Hm-1
Permit­tivity of vacuum
ε
8.85*10-12 Fm -1
Planck's Constant
h
6.63*10-34 Js
Atomic Mass Unit
amu
1.66*10-27 kg
Energy equivalent of 1 amu
MeV
931.5 MeV
Electron rest mass
mₑ
9.1*10-31= 0.511 MeV
Avogadro constant
Nₐ
6.02*1023 mol-1
Faraday Constant
F
9.648*104 C mol-1
Stefan­-Bo­ltzmann Constant
σ
5.67*10-8 W m-2K-4
Wien Constant
b
2.8910-3^ mK
Rydberg Constant
R∞
1.097*107 m-1
Triple point for water
K / oC / oF
273.16K (0.01oC)
Molar volume of ideal gas
m3 mol-1
22.4 L = 22.4*10-3 m3 mol-1

Order of Magnitude

Power of 10 required to represent a quantity.
49 = 4.9*101 ≈ 101 → order of magnitude = 1
0.051 = 5.1*10-2 ≈ 10-2 → order of magnitude = -2
 

System of Units

 
MKS
CGS
FPS
MKSQ
MKSA
(i)
Length (m)
Length (cm)
Length (ft)
Length (m)
Length (m)
(ii)
Mass (kg)
Mass (g)
Mass (pound)
Mass (kg)
Mass (kg)
(iii)
Time (s)
Time (s)
Times (s)
Time (s)
Time (s)
(iv)
-
-
-
Charge (Q)
Current (A)

Fundam­ental Quantities in S.I. System

Sr. No.
Physical Quantity
Name of Unit
Symbol
1
Mass
kilogram
kg
2
Length
meter
m
3
Time
second
s
4
Temper­ature
kelvin
K
5
Luminous Intensity
candela
Cd
6
Electric Current
ampere
A
7
Amount of Substance
mole
mol

Dimens­ional Formula

The relation which expresses physical quantities in terms of approp­riate powers of fundam­ental quanti­ties.

Use of Dimens­ional Analysis

To check the dimens­ional correc­tness of a given physical relation.
To derive relati­onship between different physical quanti­ties.
To convert units of a physical quantity from one system to another.

Units of Important Physical Quantities

Physical Quantity
Unit
Physical Quantity
Unit
Angular accele­ration
rad s-2
Frequency
hertz
Moment of Inertia
kg m2
Resistance
kh m2 A-2 s-3
Self-I­ndu­ctance
henry
Surface Tension
N/m
Magnetic Flux
weber
Universal Gas Constant
J K-1 mol-1
Pole Strength
A m
Dipole Moment
C m
Viscosity*
poise
Stefan Constant
W m-2 K^-4*
Reactance
ohm
Permit­tivity of free space εₒ ​
C2/N m2
Specific Heat
J/kg oC
Permea­bility of free space µₒ
weber/ A m
Strength of magnetic field
N A-1 m-1
Planck's Constant
J s
Astron­omical distance
Parsec
Entropy
J/K

Error in Summation and Difference

x = a + b then, △x = ± (△a + △b)

Error in Product and Division

If X = YaZb then the maximum possible fractional error in X is given by the above equation
           
 

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