Cheatography

# Units, Dimension & Measurements Cheat Sheet by mvdassir_

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