Units, Dimension & Measurements Cheat Sheet

A Education › Physics cheat sheet in English by mvdassir_

Units, Dimension, Measurements & Practical Physics.

13,155 views 1,788 downloads 19 Aug 2022 History

PRs

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 (0.01^oC)
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 = 4.910¹ ≈ 10¹ → order of magnitude = 1
0.051 = 5.110^-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 = Y^aZ^b then the maximum possible fractional error in X is given by the above equation

Badges

Downloaded from Unusual Locations × 3

Comments

No comments yet.