Ch 01: Physical Quantities & Units

📐 Physical Quantities

Quantities that can be measured directly and indirectly
Expressed by a numerical value and an appropriate unit
e.g. Mass, Length, Force, etc.

🎯 Based on Direction & Magnitude

(a) Scalar Quantity

Only magnitude required
e.g. Distance, Speed, Mass, Work, Time, Energy, Electric current, Temperature, Pressure

(b) Vector Quantity

Both magnitude and direction required
e.g. Displacement, Velocity, Acceleration, Force, Momentum

⚠ Exam Trap

Speed = Scalar | Velocity = Vector. Distance = Scalar | Displacement = Vector. Mass = Scalar | Force = Vector. These commonly confused pairs should be distinguished carefully.

📋 Based on Properties

Fundamental	Derived	Former supplementary units
Does NOT depend on other quantities	Depends on fundamental quantities	Radian and steradian are now dimensionless derived units
Completely independent	Derived with help of fundamental quantities	Two historical supplementary units; separate class abolished in 1995
e.g. Length, Mass, Time	e.g. Force, Work, Pressure	e.g. Plane angle, Solid angle

📏 Systems of Units

System	Also Called	Length	Mass	Time	Key Fact
FPS	British System	Foot	Pound	Second	FPS: British/English usage. 1 lb = 453.59237 g exactly
CGS	Centimetre–gram–second metric system	Centimeter	Gram	Second	India adopted metric standards through the Standards of Weights and Measures Act, 1956; this was not specifically CGS adoption
MKS	—	Meter	Kilogram	Second	Metre–kilogram–second mechanical base set
SI	International System	Meter	Kilogram	Second	The name SI was adopted by the 11th CGPM in 1960. Seven base units; radian and steradian are dimensionless derived units

⚠ Exam Trap

SI name adopted by the 11th CGPM (1960). FPS uses foot, pound and second; CGS uses centimetre, gram and second. 1 lb = 453.59237 g exactly. SI has seven base units; radian and steradian are dimensionless derived units (separate supplementary class abolished in 1995).

🔢 7 Fundamental (SI) Units

#	Quantity	Unit	Symbol
1	Length	Meter	m
2	Mass	Kilogram	kg
3	Time	Second	s
4	Temperature	Kelvin	K
5	Electric Current	Ampere	A
6	Luminous Intensity	Candela	cd
7	Amount of Substance	Mole	mol

⚡ Quick Recall — Mnemonic

Length · Mass · Time · Temperature · Electric current · Luminous intensity · Amount of substance → LMT-TELA

➕ Radian & Steradian — Former Supplementary Units

Quantity	Unit	Symbol
Plane Angle	Radian	rad
Solid Angle	Steradian	sr

🌌 Important Experimental Units

Unit	Value / Equivalent	Used For
1 Light Year	9.46 × 10¹⁵ m	Distance light travels in one year
1 Parsec	3.26 light years = 3.08 × 10¹⁶ m	Astronomical distance
1 Astronomical Unit (AU)	1.496 × 10¹¹ m ≈ 1.5 × 10¹¹ m	Earth-Sun distance
1 Angstrom (Å)	10⁻¹⁰ m	Atomic scale distances
1 amu	1.66 × 10⁻²⁷ kg	Atomic mass unit
1 Slug	14.59 kg	FPS mass unit
1 Svedberg Unit	10⁻¹³ s	Sedimentation coefficient
1 Chandrasekhar Limit	1.4 × mass of sun = 2.765 × 10³⁰ kg	Maximum mass of white dwarf
1 Barrel	158.98 litres	Volume (oil)
Dobson Unit	—	Thickness of Ozone layer
British Thermal Unit (BTU)	—	Heat
Cusec	—	Flow of Water

Distance order:1 Parsec > 1 Light Year > 1 Astronomical Unit

⚠ Exam Trap

1 Parsec = 3.26 light years (NOT 3.26 AU). Parsec > Light year > AU. Dobson unit = Ozone layer thickness. Cusec = water flow. Chandrasekhar limit = 1.4 solar masses.

⚗️ Derived Quantities & Units

Quantity	Unit	Symbol	Quantity	Unit	Symbol
Work / Energy	Joule	J	Momentum	kg·m/s	kg-m/s
Force	Newton	N	Surface Tension	Newton/meter	N/m
Power	Watt	W	Potential Difference	Volt	V
Pressure	Pascal	Pa	Electric Resistance	Ohm	Ω
Acceleration	m/s²	m/s²	Electric Capacitance	Farad	F
Area	Square meter	m²	Magnetic Flux	Weber	Wb
Volume	Cubic meter	m³	Luminous Flux	Lumen	lm
Speed	Meter/sec	m/s	Illuminance	Lux	lx
Angular Velocity	Radian/sec	rad/s	Frequency	Hertz	Hz
Impulse	Newton·sec	Ns	Electric Charge	Coulomb	C

⚠ Exam Trap

Work = Energy = Joule. Power = Watt. Force = Newton. Pressure = Pascal. Frequency = Hertz. Resistance = Ohm (Ω). Magnetic flux = Weber (not Watt!).

⚡ Quick Recall

Impulse = Force × Time = Ns = same as Momentum (kg·m/s). Both have same dimensional formula [MLT⁻¹].

🔟 Powers of 10 — Prefixes

⬆ LARGER (Positive powers)

Power	Prefix	Symbol
10¹⁸	Exa	E
10¹⁵	Peta	P
10¹²	Tera	T
10⁹	Giga	G
10⁶	Mega	M
10³	Kilo	k
10²	Hecto	h
10¹	Deca	da

⬇ SMALLER (Negative powers)

Power	Prefix	Symbol
10⁻¹	Deci	d
10⁻²	Centi	c
10⁻³	Milli	m
10⁻⁶	Micro	μ
10⁻⁹	Nano	n
10⁻¹²	Pico	p
10⁻¹⁵	Femto	f
10⁻¹⁸	Atto	a

⚡ Quick Recall — Mnemonic (Large → Small)

Every Person Trying Good Marks Keeps Hard Dedication → Exa Peta Tera Giga Mega Kilo Hecto Deca

Dear Children Make Many New Plans For Adventures → Deci Centi Milli Micro Nano Pico Femto Atto

⚠ Exam Trap

Mega = 10⁶, Giga = 10⁹, Tera = 10¹². Micro = 10⁻⁶, Nano = 10⁻⁹, Pico = 10⁻¹². Kilo = k (small k) but Kelvin = K (capital K) — different symbols!

📐 Dimensional Formula

Powers applied to symbols of fundamental units
Equation expressed by [M, L, T] = Dimensional formula

📋 Dimensional Formulae — Complete Table

Quantity	Dimensional Formula	Quantity	Dimensional Formula
Density	[ML⁻³T⁰]	Velocity / Speed	[M⁰LT⁻¹]
Momentum	[MLT⁻¹]	Acceleration	[M⁰LT⁻²]
Force	[MLT⁻²]	Impulse	[MLT⁻¹]
Pressure	[ML⁻¹T⁻²]	Work & Energy	[ML²T⁻²]
Power	[ML²T⁻³]	Surface Tension	[ML⁰T⁻²]
Frequency	[M⁰L⁰T⁻¹]	Stress	[ML⁻¹T⁻²]
Coefficient of Viscosity	[ML⁻¹T⁻¹]	Modulus of Elasticity	[ML⁻¹T⁻²]
Specific Heat	[M⁰L²T⁻²K⁻¹]	Resistance	[ML²T⁻³A⁻²]
Electric Capacitance	[M⁻¹L⁻²T⁴A²]	Electric Field	[MLT⁻³A⁻¹]

⚠ Exam Trap

Momentum = Impulse = [MLT⁻¹] (same formula!). Force = [MLT⁻²]. Work = Energy = [ML²T⁻²]. Power = [ML²T⁻³]. Pressure = Stress = Modulus of Elasticity = [ML⁻¹T⁻²] (all three have the same dimensional formula).

⚡ Quick Recall

Frequency = [T⁻¹] only (no M, no L). Surface tension = [MT⁻²] (no L). Density = [ML⁻³] (no T). Remember these three distinctive dimensional formulae.

⚛️ Chapter 01 — Physical Quantities & Units