Physics Formula Handbook – NDA Physics

Top 50 Must-Know NDA Physics Formulae

One-page quick reference. ★★★ formulas only. No explanations.

★★★  KINEMATICS

   v = u + at

   v² = u² + 2as

   s = ut + ½at²

   R = u²sin2θ / g (projectile range)

   1 m s⁻¹ = 3.6 km h⁻¹

★★★  LAWS OF MOTION

   F = ma

   Impulse J = FΔt = Δp

   f_k = μ_k × N

★★★  WORK, ENERGY & POWER

   W = Fs cosθ

   KE = ½mv²

   P = W/t = Fv

★★★  GRAVITATION

   F = Gm₁m₂/r²

   g = GM/R²

   v_escape = √(2gR)

   v_orbital = √(gR)

★★★  ROTATIONAL MOTION

   τ = Iα = rF sinθ

   L = Iω

   KE_rot = ½Iω²

★★★  OSCILLATIONS & WAVES

   T = 2π√(L/g) (pendulum)

   v = fλ

★★★  FLUID MECHANICS

   F_buoyancy = ρ_fluid × V × g

   P = P₀ + ρgh

   β = 2α  |  γ = 3α

★★★  HEAT & THERMODYNAMICS

   Q = mcΔT

   Q = mL (latent heat)

   K = °C + 273

   °F = 32 + 1.8 × °C

   η_Carnot = 1 − T_c/T_h

★★★  ELECTRICITY

   V = IR

   R = ρL/A

   P = VI = I²R = V²/R

   H = I²Rt

   R_new = n²R (stretched wire)

★★★  MAGNETISM & EMI

   B = μ₀nI (solenoid)

   F = qvB sinθ

   τ = NBIA sinθ

   V₁/V₂ = N₁/N₂ (transformer)

★★★  OPTICS

   1/v + 1/u = 1/f (mirror)

   1/v − 1/u = 1/f (lens)

   P = 1/f(metres)

   n₁sinθ₁ = n₂sinθ₂ (Snell)

   Apparent depth = Real/n

   M_telescope = f_obj / f_eye

★★★  MODERN PHYSICS

   E = hf

   E = mc²

   λ_min = hc/(eV)

   E_n = −13.6/n² eV (Bohr)

   N(t) = N₀(½)^(t/t½)

Symbols Dictionary

Latin Symbols (A – Z)

Symbol	Meaning	SI Unit
A	Area / Mass number / Amplitude	m² / dimensionless / m
a	Linear acceleration / Semi-major axis	m s⁻² / m
B	Magnetic flux density (magnetic field)	Tesla (T)
c	Speed of light in vacuum	m s⁻¹
C	Capacitance / Thermal capacity	F / J K⁻¹
d	Distance / Diameter / Separation	m
E	Energy / Electric field / EMF	J / V m⁻¹ / V
e	Elementary (electron) charge	Coulomb (C)
F	Force	Newton (N)
f	Frequency / Focal length	Hz / m
g	Acceleration due to gravity	m s⁻²
G	Universal gravitational constant	N m² kg⁻²
h	Height / Planck’s constant	m / J s
H	Magnetic field intensity / Heat / Henry	A m⁻¹ / J / H
I	Electric current / Moment of inertia / Intensity	A / kg m² / W m⁻²
J	Impulse	N s
K	Kinetic energy	J
k	Spring constant / Boltzmann constant / Coulomb constant	N m⁻¹ / J K⁻¹ / N m² C⁻²
L	Angular momentum / Self-inductance / Length	kg m² s⁻¹ / H / m
M	Magnification / Molar mass / Mutual inductance	dimensionless / kg mol⁻¹ / H
m	Mass	kg
n	Refractive index / Turns per unit length / Quantum number	dimensionless / m⁻¹ / dimensionless
N	Normal force / Number of turns / Number of particles	N / dimensionless / dimensionless
P	Power / Pressure / Lens power	W / Pa / Dioptre (D)
p	Momentum / Pressure	kg m s⁻¹ / Pa
Q	Charge / Heat	C / J
q	Charge	C
R	Resistance / Radius of curvature / Gas constant	Ω / m / J mol⁻¹ K⁻¹
r	Radius / Distance	m
S	Entropy / Surface area	J K⁻¹ / m²
T	Period / Temperature / Tension	s / K / N
t	Time	s
U	Potential energy / Internal energy	J
u	Object distance / Initial velocity	m / m s⁻¹
V	Voltage / Volume / Velocity	V / m³ / m s⁻¹
v	Speed / Velocity / Image distance	m s⁻¹ / m s⁻¹ / m
W	Work / Weight	J / N
X	Reactance (inductive or capacitive)	Ω
Z	Impedance / Atomic number	Ω / dimensionless

Greek Symbols

Symbol	Name	Meaning	SI Unit
α	Alpha	Linear thermal expansion coefficient / Angular acceleration / Alpha particle	K⁻¹ / rad s⁻² / —
β	Beta	Areal thermal expansion coefficient = 2α	K⁻¹
γ	Gamma	Volumetric expansion coefficient = 3α / Ratio C_p/C_v	K⁻¹ / dimensionless
ε₀	Epsilon-naught	Permittivity of free space	F m⁻¹
η	Eta	Efficiency (Carnot etc.) / Viscosity	dimensionless / Pa s
θ	Theta	Angle	rad or °
λ	Lambda	Wavelength / Decay constant / de Broglie wavelength	m / s⁻¹ / m
μ	Mu	Coefficient of friction / Permeability	dimensionless / H m⁻¹
μ₀	Mu-naught	Permeability of free space	H m⁻¹ = T m A⁻¹
ν	Nu	Frequency (alternate symbol)	Hz
ρ	Rho	Density / Resistivity	kg m⁻³ / Ω m
σ	Sigma	Stress / Conductivity / Stefan–Boltzmann constant	Pa / S m⁻¹ / W m⁻² K⁻⁴
τ	Tau	Torque / Time constant	N m / s
φ	Phi	Work function / Magnetic flux / Phase angle	eV / Wb / rad
ω	Omega	Angular velocity / Angular frequency	rad s⁻¹

Frequently Confused Symbols

The same symbol may represent different quantities in different chapters.

Symbol	Meaning	Chapter / Context
P	Pressure	Fluid Mechanics, Thermodynamics (Ch 8, 9)
P	Power (mechanical or electrical)	Mechanics, Electricity (Ch 4, 10)
P	Lens Power	Optics (Ch 12)
R	Radius	Mechanics, Gravitation (Ch 2, 5, 6)
R	Radius of curvature	Optics (Ch 12)
R	Resistance	Electricity (Ch 10)
R	Universal gas constant	Thermodynamics (Ch 9)
V	Voltage / Potential difference	Electricity (Ch 10)
V	Volume	Fluid Mechanics, Thermodynamics (Ch 8, 9)
H	Henry: unit of inductance	Magnetism (Ch 11)
H	Heat generated	Electricity (Ch 10)
k	Spring constant	Oscillations (Ch 7)
k	Boltzmann constant	Thermodynamics (Ch 9)
k	Coulomb’s constant	Electricity (Ch 10)
f	Frequency	Waves, EM spectrum (Ch 7, 13)
f	Focal length	Optics (Ch 12)
T	Period	Oscillations, Waves (Ch 7)
T	Temperature	Thermodynamics (Ch 9)
T	Tension	Mechanics (Ch 3, 7)
n	Refractive index	Optics (Ch 12)
n	Turns per unit length	Magnetism (Ch 11)
n	Principal quantum number	Modern Physics (Ch 13)
E	Energy (photon, kinetic, binding)	Various chapters
E	Electric field	Electricity (Ch 10)
E	EMF (electromotive force)	Electricity (Ch 10)
σ	Stress	Fluid Mechanics (Ch 8)
σ	Electrical conductivity	Electricity (Ch 10)
σ	Stefan–Boltzmann constant	Thermodynamics (Ch 9)

Universal Physical Constants

Constant	Symbol	Value	SI Unit
Speed of light in vacuum	c	3.00 × 10⁸	m s⁻¹
Universal gravitational constant	G	6.674 × 10⁻¹¹	N m² kg⁻²
Planck’s constant	h	6.626 × 10⁻³⁴	J s
Electron charge	e	1.6 × 10⁻¹⁹	C
Electron mass	m_e	9.11 × 10⁻³¹	kg
Proton mass	m_p	1.67 × 10⁻²⁷	kg
Avogadro’s number	N_A	6.022 × 10²³	mol⁻¹
Boltzmann constant	k_B	1.38 × 10⁻²³	J K⁻¹
Universal gas constant	R	8.314	J mol⁻¹ K⁻¹
Permittivity of free space	ε₀	8.85 × 10⁻¹²	F m⁻¹
Permeability of free space	μ₀	4π × 10⁻⁷	H m⁻¹ = T m A⁻¹
Coulomb’s constant	k = 1/(4πε₀)	9 × 10⁹	N m² C⁻²
Stefan–Boltzmann constant	σ	5.67 × 10⁻⁸	W m⁻² K⁻⁴
Atomic mass unit	u	1.66 × 10⁻²⁷	kg
Standard acceleration due to gravity	g	9.8	m s⁻²

NDA Approximation Values

Use these values in NDA numerical calculations.

Quantity	NDA Working Value
Acceleration due to gravity g	10 m s⁻² (use instead of 9.8 unless specified)
Speed of light c	3 × 10⁸ m s⁻¹
Speed of sound in air (20°C)	330–343 m s⁻¹ ≈ 330 m s⁻¹
Density of water	1000 kg m⁻³ = 1 g cm⁻³
Density of air (STP)	1.3 kg m⁻³
Atmospheric pressure	1 atm = 10⁵ Pa ≈ 101,325 Pa
Absolute zero	0 K = −273°C
Room temperature	300 K = 27°C
π	22/7 ≈ 3.14
√2	1.414 ≈ 1.41
√3	1.732 ≈ 1.73
1 eV in Joules	1.6 × 10⁻¹⁹ J
1 kWh in Joules	3.6 × 10⁶ J
1 hp in Watts	746 W
1 cal in Joules	4.18 J

SI Base Units

Base Quantity	SI Unit	Symbol
Length	Metre	m
Mass	Kilogram	kg
Time	Second	s
Electric current	Ampere	A
Temperature	Kelvin	K
Amount of substance	Mole	mol
Luminous intensity	Candela	cd

SI Prefixes

Prefix	Symbol	Power of 10	Example
Tera	T	10¹²	1 THz = 10¹² Hz
Giga	G	10⁹	1 GW = 10⁹ W
Mega	M	10⁶	1 MHz = 10⁶ Hz
Kilo	k	10³	1 km = 10³ m
Hecto	h	10²	1 hPa = 100 Pa
Deca	da	10¹	1 dag = 10 g
— (base)	—	10⁰	base unit
Deci	d	10⁻¹	1 dL = 0.1 L
Centi	c	10⁻²	1 cm = 10⁻² m
Milli	m	10⁻³	1 mm = 10⁻³ m
Micro	μ	10⁻⁶	1 μm = 10⁻⁶ m
Nano	n	10⁻⁹	1 nm = 10⁻⁹ m
Pico	p	10⁻¹²	1 pF = 10⁻¹² F
Femto	f	10⁻¹⁵	1 fm = 10⁻¹⁵ m

Unit Conversion Tables

Length

1 m = 100 cm = 1000 mm = 10⁶ μm = 10⁹ nm

1 km = 1000 m = 10³ m

1 Å (Ångström) = 10⁻¹⁰ m = 0.1 nm

1 nm = 10⁻⁹ m = 10 Å

1 light-year = 9.46 × 10¹⁵ m

1 inch = 2.54 cm

Mass

1 kg = 1000 g = 10³ g

1 tonne = 1000 kg

1 u (atomic mass unit) = 1.66 × 10⁻²⁷ kg

1 g = 10⁻³ kg

Time

1 min = 60 s

1 h = 3600 s

1 day = 86,400 s

1 year ≈ 3.15 × 10⁷ s

Speed

1 m s⁻¹ = 3.6 km h⁻¹

1 km h⁻¹ = 5/18 m s⁻¹ ≈ 0.278 m s⁻¹

1 km s⁻¹ = 1000 m s⁻¹

Force & Pressure

1 N = 10⁵ dyne

1 kN = 1000 N

1 Pa = 1 N m⁻²

1 kPa = 1000 Pa

1 atm = 101,325 Pa ≈ 10⁵ Pa

1 bar = 10⁵ Pa

1 mmHg = 133.3 Pa

Energy & Work

1 kJ = 1000 J

1 eV = 1.6 × 10⁻¹⁹ J

1 MeV = 1.6 × 10⁻¹³ J

1 kWh = 3.6 × 10⁶ J

1 cal = 4.18 J

1 kcal = 4180 J

Power

1 kW = 1000 W

1 MW = 10⁶ W

1 hp = 746 W

Temperature

K = °C + 273.15

°C = (°F − 32) / 1.8 = (°F − 32) × 5/9

°F = 32 + 1.8 × °C = 32 + (9/5)°C

Electrical Units

1 kΩ = 1000 Ω  |  1 MΩ = 10⁶ Ω

1 mA = 10⁻³ A  |  1 μA = 10⁻⁶ A

1 kV = 1000 V  |  1 mV = 10⁻³ V

1 μF = 10⁻⁶ F  |  1 pF = 10⁻¹² F

1 mH = 10⁻³ H  |  1 μH = 10⁻⁶ H

Frequency

1 kHz = 10³ Hz  |  1 MHz = 10⁶ Hz  |  1 GHz = 10⁹ Hz  |  1 THz = 10¹² Hz

Optics

1 Dioptre (D) = 1 m⁻¹

f (metres) = 1/P; f (cm) × P(D) = 100

1 nm = 10⁻⁹ m  |  1 Å = 10⁻¹⁰ m = 0.1 nm

Visible light: 380 nm (violet) to 780 nm (red)

X-ray range: 0.01 nm to 10 nm (≈ 1 Å to 1 nm)

Modern Physics

1 eV = 1.6 × 10⁻¹⁹ J  |  1 MeV = 1.6 × 10⁻¹³ J

1 u = 1.66 × 10⁻²⁷ kg  |  rest energy of 1 u = 931.5 MeV

Ionisation energy of hydrogen = 13.6 eV (not MeV)

Sign Convention Summary

Cartesian Sign Convention (Mirrors and Lenses)

Situation	Sign Rule
Object position	Always to the LEFT of the optical device: distances in this direction are NEGATIVE
Distances in direction of incident light (left→right)	POSITIVE
Distances opposite to incident light (right→left)	NEGATIVE
Heights above principal axis	POSITIVE
Heights below principal axis	NEGATIVE

Mirror Sign Convention

Quantity	Sign	Reason
Object distance (u)	Always negative	Object always on same side as incident light
Focal length (concave)	Negative	Centre of curvature on reflection side
Focal length (convex)	Positive	Centre of curvature on opposite side
Image distance: real image	Negative	Same side as object (reflection side)
Image distance: virtual image	Positive	Behind mirror
Radius of curvature: R = 2f	Same sign as f	Follows focal length sign

Lens Sign Convention

Quantity	Sign	Reason
Object distance (u)	Always negative	Object always on incident side
Focal length (convex lens)	Positive → Positive power	Converging lens
Focal length (concave lens)	Negative → Negative power	Diverging lens
Image distance: real image	Positive	Opposite side from object (transmission)
Image distance: virtual image	Negative	Same side as object

Work, Heat, and Thermodynamics Signs

Quantity	Positive (+)	Negative (−)
Work W	Force and displacement in same direction (θ < 90°)	Force opposite to displacement (θ > 90°)
Heat Q (First Law)	Heat supplied TO the system	Heat removed FROM the system
Work W (First Law)	Work done BY the system (expansion)	Work done ON the system (compression)
Torque τ	Counterclockwise (anticlockwise)	Clockwise
EMF terminal voltage	V = E − Ir (always ≤ EMF under load)	—

Conventional Current vs Electron Flow

Type	Direction	Used in Formulae?
Conventional current	Positive terminal → external circuit → negative terminal	YES: all circuit formulas use conventional current
Electron flow	Negative terminal → external circuit → positive terminal (opposite to conventional)	NO: electrons flow opposite to I in formulas

Dimensional Formula Sheet

Seven Base Dimensions

Base Quantity	Dimension Symbol	SI Unit
Mass	M	kg
Length	L	m
Time	T	s
Electric current	A	A
Temperature	Θ	K
Amount of substance	mol	mol
Luminous intensity	cd	cd

Derived Quantities: Dimensional Formulae

Quantity	Formula Basis	Dimensional Formula	SI Unit
Velocity	s/t	[L T⁻¹]	m s⁻¹
Acceleration	v/t	[L T⁻²]	m s⁻²
Force	ma	[M L T⁻²]	Newton (N)
Weight	mg	[M L T⁻²]	Newton (N)
Momentum	mv	[M L T⁻¹]	kg m s⁻¹
Impulse	FΔt	[M L T⁻¹]	N s
Work / Energy	Fs	[M L² T⁻²]	Joule (J)
Power	W/t	[M L² T⁻³]	Watt (W)
Pressure	F/A	[M L⁻¹ T⁻²]	Pascal (Pa)
Density	m/V	[M L⁻³]	kg m⁻³
Frequency	1/T	[T⁻¹]	Hertz (Hz)
Angular velocity	θ/t	[T⁻¹]	rad s⁻¹
Angular acceleration	ω/t	[T⁻²]	rad s⁻²
Torque	rF sinθ	[M L² T⁻²]	N m
Moment of inertia	mr²	[M L²]	kg m²
Angular momentum	Iω	[M L² T⁻¹]	kg m² s⁻¹
Gravitational constant G	Fr²/m₁m₂	[M⁻¹ L³ T⁻²]	N m² kg⁻²
Surface tension	F/L	[M T⁻²]	N m⁻¹
Viscosity (dynamic)	F/(A × dv/dx)	[M L⁻¹ T⁻¹]	Pa s
Stress	F/A	[M L⁻¹ T⁻²]	Pa
Strain	ΔL/L	Dimensionless	—
Young’s Modulus	Stress/Strain	[M L⁻¹ T⁻²]	Pa
Specific heat capacity	Q/(mΔT)	[L² T⁻² Θ⁻¹]	J kg⁻¹ K⁻¹
Thermal conductivity	Qd/(AΔTt)	[M L T⁻³ Θ⁻¹]	W m⁻¹ K⁻¹
Electric charge	It	[A T]	Coulomb (C)
Electric potential (Voltage)	W/Q	[M L² T⁻³ A⁻¹]	Volt (V)
Resistance	V/I	[M L² T⁻³ A⁻²]	Ohm (Ω)
Resistivity	RA/L	[M L³ T⁻³ A⁻²]	Ω m
Capacitance	Q/V	[M⁻¹ L⁻² T⁴ A²]	Farad (F)
Electric field	F/q	[M L T⁻³ A⁻¹]	V m⁻¹
Magnetic flux	BA	[M L² T⁻² A⁻¹]	Weber (Wb)
Magnetic flux density	F/(IL)	[M T⁻² A⁻¹]	Tesla (T)
Inductance	EMF/(dI/dt)	[M L² T⁻² A⁻²]	Henry (H)
Planck’s constant	E/f	[M L² T⁻¹]	J s
Power of lens	1/f	[L⁻¹]	Dioptre (D)
Radioactive decay constant	1/t	[T⁻¹]	s⁻¹

Dimensional Shortcuts: Same Dimensions

Pair / Group	Common Dimension	NDA Significance
Planck’s constant h ≡ Angular momentum L	[M L² T⁻¹]	h = E/f = J·s; L = Iω = kg·m²·s⁻¹
Pressure ≡ Energy density ≡ Young’s modulus	[M L⁻¹ T⁻²]	Pa = J m⁻³ = N m⁻²
Torque ≡ Work ≡ Energy	[M L² T⁻²]	Different physical meanings; same dimensions
Impulse ≡ Linear momentum	[M L T⁻¹]	J = FΔt = Δp = mv
Frequency ≡ Angular velocity	[T⁻¹]	f = 1/T; ω = 2πf: same dim, different values
Strain, Magnification, Refractive index	Dimensionless	Ratios of same-unit quantities

Chapter-wise Formula Handbook

Priority:  ★★★ Very High Frequency  |  ★★ Frequently Used  |  ★ Supporting

Chapter 1: Units & Measurements

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	% Error = (ΔA/A) × 100	Percentage error in measurement	A = measured quantity; ΔA = absolute error	%	Absolute error known	Using relative error incorrectly
★★	Least count = Smallest scale division / Number of divisions	Smallest measurable value	—	Same unit as scale	Vernier or screw gauge	Forgetting to add zero error
★	Relative error = ΔA/A	Fractional error	A = value; ΔA = error	Dimensionless	Always	Not the same as percentage error (multiply by 100 for %)
★	For sum/diff: ΔZ = ΔA + ΔB	Max absolute error in sum/difference	ΔA, ΔB = errors in A, B	Same unit as Z	Addition/subtraction of quantities	Not applicable to multiplication
★	For product/quotient: ΔZ/Z = ΔA/A + ΔB/B	Max relative error in product/quotient	—	Dimensionless	Multiplication or division	Forgetting to add both terms

Chapter 2: Kinematics

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	v = u + at	Final velocity (UAM)	v=final; u=initial velocity (m s⁻¹); a=acceleration (m s⁻²); t=time (s)	m s⁻¹	Uniform acceleration only	Does not apply to non-uniform acceleration
★★★	v² = u² + 2as	Final velocity without time	s=displacement (m)	m s⁻¹	Uniform acceleration only	Forgetting to take square root for v
★★★	s = ut + ½at²	Displacement (UAM)	s=displacement (m)	m	Uniform acceleration only	Sign of a matters (deceleration = negative a)
★★	s_n = u + a(2n−1)/2	Displacement in nth second	n=nth second (integer)	m	Uniform acceleration; integer n only	Confusing s_n with total displacement
★★	s = ½(u+v)t	Displacement via average velocity	u=initial; v=final velocity	m	Uniform acceleration only	Requires both u and v known
★★★	R = u²sin2θ / g	Horizontal range (projectile)	u=launch speed; θ=launch angle; g=9.8 or 10 m s⁻²	m	Projectile; no air resistance	sin(2×45°)=1 for max range at 45°
★★	H = u²sin²θ / 2g	Maximum height (projectile)	—	m	Projectile; no air resistance	sin²θ not sin2θ
★★	T = 2u sinθ / g	Total time of flight (projectile)	—	s	Projectile; flat ground	T = 2 × time to reach maximum height
★★	v_rel = v_A − v_B	Relative velocity of A with respect to B	v_A, v_B = velocities of A and B	m s⁻¹	Same direction: subtract; opposite: add	Direction matters: vector subtraction
★★	v = rω	Linear velocity in circular motion	r=radius (m); ω=angular velocity (rad s⁻¹)	m s⁻¹	Uniform circular motion	v is tangential, not radial
★★	a_c = v²/r = rω²	Centripetal acceleration	—	m s⁻²	Uniform circular motion	a_c directed toward centre: not outward
★	1 m s⁻¹ = 3.6 km h⁻¹	Speed unit conversion	—	—	Always	Forgetting factor 3.6 in conversion

REMEMBER: SUVAT: Five Equations v = u + at v² = u² + 2as s = ut + ½at² s = ½(u + v)t s_n = u + a(2n−1)/2  ← displacement in nth second only

REMEMBER: PROJECTILE: Three Formulae Range R = u²sin2θ / g (maximum at θ = 45°) Max height H = u²sin²θ / 2g Time of flight T = 2u sinθ / g

Chapter 3: Laws of Motion

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	F = ma	Net force on a body	F=force (N); m=mass (kg); a=acceleration (m s⁻²)	Newton (N)	Net (resultant) force and acceleration	F is net force, not just applied force
★★★	W = mg	Weight of a body	g=9.8 or 10 m s⁻²	Newton (N)	Always (near Earth surface)	Weight ≠ Mass; W in N, m in kg
★★★	p = mv	Momentum	p=momentum; v=velocity	kg m s⁻¹	Always	p is a vector: direction matters
★★★	J = FΔt = Δp	Impulse = change in momentum	J=impulse (N s)	N s = kg m s⁻¹	Force applied for short duration	Impulse ≠ Force; Impulse ≠ Energy
★★	f_s ≤ μ_s N	Maximum static friction	μ_s=coefficient of static friction; N=normal force (N)	Newton (N)	Body about to slide	f_s can be less than μ_s N when not at threshold
★★	f_k = μ_k N	Kinetic friction force	μ_k=coefficient of kinetic friction	Newton (N)	Body already sliding	μ_k < μ_s always
★★	tanθ = v²/(rg)	Banking angle for circular road	θ=banking angle; r=radius of road curve	rad or °	Frictionless banked road; circular motion	Use rg not rg²
★	Σp_before = Σp_after	Conservation of momentum (total momentum conserved)	—	kg m s⁻¹	No external force on system	Must include all objects in system

Chapter 4: Work, Energy & Power

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	W = Fs cosθ	Work done by a force	F=force (N); s=displacement (m); θ=angle between F and s	Joule (J)	Constant force; linear displacement	W=0 when θ=90°; W<0 when θ>90°
★★★	KE = ½mv²	Kinetic energy	m=mass (kg); v=speed (m s⁻¹)	Joule (J)	Any moving body	KE is always positive (scalar)
★★★	PE = mgh	Gravitational potential energy	g=9.8 or 10 m s⁻²; h=height above reference (m)	Joule (J)	Near Earth surface; uniform g	h measured from reference level: choose consistently
★★	PE_spring = ½kx²	Elastic PE in spring	k=spring constant (N m⁻¹); x=extension (m)	Joule (J)	Within elastic limit (Hooke’s law valid)	x from natural length: not total length
★★★	W_net = ΔKE = KE_final − KE_initial	Work-Energy theorem	—	Joule (J)	Any force; any motion	W_net is net work: include all forces
★★★	P = W/t	Power (rate of work)	P=power (W); W=work (J); t=time (s)	Watt (W)	Average power over time t	P=Fv for instantaneous power at speed v
★★	P = Fv cosθ	Instantaneous power	F=force; v=speed; θ=angle between F and v	Watt (W)	Instantaneous (not average)	P = Fv only when F and v are parallel (θ=0°)
★★	η = W_output / W_input	Efficiency	η = fraction or %; W in same units	Dimensionless (or %)	Any machine or device	η ≤ 1 always; ideal machine η = 1
★	1 hp = 746 W	Power unit conversion	—	—	Always	NDA uses 746 W; sometimes approximated as 750 W

REMEMBER: ENERGY FORMS KE = ½mv² PE_grav = mgh PE_spring = ½kx² Work-Energy: W_net = ΔKE Power: P = W/t = Fv

Chapter 5: Gravitation

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	F = Gm₁m₂/r²	Gravitational force between two masses	G=6.674×10⁻¹¹; m₁,m₂=masses (kg); r=separation (m)	Newton (N)	Point masses; any separation	r is centre-to-centre distance
★★★	g = GM/R²	Surface gravity of a planet	M=planet mass (kg); R=planet radius (m)	m s⁻²	At surface; spherical planet	g at surface, not altitude
★★	g_h = g(1 − 2h/R)	g at height h (h << R)	h=height above surface (m); R=radius of Earth	m s⁻²	h much less than R	Approximate formula: not valid for large h
★★	g_d = g(1 − d/R)	g at depth d	d=depth below surface (m)	m s⁻²	Inside Earth (uniform density)	g = 0 at Earth’s centre
★★★	v_orbital = √(gR) = √(GM/R)	Orbital velocity (near surface)	R=radius of Earth; g=9.8 m s⁻²	m s⁻¹	Circular orbit at Earth’s surface height	v_orbital ≈ 7.9 km s⁻¹ for Earth
★★★	v_escape = √(2gR) = √(2GM/R) = √2 × v_orbital	Escape velocity	—	m s⁻¹	From surface of planet; no air resistance	v_escape ≈ 11.2 km s⁻¹ for Earth
★★	T² ∝ r³ (Kepler’s Third Law)	Period² ∝ orbit radius³	T=period; r=semi-major axis	—	Elliptical orbits; same central body	T²/r³ = constant for all planets around Sun
★	PE_grav = −GMm/r	Gravitational potential energy	Negative: bound system	Joule (J)	Any separation; reference at infinity	PE = 0 at infinity; becomes more negative closer

REMEMBER: GRAVITATION: KEY RELATIONS F = Gm₁m₂/r² (double r → F/4) g = GM/R² v_escape = √2 × v_orbital Kepler: T² ∝ r³

Chapter 6: Rotational Motion

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	τ = Iα	Rotational analogue of F = ma	τ=torque (N m); I=moment of inertia (kg m²); α=angular acceleration (rad s⁻²)	N m	Rigid body; net torque	Analogous to F=ma: I is rotational mass
★★★	τ = rF sinθ	Torque magnitude	r=moment arm (m); F=force (N); θ=angle between r and F	N m	Any force at any angle	τ=0 when F is parallel to r (θ=0° or 180°)
★★★	L = Iω	Angular momentum	I=moment of inertia; ω=angular velocity (rad s⁻¹)	kg m² s⁻¹	Rigid body rotation	L is conserved when net τ = 0
★★	L = mvr	Angular momentum of a point mass	m=mass; v=speed; r=perpendicular distance from axis	kg m² s⁻¹	Point mass; circular motion	r is perpendicular distance: not radial distance
★★★	KE_rot = ½Iω²	Rotational kinetic energy	—	Joule (J)	Rigid body rotation	Analogous to KE = ½mv²
★★	P = τω	Rotational power	τ=torque (N m); ω=angular velocity	Watt (W)	Rotating systems	Analogous to P = Fv
★★	v = rω (rolling)	Linear velocity of rolling body	r=radius of wheel; ω=angular velocity	m s⁻¹	Pure rolling (no slipping)	Slipping if v ≠ rω
★	I_parallel = I_cm + Md²	Parallel axis theorem	I_cm=moment of inertia about centre of mass; d=distance to new axis	kg m²	Any body; parallel axes only	d is distance between axes, not from surface
★	I_z = I_x + I_y	Perpendicular axis theorem	For thin lamina in x-y plane	kg m²	Thin flat laminas only: not 3D objects	Only for 2D laminas in the plane of x-y axes

REMEMBER: MOMENTS OF INERTIA: 7 STANDARD BODIES Ring (about diameter): I = ½MR² Ring (about centre): I = MR² Solid disc (about centre): I = ½MR² Solid sphere: I = 2/5 MR² Hollow sphere: I = 2/3 MR² Thin rod (about centre): I = ML²/12 Thin rod (about one end): I = ML²/3

Chapter 7: Oscillations & Waves

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	T = 2π√(L/g)	Period of simple pendulum	L=length of pendulum (m); g=9.8 or 10 m s⁻²	second (s)	Small oscillations; rigid support; no damping	T does not depend on mass or amplitude (for small angles)
★★	T = 2π√(m/k)	Period of spring-mass system	m=mass (kg); k=spring constant (N m⁻¹)	second (s)	Elastic spring; horizontal or vertical	T does not depend on amplitude (SHM only)
★★★	ω = 2πf = 2π/T	Angular frequency	f=frequency (Hz); T=period (s)	rad s⁻¹	SHM; oscillations	ω ≠ angular velocity for rotation (different contexts)
★★	x = A cos(ωt)	Displacement in SHM	A=amplitude (m); ω=angular frequency	m	SHM from equilibrium position	At t=0: x=A (maximum); oscillates between +A and −A
★★	v = ω√(A² − x²)	Velocity in SHM at position x	A=amplitude; x=displacement from equilibrium	m s⁻¹	SHM	v is maximum at x=0; v=0 at x=±A
★	a = −ω²x	Acceleration in SHM	Negative sign: directed toward equilibrium	m s⁻²	SHM only	a is proportional to x and opposite in direction
★★	E_SHM = ½kA² = ½mω²A²	Total energy in SHM	A=amplitude (constant)	Joule (J)	SHM; no damping	Total energy constant; KE and PE interchange
★★★	v = fλ	Wave speed	v=speed (m s⁻¹); f=frequency (Hz); λ=wavelength (m)	m s⁻¹	All waves	f unchanged at interface; v and λ change
★★	v_sound = √(γP/ρ) = √(γRT/M)	Speed of sound in ideal gas	γ=Cp/Cv; P=pressure; ρ=density; R=8.314; T=temp (K); M=molar mass	m s⁻¹	Ideal gas; adiabatic propagation	v independent of pressure at constant T

REMEMBER: SHM: Four Equations x = A cos(ωt) v = ω√(A² − x²) a = −ω²x E = ½kA² = ½mω²A²

Chapter 8: Fluid Mechanics

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	P = F/A	Pressure	P=pressure (Pa); F=normal force (N); A=area (m²)	Pascal (Pa)	Force distributed uniformly over area	P is scalar; F⊥ only (normal component)
★★★	P = P₀ + ρgh	Hydrostatic pressure at depth h	ρ=density (kg m⁻³); g≈10 m s⁻²; h=depth (m)	Pascal (Pa)	Fluid at rest; uniform density	P depends on height h only: not container shape
★★★	F_b = ρ_fluid × V_sub × g	Buoyancy (upward force on submerged body)	V_sub=submerged volume (m³)	Newton (N)	Body wholly or partly immersed	F_b = WEIGHT of displaced fluid: not mass
★★	Apparent depth = Real depth / n	Apparent depth of submerged object	n=refractive index of fluid	m	Object in denser medium viewed from above	Divide by n: not multiply
★★	P + ½ρv² + ρgh = constant	Bernoulli’s principle (energy per unit volume)	v=fluid speed; h=height	Pa = J m⁻³	Ideal fluid; steady (laminar) flow; incompressible	Not valid for viscous or turbulent flow
★★	β = 2α  |  γ = 3α	Areal and volumetric expansion coefficients	α=linear; β=areal; γ=volumetric (all in K⁻¹)	K⁻¹	Isotropic solids only	β ≠ α; γ ≠ 2α
★★	ρ_mix (equal volumes) = (ρ₁ + ρ₂)/2	Average density: equal volumes mixed	Arithmetic mean	kg m⁻³	Equal volumes only	Different formula for equal masses
★	ρ_mix (equal masses) = 2ρ₁ρ₂/(ρ₁ + ρ₂)	Average density: equal masses mixed	Harmonic mean	kg m⁻³	Equal masses only	≠ arithmetic mean
★	v_terminal = 2r²(ρ_s − ρ_f)g / (9η)	Terminal velocity (Stokes’ Law)	r=sphere radius; ρ_s=sphere density; ρ_f=fluid density; η=viscosity	m s⁻¹	Laminar flow; spherical body; low speed	Only for very slow viscous flow (Stokes regime)
★	Y = Fl / (AΔl)	Young’s Modulus	F=force (N); l=original length (m); A=cross-section (m²); Δl=extension (m)	Pascal (Pa)	Within elastic limit; uniform cross-section	Y = Stress/Strain; not valid beyond elastic limit

REMEMBER: EXPANSION COEFFICIENTS β (areal) = 2α (linear) γ (volumetric) = 3α (linear) Memory: Area = 2D → 2α; Volume = 3D → 3α

Chapter 9: Heat & Thermodynamics

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	K = °C + 273	Convert Celsius to Kelvin	K=Kelvin; °C=Celsius	K	Temperature conversions	Absolute zero = 0 K = −273°C (not −300°C)
★★★	°F = 32 + 1.8 × °C	Convert Celsius to Fahrenheit	°F=Fahrenheit	°F	Temperature conversions	F = C at −40°; 113°F = 45°C = 318 K
★★★	Q = mcΔT	Heat absorbed or released (sensible heat)	m=mass (kg); c=specific heat (J kg⁻¹ K⁻¹); ΔT=temperature change (K or °C)	Joule (J)	No phase change; constant specific heat	Does not apply during phase changes (use Q = mL)
★★★	Q = mL	Latent heat during phase change	L=specific latent heat (J kg⁻¹)	Joule (J)	Phase change only; constant temperature during change	Temperature does NOT change during phase change
★★	PV = nRT	Ideal gas equation of state	P=pressure (Pa); V=volume (m³); n=moles (mol); R=8.314; T=temperature (K)	—	Ideal gas; T must be in Kelvin	T in Kelvin: not Celsius
★★	PV = constant (Boyle’s Law)	Isothermal process	—	—	Constant temperature; ideal gas	10% P increase → 9.1% V decrease (not 10%)
★★	V/T = constant (Charles’ Law)	Isobaric process	—	—	Constant pressure; ideal gas	T must be in Kelvin: not Celsius
★★★	ΔU = Q − W	First Law of Thermodynamics	ΔU=change in internal energy (J); Q=heat added to system (J); W=work done by system (J)	Joule (J)	All thermodynamic processes	W>0 when system expands; Q>0 when heat enters
★★★	η_Carnot = 1 − T_c/T_h	Carnot engine efficiency	T_c=cold reservoir temperature (K); T_h=hot reservoir temperature (K)	fraction or %	Ideal (reversible) Carnot cycle; T in Kelvin	T must be in Kelvin; η < 1 always
★	E = σT⁴	Power radiated per unit area (blackbody)	σ=5.67×10⁻⁸ W m⁻² K⁻⁴; T=temperature (K)	W m⁻²	Perfect blackbody; T in Kelvin	T in Kelvin: not Celsius
★	dT/dt = −k(T − T_s)	Newton’s Law of Cooling	k=cooling constant; T_s=surroundings temperature	K s⁻¹	Small temperature excess; slow cooling	Not applicable during phase changes

REMEMBER: TEMPERATURE CONVERSIONS K = °C + 273 °F = 32 + 1.8 × °C °C = (°F − 32) / 1.8 → 113°F = 45°C = 318 K → F = C at −40°

REMEMBER: GAS LAWS Boyle’s: PV = constant (constant T) Charles’: V/T = constant (constant P) Gay-Lussac’s: P/T = constant (constant V) Ideal Gas: PV = nRT

Chapter 10: Electricity

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	I = Q/t	Electric current	I=current (A); Q=charge (C); t=time (s)	Ampere (A)	Direct current (DC)	I = charge/time: not charge × time
★★	V = W/Q	Potential difference	V=potential difference (V); W=work done (J)	Volt (V)	Always	Volt = J C⁻¹; not J × C
★★★	V = IR (Ohm’s Law)	Voltage across a resistor	R=resistance (Ω)	Volt (V)	Ohmic conductors only; constant temperature	Does NOT apply to semiconductors, diodes, LEDs
★★★	R = ρL/A	Resistance of a wire	ρ=resistivity (Ω m); L=length (m); A=cross-section area (m²)	Ohm (Ω)	Uniform wire; constant temperature	ρ depends on MATERIAL only: not L or A
★★	σ = 1/ρ	Conductivity	ρ=resistivity	S m⁻¹	Always	σρ = 1 always
★★	R_stretched = n²R	Resistance after stretching wire n times	n=stretch factor; volume conserved	Ohm (Ω)	Wire stretched uniformly (volume conserved)	n²R not nR: area decreases by factor n simultaneously
★★	R_series = R₁ + R₂ + …	Series equivalent resistance	—	Ohm (Ω)	Resistors in series (same current)	R_series > any individual R
★★★	1/R_parallel = 1/R₁ + 1/R₂ + …	Parallel equivalent resistance	—	Ohm (Ω)	Resistors in parallel (same voltage)	R_parallel < smallest individual R
★★★	P = VI = I²R = V²/R	Electrical power	P=power (W)	Watt (W)	Resistive components (Ohm’s Law applies)	IR² is NOT a valid power formula: never use it
★★★	H = I²Rt	Heat generated by current (Joule’s Law)	H=heat (J); R=resistance (Ω); t=time (s)	Joule (J)	Resistive heating; constant R	Double I → 4× heat (I is squared)
★★	Energy = Pt = kWh	Electrical energy consumed	1 kWh = 3.6×10⁶ J	J or kWh	—	P must be in kW and t in hours for kWh
★★	C = ε₀A/d	Capacitance of parallel plate capacitor	ε₀=8.85×10⁻¹²; A=plate area (m²); d=separation (m)	Farad (F)	Parallel plate; vacuum between plates	Doubling both A and d → C unchanged
★	V_terminal = E − Ir	Terminal voltage of a cell	E=EMF (V); I=current (A); r=internal resistance (Ω)	Volt (V)	Cell delivering current; load connected	V < E when current flows; V = E at open circuit

REMEMBER: POWER FORMULAS: VALID AND INVALID P = VI  ← Valid P = I²R ← Valid P = V²/R ← Valid P = IR²  ← INVALID: never use this

Chapter 11: Magnetism & Electromagnetic Induction

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★	B = μ₀I / (2πr)	Magnetic field due to infinite straight wire	μ₀=4π×10⁻⁷; I=current (A); r=distance from wire (m)	Tesla (T)	Long straight wire; point outside wire	B ∝ I; B ∝ 1/r (not 1/r²)
★★★	B = μ₀nI	Magnetic field inside a solenoid	n=turns per unit length (m⁻¹); I=current (A)	Tesla (T)	Inside long solenoid; uniform field	B does NOT depend on diameter of solenoid
★★	B = μ₀NI / (2R)	Magnetic field at centre of circular coil	N=number of turns; I=current (A); R=radius (m)	Tesla (T)	Flat circular coil; at exact centre	Double N and halve R → 4× field
★★★	F = qvB sinθ	Force on a moving charge in magnetic field	q=charge (C); v=speed (m s⁻¹); B=field (T); θ=angle between v and B	Newton (N)	Charged particle moving in magnetic field	F = 0 when v ∥ B (θ=0° or 180°)
★★	τ = NBIA sinθ	Torque on a current-carrying coil	N=turns; B=field (T); I=current (A); A=area (m²); θ=angle between coil plane and B	Newton-metre (N m)	Rectangular coil in uniform field	Maximum when coil PLANE parallel to B (θ=90°); zero when perpendicular
★★★	ε = −dΦ/dt	Faraday’s Law: induced EMF	Φ=magnetic flux (Wb); t=time (s)	Volt (V)	Changing magnetic flux through any closed loop	Negative sign from Lenz’s Law: opposes change
★★	Φ = BA cosθ	Magnetic flux	B=field (T); A=area (m²); θ=angle between B and normal to area	Weber (Wb)	Uniform field; flat surface	Φ is maximum when B ⊥ surface (θ=0°)
★★★	V₁/V₂ = N₁/N₂ = I₂/I₁	Transformer ratio	V=voltage (V); N=turns; I=current (A)	—	Ideal transformer; AC only	Transformer does NOT work on DC
★	X_L = ωL = 2πfL	Inductive reactance	ω=angular frequency; L=inductance (H)	Ohm (Ω)	AC circuits with inductance	X_L increases with frequency
★	X_C = 1/(ωC) = 1/(2πfC)	Capacitive reactance	C=capacitance (F)	Ohm (Ω)	AC circuits with capacitance	X_C decreases with frequency
★	Z = √(R² + (X_L − X_C)²)	Impedance of series LCR circuit	R=resistance (Ω)	Ohm (Ω)	Series LCR; AC circuit	At resonance X_L = X_C → Z = R (minimum)
★	ω₀ = 1/√(LC)	Resonance frequency of LCR circuit	L=inductance (H); C=capacitance (F)	rad s⁻¹	LCR series circuit	At resonance: maximum current; minimum impedance
★	V_rms = V₀/√2 ≈ 0.707 V₀	RMS voltage of AC supply	V₀=peak voltage; √2 ≈ 1.414	Volt (V)	Sinusoidal AC supply	India 220 V is RMS; peak = 220√2 ≈ 311 V

REMEMBER: FLEMING’S RULES Left Hand = Motor (force on current in field) Forefinger → B (magnetic field) Middle finger → I (current) Thumb → Force (motion)   Right Hand = Generator (induced current) Forefinger → B (magnetic field) Thumb → Motion of conductor Middle finger → Induced current

Chapter 12: Optics

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	1/v + 1/u = 1/f (Mirror Formula)	Image distance; focal length; object distance	v=image distance; u=object distance; f=focal length: all with sign (Cartesian)	m (all three)	Spherical mirrors; Cartesian sign convention	u always negative; f negative for concave, positive for convex
★★	R = 2f	Radius of curvature relationship	R=radius of curvature; f=focal length	m	Spherical mirrors (concave and convex)	R = 2f: not R = f
★★	m = −v/u (Mirror Magnification)	Linear magnification	m=magnification (dimensionless); v=image distance; u=object distance	Dimensionless	Spherical mirrors	Negative m = real image (inverted); positive m = virtual (erect)
★★★	1/v − 1/u = 1/f (Lens Formula)	Image formed by thin lens	v=image distance; u=object distance; f=focal length	m (all three)	Thin lenses; Cartesian sign convention	u always negative; note MINUS between 1/v and 1/u (not +)
★★	m = v/u (Lens Magnification)	Linear magnification for lens	—	Dimensionless	Thin lenses	Positive m = virtual (erect); negative m = real (inverted)
★★★	P = 1/f (f in metres)	Lens power	P=power (Dioptre); f=focal length (metres only)	Dioptre (D = m⁻¹)	Thin lens; f must be in metres	f in cm gives wrong answer; convex=positive; concave=negative
★★★	P_total = P₁ + P₂ + …	Combined power of lenses in contact	P₁, P₂ = individual powers	Dioptre (D)	Thin lenses in contact; same medium	Add powers: not focal lengths
★	1/f = (n−1)(1/R₁ − 1/R₂) (Lens-Maker’s)	Focal length from lens geometry	n=refractive index; R₁,R₂=radii of curvature (with sign)	m	Thin lens; known geometry and material	Sign convention for R₁, R₂ must be applied carefully
★★★	n = c/v	Refractive index	n=refractive index; c=speed in vacuum; v=speed in medium	Dimensionless	Any optical medium	n > 1 always; n=1 for vacuum; v = c/n
★★★	n₁sinθ₁ = n₂sinθ₂ (Snell’s Law)	Refracted ray direction	θ₁, θ₂ = angles from normal; n₁, n₂ = refractive indices	—	Any boundary; any angle except parallel incidence	Frequency unchanged at boundary; speed and λ change
★★	Apparent depth = Real depth / n	Apparent position of submerged object	n=refractive index of medium containing the object	m	Object in denser medium viewed from less dense medium	Divide by n: not multiply; object appears closer
★★	sinθ_c = 1/n (Critical Angle)	Critical angle for TIR	θ_c=critical angle; n=refractive index of denser medium	rad or °	Light going from denser to rarer medium	TIR occurs when angle > θ_c; n must be relative to rarer medium
★★★	M = f_obj / f_eye (Telescope Magnification)	Magnifying power of refracting telescope	f_obj=focal length of objective; f_eye=focal length of eyepiece	Dimensionless	Normal adjustment (final image at infinity)	f_obj > f_eye for telescope; f_obj < f_eye for microscope
★★★	P = −1/far-point (metres) (Myopia)	Corrective lens power for myopia	Far-point distance in metres	Dioptre (D)	Myopia (short-sightedness); far-point given	Negative power → concave lens for myopia

REMEMBER: CONCAVE MIRROR: 5 POSITIONS Beyond C: Real, Inverted, Diminished At C: Real, Inverted, Same size Between C,F: Real, Inverted, Magnified At F: Real, Inverted, At infinity Between F,P: Virtual, Erect, Magnified  ← Dentist’s mirror At infinity: Real, Inverted, At F

REMEMBER: CONVEX LENS: 5 POSITIONS Beyond 2f: Real, Inverted, Diminished At 2f: Real, Inverted, Same size Between f,2f: Real, Inverted, Magnified At f: Real, Inverted, At infinity Between f,O: Virtual, Erect, Magnified  ← Magnifying glass At infinity: Real, Inverted, At f

REMEMBER: CONVEX MIRROR & CONCAVE LENS: ALWAYS ONE ANSWER Convex mirror: ALWAYS Virtual, Erect, Diminished Concave lens: ALWAYS Virtual, Erect, Diminished

Chapter 13: Modern Physics

Priority	Formula	What It Gives	Variables	SI Unit	Applicable When	NDA Trap
★★★	E = hf = hc/λ	Energy of one photon	h=6.626×10⁻³⁴ J s; f=frequency (Hz); λ=wavelength (m)	Joule (J) or eV	Any electromagnetic photon	Higher f (shorter λ) → higher photon energy
★★★	E = mc²	Mass-energy equivalence	m=mass (kg); c=3×10⁸ m s⁻¹	Joule (J)	Nuclear reactions; any mass-energy conversion	Proposed by Einstein: not Rutherford, Bohr, or Heisenberg
★★	KE = hf − φ (Einstein’s Photoelectric Equation)	Kinetic energy of emitted photoelectron	φ=work function of metal; f=photon frequency	Joule (J) or eV	Photon frequency > threshold frequency	KE = 0 at threshold; intensity affects number not energy of electrons
★★★	λ_min = hc/(eV)	Minimum wavelength of X-rays	e=1.6×10⁻¹⁹ C; V=accelerating voltage	m (typically nm or Å)	X-ray tube; given accelerating voltage V	Double V → halve λ_min (inversely proportional to V)
★★	E_n = −13.6/n² eV (Bohr Model)	Energy of electron in nth orbit of hydrogen	n=principal quantum number (1,2,3,…)	eV	Hydrogen atom only; Bohr model	E₁ = −13.6 eV (ground state); ionisation energy = +13.6 eV
★	λ_deBroglie = h/(mv) = h/p	de Broglie wavelength of a particle	m=mass; v=speed; p=momentum	m	Any moving particle	Significant only for very small particles (electrons, protons)
★★★	N(t) = N₀(½)^(t/t½)	Radioactive decay: number remaining	N₀=initial nuclei; t=elapsed time; t½=half-life	dimensionless (count)	Radioactive decay; constant half-life	After n half-lives: N = N₀/2ⁿ
★★	N_neutrons = A − Z	Neutron count in a nucleus	A=mass number; Z=atomic number (protons)	dimensionless	All nuclei	Electrons not in nucleus: only protons and neutrons
★	BE = Δm × c²	Binding energy of nucleus	Δm=mass defect (kg)	Joule or MeV	Nuclear binding energy calculation	1 u corresponds to 931.5 MeV binding energy
★	[h] = [M L² T⁻¹] = [Angular momentum]	Dimensions of Planck’s constant	Same as angular momentum L = Iω = mvr	—	Dimensional analysis problems	Not linear momentum [M L T⁻¹]; not torque [M L² T⁻²]

REMEMBER: NUCLEAR PHYSICS: KEY FORMULAS E = mc² (Einstein: not Rutherford or Bohr) λ_min = hc/(eV)  ← double V, halve λ_min E_n = −13.6/n² eV (Bohr: ionisation = 13.6 eV) N(t) = N₀(½)^(t/t½) Neutrons = A − Z Nucleus = PROTONS + NEUTRONS (no electrons)

Common NDA Formula Confusions

32 traps drawn from NDA PYQ analysis 2010–2026. Every entry has been tested in at least one NDA paper.

Wrong Version (avoid)	Correct Version	Chapter
R = f (spherical mirror focal length = R)	R = 2f (radius is twice focal length)	12
P = IR² (power formula)	P = VI = I²R = V²/R  |  IR² is INVALID	10
Stretch wire n times → R = nR	R_new = n²R (volume conserved → area decreases by n)	10
10% pressure increase → 10% volume decrease	V_new = V/1.1 → 9.1% decrease (multiplicative, not additive)	8, 9
Convex lens has negative power	Convex lens (converging) = POSITIVE power; Concave = NEGATIVE	12
Microscope: f_objective > f_eyepiece	Microscope: f_obj < f_eye; Telescope: f_obj > f_eye (opposite)	12
Twinkling of stars = scattering	Twinkling = ATMOSPHERIC REFRACTION (not scattering)	12
Violet deviates least in a prism	VIOLET deviates MOST (highest n); Red deviates least	12
Resistivity depends on length and area	ρ depends on MATERIAL ONLY: not on L or A	10
g is the same at all heights and depths	g decreases both with height (2h/R) and depth (d/R)	5
Weight = Mass	W = mg (Weight in N; Mass in kg: completely different quantities)	3
Parallel resistance = average of individual values	1/R_p = 1/R₁ + 1/R₂ → R_p < smallest individual R	10
Lens powers multiply when combined	P_total = P₁ + P₂ (add powers: do not multiply)	12
Transformer changes DC voltage	Transformer works on AC ONLY: not DC	11
Solenoid B depends on diameter	B = μ₀nI: diameter does NOT appear: irrelevant	11
Light slows down entering air from water	Light SPEEDS UP going from denser (water) to rarer (air)	12
Apparent depth = n × Real depth	Apparent depth = Real depth / n (DIVIDE by n)	12
Cathode rays travel anode → cathode	Cathode rays travel CATHODE → ANODE	13
Electrons deflected only by electric field	Electrons deflected by BOTH electric AND magnetic fields	13
Rutherford’s experiment discovered the electron	Rutherford discovered the ATOMIC NUCLEUS; Thomson discovered electron	13
Ionisation energy of hydrogen = 13.6 MeV	13.6 eV (NOT MeV; 1 MeV = 10⁶ eV: a million times larger)	13
Frequency changes during refraction	Frequency is UNCHANGED at any interface; speed and wavelength change	12
Torque maximum when coil ⊥ to magnetic field	Max torque when coil PLANE PARALLEL to field; zero when perpendicular	11
Fission in the Sun; Fusion in nuclear reactors	SUN = nuclear FUSION (H → He); REACTOR = controlled FISSION	13
X-rays can be used for radar systems	X-rays NOT used for radar; radar uses radio waves and microwaves	13
Plane mirror gives a real image	Plane mirror ALWAYS gives a VIRTUAL image: cannot be projected	12
β = α and γ = 2α (expansion coefficients)	β = 2α and γ = 3α (two-dimensional and three-dimensional)	8, 9
EMF = Terminal voltage under load	V_terminal = E − Ir (terminal voltage always less than EMF when current flows)	10
Escape velocity = Orbital velocity	v_escape = √2 × v_orbital (escape is √2 times larger)	5
V_rms = V₀ (RMS = peak voltage)	V_rms = V₀/√2 ≈ 0.707 × V₀ (India 220V is RMS; peak ≈ 311V)	11
Apparent depth = n × real depth	Apparent depth = real depth / n (submerged object appears closer)	12
Half coil coverage → only half image formed	Half lens coverage → FULL image forms, but with reduced BRIGHTNESS only	12

Formula Index: Alphabetical

Locate any formula by name. Numbers refer to chapters.

Formula Name	Formula	Chapter
Acceleration (linear)	a = Δv/Δt  |  a = F/m	2, 3
Acceleration (centripetal)	a_c = v²/r = rω²	2
Angular frequency	ω = 2πf = 2π/T	7
Angular momentum (particle)	L = mvr	6
Angular momentum (rigid body)	L = Iω	6
Angular velocity	ω = Δθ/Δt	6
Apparent depth	Apparent depth = Real depth / n	8, 12
Banking angle	tanθ = v²/(rg)	3
Bernoulli’s Principle	P + ½ρv² + ρgh = constant	8
Binding energy	BE = Δm × c²	13
Bohr energy levels	E_n = −13.6/n² eV	13
Boyle’s Law	PV = constant (constant T)	9
Buoyancy	F_b = ρ_fluid × V_sub × g	8
Capacitance (parallel plate)	C = ε₀A/d	10
Carnot efficiency	η = 1 − T_c/T_h	9
Centripetal acceleration	a_c = v²/r = rω²	2
Charge	Q = It	10
Charles’ Law	V/T = constant (constant P)	9
Combined lenses	P_total = P₁ + P₂	12
Conductivity	σ = 1/ρ	10
Critical angle	sinθ_c = 1/n	12
Cutoff wavelength (X-ray)	λ_min = hc/(eV)	13
de Broglie wavelength	λ = h/(mv)	13
Decay (radioactive)	N(t) = N₀(½)^(t/t½)	13
Electric field	E = F/q = V/d	10
Electrical energy	E = Pt  |  1 kWh = 3.6×10⁶ J	10
Electrical power	P = VI = I²R = V²/R	10
EMF vs terminal voltage	V = E − Ir	10
Energy (kinetic)	KE = ½mv²	4
Energy (photon)	E = hf = hc/λ	13
Energy (potential)	PE = mgh  |  PE = ½kx²	4
Escape velocity	v_e = √(2gR) = √2 × v_orbital	5
Expansion coefficients	β = 2α  |  γ = 3α	8, 9
Faraday’s Law	ε = −dΦ/dt	11
First Law (Thermodynamics)	ΔU = Q − W	9
Fleming’s Left-Hand Rule (Motor)	FBI: Forefinger=B, Middle=I, Thumb=Force	11
Fleming’s Right-Hand Rule (Generator)	FMI: Forefinger=B, Thumb=Motion, Middle=Current	11
Force (gravitational)	F = Gm₁m₂/r²	5
Force (magnetic on charge)	F = qvB sinθ	11
Frequency	f = 1/T	7
Friction (kinetic)	f_k = μ_k N	3
g at depth	g_d = g(1 − d/R)	5
g at height	g_h ≈ g(1 − 2h/R)	5
g at surface	g = GM/R²	5
Half-life (radioactive)	N = N₀(½)^(t/t½)	13
Heat (latent)	Q = mL	9
Heat (sensible)	Q = mcΔT	9
Hooke’s Law	F = kx	7
Ideal gas equation	PV = nRT	9
Impedance (LCR)	Z = √(R² + (X_L−X_C)²)	11
Impulse	J = FΔt = Δp	3
Inductance (unit)	Henry (H)  |  e = −L(dI/dt)	11
Inductive reactance	X_L = ωL = 2πfL	11
Ionisation energy (hydrogen)	13.6 eV (ground state n=1)	13
Joule’s Law (heating)	H = I²Rt	10
Kepler’s Third Law	T² ∝ r³	5
Kinetic energy	KE = ½mv²	4
Latent heat	Q = mL	9
Lens formula	1/v − 1/u = 1/f	12
Lens power	P = 1/f (f in metres)	12
Lens-Maker’s equation	1/f = (n−1)(1/R₁−1/R₂)	12
Magnification (lens)	m = v/u	12
Magnification (mirror)	m = −v/u	12
Magnification (telescope)	M = f_obj/f_eye	12
Mass-energy equivalence	E = mc²	13
Mirror formula	1/v + 1/u = 1/f	12
Momentum	p = mv	3
Myopia correction	P = −1/far-point (m)	12
Newton’s Law of Cooling	dT/dt = −k(T−T_s)	9
Neutron count	N_neutrons = A − Z	13
Ohm’s Law	V = IR	10
Orbital velocity	v_o = √(gR) = √(GM/R)	5
Parallel resistance	1/R_p = 1/R₁ + 1/R₂ + …	10
Pendulum period	T = 2π√(L/g)	7
Photoelectric equation	KE = hf − φ	13
Photon energy	E = hf	13
Power (mechanical)	P = W/t = Fv cosθ	4
Power (electrical)	P = VI = I²R = V²/R	10
Power of lens	P = 1/f(m)	12
Pressure (hydrostatic)	P = P₀ + ρgh	8
Pressure (definition)	P = F/A	8
Projectile (range)	R = u²sin2θ/g	2
Radius of curvature	R = 2f (spherical mirrors only)	12
Radioactive decay	N(t) = N₀(½)^(t/t½)	13
Reactance (capacitive)	X_C = 1/(ωC)	11
Reactance (inductive)	X_L = ωL	11
Refractive index	n = c/v	12
Resistance	R = V/I  |  R = ρL/A	10
Resistivity	ρ = RA/L (material property only)	10
Rotational KE	KE_rot = ½Iω²	6
Series resistance	R_s = R₁ + R₂ + …	10
SHM displacement	x = A cos(ωt)	7
SHM energy	E = ½kA²	7
SHM velocity	v = ω√(A²−x²)	7
Snell’s Law	n₁sinθ₁ = n₂sinθ₂	12
Solenoid field	B = μ₀nI	11
Speed (wave)	v = fλ	7
Speed of sound	v = √(γRT/M)	7
Spring period	T = 2π√(m/k)	7
Stefan’s Law	E = σT⁴	9
Surface gravity	g = GM/R²	5
Temperature conversions	K = °C + 273  |  °F = 32 + 1.8°C	9
Terminal velocity (Stokes)	v_t = 2r²(ρ_s−ρ_f)g/(9η)	8
Terminal voltage (cell)	V = E − Ir	10
Torque (rotational)	τ = Iα  |  τ = rF sinθ	6
Torque (on coil in field)	τ = NBIA sinθ	11
Transformer ratio	V₁/V₂ = N₁/N₂ = I₂/I₁	11
Velocity (linear)	v = Δs/Δt	2
Voltage (potential difference)	V = W/Q	10
Wave speed	v = fλ	7
Weight	W = mg	3
Work	W = Fs cosθ	4
Work-Energy theorem	W_net = ΔKE	4
X-ray cutoff wavelength	λ_min = hc/(eV)	13
Young’s Modulus	Y = Fl/(AΔl) = Stress/Strain	8

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