The 32 formulas NDA Physics actually tests

Dimensions of force, energy, pressure, power

[F] = M L T⁻² [E] = M L² T⁻² [P] = M L⁻¹ T⁻² [W/t] = M L² T⁻³

M = mass

L = length

T = time

Note:Recognise these by structure: anything with L² is energy/torque; anything with L⁻¹ is pressure or related to it.

CGS ↔ SI conversions

1 dyne = 10⁻⁵ N 1 erg = 10⁻⁷ J 1 poise = 0.1 Pa·s

dyne = CGS force unit (g·cm·s⁻²)

erg = CGS energy unit

poise = CGS dynamic viscosity

Astronomical distances

1 light year ≈ 9.46 × 10¹⁵ m 1 parsec ≈ 3.26 light years ≈ 2.06 × 10⁵ AU

AU = astronomical unit ≈ 1.5 × 10¹¹ m (Earth–Sun distance)

Equations of motion (constant acceleration)

v = u + at s = ut + ½at² v² = u² + 2as

u = initial velocity

v = final velocity

a = acceleration (negative for deceleration)

s = displacement (signed)

t = time

Note:These hold only for CONSTANT a. If a changes (e.g. two-phase motion), apply them piecewise and add. Sign convention: pick a +direction and stick to it.

Circular motion (centripetal acceleration)

a_c = v²/R = ω²R where ω = 2π/T

R = radius

v = tangential speed

ω = angular velocity

T = period

Note:For UNIFORM circular motion |v| is constant, but v itself changes direction so there's still acceleration (always toward centre).

Newton's second law

F = ma = dp/dt

F = net force

m = mass

a = acceleration

p = momentum

Momentum and impulse

p = mv J = F·Δt = Δp

p = momentum (vector)

J = impulse

Δp = change in momentum

Note:Impulse–momentum theorem is the lever for force-time graph problems: ∫F dt = area under F-t curve = Δp.

Conservation of momentum (isolated system)

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

u = before-collision velocity

v = after-collision velocity

Note:Always conserved if no external force. Energy may or may not be conserved (elastic vs inelastic). For recoil: 0 = m_gun·v_gun + m_bullet·v_bullet ⟹ v_gun is opposite-sign and much smaller (mass ratio).

Work done by a force

W = F·d·cosθ

F = magnitude of force

d = displacement

θ = angle between F and d

Note:Force perpendicular to displacement does ZERO work (cos 90° = 0). Classic trap: gravity on horizontal motion, magnetic force on charged particle.

Kinetic and potential energy

KE = ½mv² PE = mgh Total ME = KE + PE

m = mass

v = speed

h = height above reference

Note:In free-fall (no air resistance), ME is conserved: ½mv₀² + mgh₀ = ½mv² + mgh. Use this to dodge integrating F over distance.

Power

P = W/t = F·v

W = work done

t = time

F·v = instantaneous power if v is the speed at which F acts

Note:Constant-power machine on smooth surface: P=Fv ⟹ Fv=const. Combined with F=ma=m(dv/dt) gives v∝√t (not v∝t).

Newton's law of gravitation

F = Gm₁m₂/r²

G = 6.67 × 10⁻¹¹ N·m²·kg⁻²

m₁, m₂ = masses

r = distance between centres

Surface gravity and escape velocity

g = GM/R² v_esc = √(2gR) = √(2GM/R)

M = planet mass

R = planet radius

v_esc = escape velocity from surface

Note:Planet-scaled ratio trap: if R halved and density 4× ⟹ M = (4ρ)(½·(4/3)πR³) = ½M_earth. New v_esc = √(2G·½M / ½R) = √(2GM/R) = same as Earth. Always compute step-by-step.

Kepler's third law (orbital period)

T² ∝ R³ ⟹ T₁/T₂ = (R₁/R₂)^(3/2)

T = orbital period

R = orbital radius

Note:Comes from balancing gravity = centripetal: GMm/R² = mv²/R = m·(2πR/T)²/R. Common shape: T₁/T₂ = (R/4R)^(3/2) = 1/8.

Hydrostatic pressure

P = hρg (gauge) P_abs = P_atm + hρg

h = depth below free surface

ρ = fluid density

g = 9.8 m/s²

Archimedes' principle (buoyant force)

F_b = V_submerged · ρ_fluid · g

V_submerged = volume of object IN the fluid (not total volume)

ρ_fluid = density of fluid (not object)

Note:Floating ⟹ F_b = mg ⟹ V_sub/V_total = ρ_object/ρ_fluid. Wholly submerged ⟹ F_b uses V_total.

Density of a mixture

Equal volumes: ρ_avg = (ρ₁+ρ₂)/2 Equal masses: ρ_avg = 2ρ₁ρ₂/(ρ₁+ρ₂)

ρ₁, ρ₂ = densities of components

Note:Equal-mass formula is the harmonic mean — always SMALLER than the arithmetic mean. The 'equal-mass < equal-volume' inequality is the recurring buoyancy ratio trap.

Sensible heat (no phase change)

Q = mcΔT

m = mass

c = specific heat capacity

ΔT = temperature change

Note:Specific heat is per-unit-mass-per-unit-ΔT. Water: c = 4186 J/(kg·K) = 1 cal/(g·°C). Ice: c ≈ 2100 J/(kg·K) — half of water.

Latent heat (phase change at constant T)

Q = mL

L = specific latent heat (kJ/kg)

Note:Water: L_fusion ≈ 334 kJ/kg, L_vaporisation ≈ 2260 kJ/kg. Phase change happens AT temperature (0 °C, 100 °C); no T change while changing phase. Forgetting a latent term in a calorimetry mix is the #1 trap.

Temperature scale conversions

T_C = (T_F − 32) × 5/9 T_K = T_C + 273.15

C = Celsius

F = Fahrenheit

K = Kelvin

Note:F = C trap: only at −40° (the scales cross). K = F trap: only at 574.25 K. Always set up the equation, don't guess.

Ideal gas law

PV = nRT

P = pressure (Pa)

V = volume (m³)

n = moles

R = 8.314 J/(mol·K)

T = absolute temperature (K)

Note:Process variants: isothermal (PV=const), isobaric (V/T=const), isochoric (P/T=const), adiabatic (PVⁿ=const, n=γ).

Simple pendulum (small angle)

T = 2π√(L/g)

T = period

L = string length

g = gravity

Note:MASS doesn't appear. Doubling mass changes nothing. Doubling L multiplies T by √2 ≈ 1.41. Moving to a planet with g/4 doubles T. This is the recurring ratio trap.

Wave equation

v = f·λ

v = wave speed

f = frequency (Hz)

λ = wavelength

Note:Speed of sound in air ≈ 343 m/s at 20 °C. Speed of light c = 3 × 10⁸ m/s. The Doppler-style change-of-medium trap: frequency stays the same, λ changes.

Sound wave property mapping

Amplitude → loudness Frequency → pitch Waveform → timbre/quality

Each perception attribute maps to one physical property — don't swap them

Note:Loudness is measured in decibels (dB), NOT in Hz (that's pitch). Amplitude is in pressure (Pa) or displacement (m).

Echo distance

d = v·t/2

d = distance to reflecting surface

v = speed of sound

t = round-trip time

Note:Divide by 2 — the round trip is 2d. Same formula powers SONAR (in water, v ≈ 1500 m/s) and the bat-echolocation question.

Mirror / lens formula (Cartesian sign convention)

1/v − 1/u = 1/f (lens) 1/v + 1/u = 1/f (mirror)

u = object distance (NEGATIVE for real object)

v = image distance (sign tells real/virtual)

f = focal length (negative for concave lens / convex mirror)

Note:Sign convention is the #1 trap. NDA uses Cartesian (distances measured from pole, +x to the right). Object always at NEGATIVE u in this convention. Magnification: m = v/u (lens) or m = −v/u (mirror).

Lens power

P = 1/f (f in metres, P in dioptres)

P > 0 for convex (converging) lens

P < 0 for concave (diverging) lens

Note:Combine thin lenses in contact: P_total = P₁ + P₂. Convert cm to m first.

Snell's law and refractive index

μ = sin i / sin r n = c/v

i = angle of incidence (from normal)

r = angle of refraction

μ, n = refractive index

c = speed of light in vacuum, v = speed in medium

Note:Higher μ = slower light in medium. Vacuum: μ = 1. Water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.4.

Total internal reflection (critical angle)

sin θ_c = 1/μ

θ_c = critical angle for the denser medium

Note:TIR happens only going DENSE → RARE (e.g. water → air, glass → air). For glass (μ=1.5), θ_c ≈ 42°.

Ohm's law

V = IR

V = potential difference (volts)

I = current (amperes)

R = resistance (ohms)

Resistor combinations

Series: R_total = R₁ + R₂ + ... Parallel: 1/R_total = 1/R₁ + 1/R₂ + ...

Series: same I through all, V splits

Parallel: same V across all, I splits

Note:For TWO parallel resistors: R = R₁R₂/(R₁+R₂). For N identical R in parallel: R/N. For N identical R in series: NR. Heat in parallel vs series with same V: P_parallel/P_series = (R_series/R_parallel) — usually 4× for two equal R.

Electrical power

P = VI = I²R = V²/R

Pick the form that matches the GIVEN: V&I, I&R, or V&R

Note:1 unit (kWh) = 1000 W × 1 h = 3.6 × 10⁶ J. Cost = P(kW) × t(h) × rate(₹/unit).

Resistivity

R = ρL/A

ρ = resistivity (material property, Ω·m)

L = length

A = cross-sectional area

Note:Stretching a wire keeps volume const: if L doubles, A halves, R quadruples (∝L²). Bending or coiling doesn't change R.

Force on a charge in a magnetic field

F = qvB sin θ (direction: F ⊥ both v and B)

q = charge

v = velocity

B = magnetic field

θ = angle between v and B

Note:Positive and negative charges deflect in OPPOSITE directions. If v ∥ B (θ=0), force is zero. Right-hand rule: thumb=v, fingers=B, palm=F for positive charge.

Planck–Einstein relation

E = hf = hc/λ

E = photon energy

h = 6.63 × 10⁻³⁴ J·s (Planck's constant)

f = frequency, λ = wavelength

c = 3 × 10⁸ m/s

Note:Higher frequency = more energetic photon. UV more energetic than visible more than IR. Dimensions of h are the same as angular momentum: M L² T⁻¹.