Comprehensive NEET Physics reference covering Units 1-11: Physics and Measurement, Kinematics, Laws of Motion, Work Energy Power, Rotational Motion, Gravitation, Properties of Matter, Thermodynamics, Kinetic Theory, Oscillations and Waves, and Electrostatics. Essential formulas, concepts, and problem-solving techniques for NEET preparation.
SI units, dimensional analysis, and error calculations
fundamentalsSI Base Units: Length (m), Mass (kg), Time (s), Current (A), Temperature (K), Amount (mol), Luminous Intensity (cd)
Least Count: Smallest measurement possible by an instrument
# Dimensional Formulas
Length [L], Mass [M], Time [T]
Force: [MLT⁻²]
Energy: [ML²T⁻²]
Power: [ML²T⁻³]
Pressure: [ML⁻¹T⁻²]
Momentum: [MLT⁻¹]
# Significant Figures Rules
- All non-zero digits are significant
- Zeros between non-zeros are significant
- Trailing zeros after decimal are significant
- Leading zeros are NOT significant
# Error Analysis
Absolute Error = |Measured - True Value|
Relative Error = Absolute Error / True Value
Percentage Error = Relative Error × 100%
# Dimensional Analysis Applications
- Check correctness of equations
- Derive relationships between quantities
- Convert units between systemsEquations of motion, velocity-time and position-time graphs
kinematicsAverage Velocity: Total displacement / Total time
Instantaneous Velocity: Velocity at a specific instant (slope of position-time graph)
Acceleration: Rate of change of velocity
# Equations of Motion (Uniform Acceleration)
v = u + at
s = ut + (1/2)at²
v² = u² + 2as
sₙₜₕ = u + a(n - 1/2)
Where:
u = initial velocity
v = final velocity
a = acceleration
t = time
s = displacement
sₙₜₕ = displacement in nth second
# Special Cases
Free Fall: a = g = 9.8 m/s² (downward)
Vertical Throw Up: a = -g
# Relative Motion
v_AB = v_A - v_B (velocity of A w.r.t B)Vector operations, resolution, and addition
kinematicsScalar: Magnitude only (mass, time, temperature)
Vector: Magnitude and direction (displacement, velocity, force)
# Vector Addition
Triangle Law: R² = A² + B² + 2AB cos θ
Parallelogram Law: Same as above
If θ = 0°: R = A + B (parallel, same direction)
If θ = 180°: R = |A - B| (antiparallel)
If θ = 90°: R = √(A² + B²) (perpendicular)
# Vector Resolution
Aₓ = A cos θ (x-component)
Aᵧ = A sin θ (y-component)
# Dot Product (Scalar Product)
A · B = AB cos θ = AₓBₓ + AᵧBᵧ + A_zB_z
Work = F · s
# Cross Product (Vector Product)
|A × B| = AB sin θ
Direction: Right-hand rule
Torque = r × FMotion in two dimensions under gravity
kinematicsProjectile motion is a combination of horizontal (uniform) and vertical (uniformly accelerated) motion.
Key Point: Horizontal and vertical motions are independent
# Initial Velocity Components
uₓ = u cos θ (horizontal)
uᵧ = u sin θ (vertical)
# Time of Flight
T = (2u sin θ)/g
# Maximum Height
H = (u² sin² θ)/(2g)
# Range (Horizontal Distance)
R = (u² sin 2θ)/g
Maximum Range: θ = 45°, R_max = u²/g
# Velocity at any time t
vₓ = u cos θ (constant)
vᵧ = u sin θ - gt
# Position at time t
x = (u cos θ)t
y = (u sin θ)t - (1/2)gt²
# Equation of Trajectory
y = x tan θ - (gx²)/(2u² cos² θ)Uniform circular motion concepts and formulas
kinematics# Angular Quantities
Angular Displacement: θ (radians)
Angular Velocity: ω = dθ/dt = 2πf = 2π/T
Angular Acceleration: α = dω/dt
# Linear-Angular Relations
v = rω (linear velocity)
aₜ = rα (tangential acceleration)
aᶜ = v²/r = rω² (centripetal acceleration)
# Centripetal Force
Fᶜ = mv²/r = mrω²
Direction: Towards center
# Time Period and Frequency
T = 2π/ω (time period)
f = 1/T = ω/(2π) (frequency)
# Important Points
- Speed is constant but velocity changes
- Acceleration is always towards center
- Net force provides centripetal forceThree laws of motion and their applications
dynamicsFirst Law (Inertia): Object at rest stays at rest, object in motion stays in motion unless acted upon by external force
Second Law: F = ma or F = dp/dt
Third Law: Action = -Reaction
# Newton's Second Law
F = ma (when mass is constant)
F = dp/dt (general form)
Impulse: J = FΔt = Δp = m(v - u)
# Momentum
p = mv
Conservation: p_initial = p_final (isolated system)
# Applications
Free Body Diagram: Essential for problem solving
Connected Bodies: Same acceleration
Pulley Systems: Tension analysis
# Equilibrium Conditions
ΣF = 0 (no linear acceleration)
Στ = 0 (no rotational acceleration)
# Common Forces
Weight: W = mg
Normal Force: N (perpendicular to surface)
Tension: T (in strings/ropes)
Friction: f (opposes motion)Static, kinetic, and rolling friction
dynamicsStatic Friction: Prevents motion, f_s ≤ μ_s N
Kinetic Friction: During motion, f_k = μ_k N
Key: μ_s > μ_k (static coefficient > kinetic coefficient)
# Friction Formulas
Static: f_s ≤ μ_s N (maximum = μ_s N)
Kinetic: f_k = μ_k N
Rolling: f_r = μ_r N (μ_r << μ_k)
Where:
μ = coefficient of friction
N = Normal force
# Laws of Friction
1. Independent of contact area
2. Proportional to normal force
3. Direction: Opposite to motion/tendency
# Angle of Friction
tan λ = μ
λ = angle of repose (for incline)
# Motion on Incline
Parallel component: mg sin θ
Perpendicular: mg cos θ
Motion starts when: tan θ > μ_sCentripetal force applications - vehicles and banking
dynamics# Vehicle on Level Circular Road
Centripetal force = Friction force
mv²/r = μN = μmg
v_max = √(μrg)
# Vehicle on Banked Road (No Friction)
tan θ = v²/(rg)
v = √(rg tan θ)
# Banked Road with Friction
For maximum speed:
tan θ = (v² - μrg)/(rg + μv²)
# Vertical Circular Motion
At highest point: T + mg = mv²/r
Minimum speed at top: v = √(rg)
At lowest point: T - mg = mv²/r
# Conical Pendulum
tan θ = v²/(rg)
T = 2π√(L cos θ/g)
Critical: Tension must be > 0 alwaysWork-energy theorem and power calculations
energyWork: W = F·s = Fs cos θ (scalar quantity)
Energy: Capacity to do work (scalar, SI unit: Joule)
Power: Rate of doing work (P = W/t)
# Work Formulas
Constant Force: W = Fs cos θ
Variable Force: W = ∫F·ds
By gravity: W = mgh (downward)
By spring: W = (1/2)kx²
# Kinetic Energy
KE = (1/2)mv²
Work-Energy Theorem: W_net = ΔKE
# Potential Energy
Gravitational: PE = mgh
Elastic (spring): PE = (1/2)kx²
# Conservation of Mechanical Energy
KE + PE = constant (conservative forces)
E_initial = E_final
# Power
P = W/t (average)
P = F·v = Fv cos θ (instantaneous)
# Conservative vs Non-conservative
Conservative: Path independent (gravity, spring)
Non-conservative: Path dependent (friction)Elastic and inelastic collisions in 1D and 2D
energyElastic: Both momentum and KE conserved
Inelastic: Only momentum conserved, KE lost
Perfectly Inelastic: Bodies stick together after collision
# Conservation Laws
Momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (always)
KE: (1/2)m₁u₁² + (1/2)m₂u₂² = (1/2)m₁v₁² + (1/2)m₂v₂² (elastic only)
# Elastic Collision (1D)
v₁ = [(m₁-m₂)u₁ + 2m₂u₂]/(m₁+m₂)
v₂ = [(m₂-m₁)u₂ + 2m₁u₁]/(m₁+m₂)
Special Cases:
- Equal masses: velocities exchange
- m₁ >> m₂, m₂ at rest: v₂ ≈ 2u₁
- m₂ >> m₁, m₂ at rest: v₁ ≈ -u₁ (bounces back)
# Coefficient of Restitution
e = (v₂ - v₁)/(u₁ - u₂)
e = 1: Elastic
e = 0: Perfectly inelastic
0 < e < 1: Inelastic
# Perfectly Inelastic
v_common = (m₁u₁ + m₂u₂)/(m₁ + m₂)
KE lost = (1/2)[m₁m₂/(m₁+m₂)](u₁-u₂)²Angular quantities, torque, and moment of inertia
rotationTorque: τ = r × F = rF sin θ (rotational analog of force)
Moment of Inertia: I = Σmr² (rotational analog of mass)
Angular Momentum: L = Iω (rotational analog of momentum)
# Rotational Kinematics (analog to linear)
ω = ω₀ + αt
θ = ω₀t + (1/2)αt²
ω² = ω₀² + 2αθ
# Torque and Angular Momentum
τ = Iα (Newton's 2nd law analog)
L = Iω
τ = dL/dt
# Rotational KE
KE_rot = (1/2)Iω²
# Total KE (rolling)
KE_total = (1/2)mv² + (1/2)Iω²
For rolling: v = rω
# Radius of Gyration
k = √(I/M)
I = Mk²MOI for common geometric shapes
rotation# Moment of Inertia Formulas
Ring (axis through center): I = MR²
Disc (axis through center): I = (1/2)MR²
Solid Sphere: I = (2/5)MR²
Hollow Sphere: I = (2/3)MR²
Rod (center): I = (1/12)ML²
Rod (end): I = (1/3)ML²
# Parallel Axis Theorem
I = I_cm + Md²
Where:
I_cm = MOI about center of mass
d = distance between parallel axes
# Perpendicular Axis Theorem (planar objects)
I_z = I_x + I_y
# Applications
- Higher I → harder to rotate
- Used in flywheels, figure skating
- Rolling motion calculationsConservation laws and equilibrium of rigid bodies
rotationConservation: If net external torque = 0, then L = constant
Equilibrium: ΣF = 0 (translational) and Στ = 0 (rotational)
# Conservation of Angular Momentum
L_initial = L_final
I₁ω₁ = I₂ω₂
Applications:
- Ice skater spinning (I↓ → ω↑)
- Diver tucking (I↓ → ω↑)
- Earth-Moon system
# Equilibrium Conditions
Translational: ΣF_x = 0, ΣF_y = 0
Rotational: Στ = 0 (about any point)
# Rolling Motion
Pure rolling: v_cm = rω
KE = (1/2)mv_cm² + (1/2)Iω²
= (1/2)mv_cm²[1 + k²/r²]
# Linear vs Rotational Comparison
Linear Rotational
s ←→ θ
v ←→ ω
a ←→ α
m ←→ I
F ←→ τ
p ←→ LNewton's law of gravitation and applications
gravitationUniversal Law: Every particle attracts every other particle with force proportional to product of masses and inversely proportional to square of distance
G = 6.67 × 10⁻¹¹ Nm²/kg²
# Newton's Law of Gravitation
F = G(m₁m₂)/r²
G = 6.67 × 10⁻¹¹ Nm²/kg²
# Acceleration due to Gravity
g = GM/R² (at surface)
Standard: g = 9.8 m/s²
# Variation with Height
g_h = g(1 - 2h/R) [h << R]
g_h = g[R²/(R+h)²] [general]
# Variation with Depth
g_d = g(1 - d/R)
At center (d = R): g = 0
# Important Relations
Weight: W = mg
g ∝ 1/R² (at surface)
g ∝ M (mass of planet)Gravitational field, potential, and escape velocity
gravitation# Gravitational Field
E = F/m = GM/r² (at distance r)
Direction: Towards the mass
# Gravitational Potential
V = -GM/r (at distance r)
V at infinity = 0 (reference)
V at surface = -GM/R
# Gravitational Potential Energy
U = -GMm/r
U at infinity = 0
U at surface = -GMm/R
# Escape Velocity
v_e = √(2GM/R) = √(2gR)
Earth: v_e = 11.2 km/s
# Important Points
- PE is always negative (bound system)
- Zero PE at infinite separation
- To escape: KE ≥ |PE|
# Binding Energy
BE = GMm/(2r) (for circular orbit)Planetary motion and satellite orbital mechanics
gravitationLaw 1: Planets move in elliptical orbits with Sun at focus
Law 2: Equal areas in equal times (areal velocity constant)
Law 3: T² ∝ r³
# Kepler's Third Law
T² ∝ r³
T²/r³ = 4π²/(GM) = constant
# Satellite Orbital Velocity
v_o = √(GM/r) = √(gR²/r)
At surface: v_o = √(gR) ≈ 7.9 km/s
# Time Period
T = 2πr/v_o = 2π√(r³/GM)
At surface: T = 2π√(R/g) ≈ 85 min
# Energy of Satellite
KE = GMm/(2r)
PE = -GMm/r
Total E = -GMm/(2r) (negative = bound)
# Geostationary Satellite
T = 24 hours
Height ≈ 36,000 km above surface
Always above same point on equator
# Relation: v_e = √2 × v_oStress, strain, and elastic moduli
properties-matterStress: Force per unit area (σ = F/A)
Strain: Relative change in dimension (dimensionless)
Hooke's Law: Stress ∝ Strain (within elastic limit)
# Hooke's Law
Stress ∝ Strain
Stress = E × Strain
# Young's Modulus (Y)
Y = (F/A)/(ΔL/L) = Longitudinal Stress/Strain
Unit: N/m² or Pa
# Bulk Modulus (K)
K = -ΔP/(ΔV/V) = Volume Stress/Strain
Compressibility: 1/K
# Modulus of Rigidity (η)
η = (F/A)/(θ) = Shear Stress/Shear Strain
# Poisson's Ratio
σ = -Lateral Strain/Longitudinal Strain
Range: 0 to 0.5
# Elastic Potential Energy
U = (1/2) × Stress × Strain × Volume
U = (1/2)(F²L)/(AY)
# Important Points
- Higher modulus → more rigid
- Stress-strain curve: elastic → yield → plasticPascal's law, pressure in fluids, and buoyancy
properties-matterPressure: P = F/A (force per unit area)
Pascal's Law: Pressure applied to enclosed fluid is transmitted equally in all directions
Archimedes Principle: Buoyant force = weight of displaced fluid
# Fluid Pressure
P = P₀ + ρgh
Where:
P₀ = atmospheric pressure
ρ = density
g = acceleration due to gravity
h = depth
# Pascal's Law Applications
- Hydraulic lift: F₁/A₁ = F₂/A₂
- Hydraulic brakes
# Buoyancy (Archimedes)
F_b = ρ_fluid × V_displaced × g
F_b = Weight of displaced fluid
# Floating Condition
Weight of body = Buoyant force
ρ_body × V_body × g = ρ_fluid × V_immersed × g
# Apparent Weight
W_apparent = W_actual - F_b
# Relative Density
RD = ρ_substance/ρ_water
For floating: ρ_body/ρ_fluid = V_immersed/V_totalViscosity, Stokes law, and Bernoulli's principle
properties-matterViscosity: Internal friction in fluids
Streamline Flow: Smooth, layered flow (v < critical velocity)
Turbulent Flow: Chaotic flow (v > critical velocity)
# Viscous Force (Stokes' Law)
F = 6πηrv
Where:
η = coefficient of viscosity
r = radius of sphere
v = velocity
# Terminal Velocity
v_t = (2r²g(ρ - σ))/(9η)
ρ = density of sphere
σ = density of fluid
# Equation of Continuity
A₁v₁ = A₂v₂ (incompressible fluid)
Mass flow rate = ρAv = constant
# Bernoulli's Equation
P + (1/2)ρv² + ρgh = constant
Pressure + KE/volume + PE/volume = const
# Applications of Bernoulli
- Venturi meter: flow measurement
- Airplane wing lift
- Atomizer/sprayer
- Magnus effect
# Energy Interpretation
Pressure energy + Kinetic energy + Potential energy = constantSurface energy, excess pressure, and capillarity
properties-matterSurface Tension: Force per unit length at liquid surface (γ = F/L)
Surface Energy: Work done to increase surface area (U = γ × ΔA)
Cohesion: Attraction between same molecules
Adhesion: Attraction between different molecules
# Surface Tension
γ = F/L = Energy/Area
Unit: N/m or J/m²
# Excess Pressure
Spherical drop: ΔP = 2γ/r
Soap bubble: ΔP = 4γ/r (two surfaces)
Cylindrical: ΔP = γ/r
# Angle of Contact (θ)
- Water-glass: θ < 90° (concave meniscus)
- Mercury-glass: θ > 90° (convex meniscus)
# Capillary Rise/Fall
h = (2γ cos θ)/(rρg)
Rise (θ < 90°): h is positive
Fall (θ > 90°): h is negative
# Work Done in Blowing Bubble
W = 8πr²γ (soap bubble, two surfaces)
W = 4πr²γ (drop, one surface)
# Factors Affecting γ
- Decreases with temperature
- Impurities can increase/decrease
- Detergents decrease γHeat, work, internal energy, and thermodynamic processes
thermodynamicsZeroth Law: Thermal equilibrium is transitive (defines temperature)
First Law: ΔQ = ΔU + ΔW (energy conservation)
Sign Convention: Heat absorbed (+), Work done by system (+)
# First Law of Thermodynamics
ΔQ = ΔU + ΔW
ΔQ = heat supplied to system
ΔU = change in internal energy
ΔW = work done by system
# Work Done by Gas
W = ∫PdV = PΔV (isobaric)
# Thermodynamic Processes
1. Isothermal (ΔT = 0)
- ΔU = 0 (for ideal gas)
- ΔQ = ΔW = nRT ln(V₂/V₁)
- PV = constant
2. Adiabatic (ΔQ = 0)
- ΔU = -ΔW
- PVᵞ = constant
- TVᵞ⁻¹ = constant
- ΔW = (P₁V₁ - P₂V₂)/(γ-1)
3. Isochoric (ΔV = 0)
- ΔW = 0
- ΔQ = ΔU = nCᵥΔT
4. Isobaric (ΔP = 0)
- ΔQ = nCₚΔT
- ΔW = PΔV = nRΔT
# Specific Heat Capacities
Cₚ - Cᵥ = R
γ = Cₚ/CᵥGas laws, kinetic interpretation, and molecular speeds
thermodynamicsAssumptions: Point masses, elastic collisions, no intermolecular forces, random motion
Ideal Gas: PV = nRT = NkT
Avogadro Number: N_A = 6.022 × 10²³ mol⁻¹
# Ideal Gas Equation
PV = nRT = NkT
Where:
R = 8.314 J/(mol·K) (universal gas constant)
k = 1.38 × 10⁻²³ J/K (Boltzmann constant)
k = R/N_A
# Kinetic Interpretation
P = (1/3)ρv²_rms = (1/3)nm/V × v²_rms
Average KE per molecule = (3/2)kT
# Molecular Speeds
RMS speed: v_rms = √(3RT/M) = √(3kT/m)
Average speed: v_avg = √(8RT/πM)
Most probable: v_mp = √(2RT/M)
Relation: v_rms > v_avg > v_mp
√3 : √(8/π) : √2
# Internal Energy
U = (f/2)nRT
f = degrees of freedom
# Degrees of Freedom
Monoatomic: f = 3 (translational)
Diatomic: f = 5 (3 trans + 2 rot)
Polyatomic: f = 6 (3 trans + 3 rot)Electric charge, Coulomb's law, and electric field
electrostaticsCharge: Property of matter (positive/negative), quantized (e = 1.6 × 10⁻¹⁹ C)
Conservation: Total charge in isolated system remains constant
Coulomb's Law: Force between point charges
# Coulomb's Law
F = k(q₁q₂)/r² = (1/4πε₀)(q₁q₂)/r²
k = 9 × 10⁹ Nm²/C²
ε₀ = 8.85 × 10⁻¹² C²/Nm² (permittivity)
# Superposition Principle
F_net = F₁ + F₂ + F₃ + ... (vector sum)
# Electric Field
E = F/q₀ (force per unit positive charge)
E = kQ/r² (point charge)
Direction: Away from +ve, towards -ve
# Electric Field Lines
- Start from +ve, end at -ve
- Never cross each other
- Density ∝ field strength
- Perpendicular to surface
# Electric Dipole
p = q × 2a (dipole moment)
Direction: -ve to +ve charge
# Field due to Dipole
Axial: E = 2kp/r³
Equatorial: E = kp/r³
Torque: τ = p × E = pE sin θ