Class 11 Physics Complete Notes - Mechanics and Heat
Comprehensive Class 11 Physics notes covering Mechanics (Units 1-4) and Heat (Unit 5) for NEB exam. Includes formulas, derivations, and solved numericals.
Table of Contents
Table of Contents
Introduction to Class 11 Physics#
Class 11 Physics under NEB is divided into Mechanics, Heat, and Thermodynamics. This guide covers the first two sections which form the foundation for Class 12 Physics and competitive exams.
Unit 1: Physical Quantities and Measurement#
Fundamental and Derived Quantities#
| Quantity | SI Unit | Symbol | Dimension |
|---|---|---|---|
| Length | Meter | m | L |
| Mass | Kilogram | kg | M |
| Time | Second | s | T |
| Temperature | Kelvin | K | Θ |
| Current | Ampere | A | I |
| Amount of Substance | Mole | mol | N |
| Luminous Intensity | Candela | cd | J |
Significant Figures Rules#
- All non-zero digits are significant
- Zeros between non-zero digits are significant
- Leading zeros are NOT significant
- Trailing zeros in decimal are significant
- Trailing zeros in whole number without decimal are ambiguous
- 0.0045 → 2 sig figs
- 45.00 → 4 sig figs
- 100 → 1 sig fig (ambiguous)
- 100.0 → 4 sig figs
- 1.23 × 10⁴ → 3 sig figs
Error Analysis#
|Measured Value - True Value|
Absolute Error / True Value
Relative Error × 100%
Unit 2: Vectors#
Vector Operations#
| Operation | Formula | Properties |
|---|---|---|
| Addition | A + B = (Ax+Bx, Ay+By) | Commutative, Associative |
| Subtraction | A - B = A + (-B) | |
| Dot Product | A·B = | A |
| Cross Product | A×B = | A |
Find the angle between vectors A = 3i + 4j and B = 4i + 3j.
A·B = 3×4 + 4×3 = 24 |A| = √(9+16) = 5, |B| = √(16+9) = 5 cosθ = 24/25 → θ = cos⁻¹(0.96) ≈ 16.26°
Resolution of Vectors#
A vector A making angle θ with x-axis:
- Ax = A cosθ
- Ay = A sinθ
- A = √(Ax² + Ay²)
- θ = tan⁻¹(Ay/Ax)
Unit 3: Kinematics#
Motion in a Straight Line#
| Equation | Variables | When to Use |
|---|---|---|
| v = u + at | u, v, a, t | No displacement |
| s = ut + ½at² | u, s, a, t | No final velocity |
| v² = u² + 2as | u, v, a, s | No time |
| s = (u+v)t/2 | u, v, s, t | Constant acceleration |
Always write down: Given, To Find, Formula, Substitution, Answer with units. This gets full marks in numericals.
Projectile Motion#
- Time of Flight: T = 2u sinθ / g
- Maximum Height: H = u² sin²θ / 2g
- Range: R = u² sin2θ / g
- Maximum Range: Rmax = u²/g (at θ = 45°)
- Equation of Trajectory: y = x tanθ - gx²/(2u²cos²θ)
A ball is thrown at 20 m/s at 30°. Find range and max height. (g = 10 m/s²)
R = 20² sin60° / 10 = 400 × 0.866 / 10 = 34.64 m H = 20² sin²30° / 20 = 400 × 0.25 / 20 = 5 m
Relative Velocity#
Vab = Va - Vb (velocity of A relative to B)
Unit 4: Dynamics#
Newton's Laws of Motion#
- First Law (Inertia): A body remains at rest or uniform motion unless acted by external force.
- Second Law: F = ma (Force = mass × acceleration)
- Third Law: Action = -Reaction (equal magnitude, opposite direction)
Friction#
| Type | Formula | Direction |
|---|---|---|
| Static | fs ≤ μsN | Opposes impending motion |
| Kinetic | fk = μkN | Opposes actual motion |
| Rolling | fr = μrN | Much smaller than kinetic |
Work, Energy, Power#
| Concept | Formula | Unit |
|---|---|---|
| Work | W = F·s = Fs cosθ | Joule (J) |
| Kinetic Energy | K = ½mv² | Joule (J) |
| Potential Energy | U = mgh | Joule (J) |
| Power | P = W/t = F·v | Watt (W) |
| Work-Energy Theorem | Wnet = ΔK |
In an isolated system, total mechanical energy (K + U) remains constant if only conservative forces act.
Circular Motion#
| Quantity | Formula | Direction |
|---|---|---|
| Angular Velocity | ω = v/r | Along axis |
| Centripetal Acceleration | ac = v²/r = ω²r | Towards center |
| Centripetal Force | Fc = mv²/r = mω²r | Towards center |
| Period | T = 2π/ω | |
| Frequency | f = 1/T = ω/2π |
Unit 5: Heat and Thermometry#
Temperature Scales#
| Scale | Freezing Point | Boiling Point | Conversion |
|---|---|---|---|
| Celsius | 0°C | 100°C | - |
| Fahrenheit | 32°F | 212°F | F = 9/5 C + 32 |
| Kelvin | 273.15 K | 373.15 K | K = C + 273.15 |
Thermal Expansion#
| Type | Formula | Coefficient |
|---|---|---|
| Linear | ΔL = αL₀ΔT | α (per °C) |
| Superficial | ΔA = βA₀ΔT | β = 2α |
| Cubical | ΔV = γV₀ΔT | γ = 3α |
Calorimetry#
Heat required to raise temperature of 1 kg substance by 1°C. Formula: Q = mcΔT
100g water at 80°C mixed with 200g water at 20°C. Find final temperature.
Heat lost = Heat gained 0.1 × 4200 × (80 - T) = 0.2 × 4200 × (T - 20) 80 - T = 2T - 40 3T = 120 → T = 40°C
Phase Changes#
| Process | Latent Heat Formula | Constant |
|---|---|---|
| Fusion (Solid→Liquid) | Q = mLf | Lf (J/kg) |
| Vaporization (Liquid→Gas) | Q = mLv | Lv (J/kg) |
| Sublimation (Solid→Gas) | Q = mLs | Ls = Lf + Lv |
Important Numerical Problems for Practice#
1. Mechanics: A 5 kg block pulled by 20 N at 30° on rough surface (μ = 0.2). Find acceleration.
- Fx = 20 cos30° = 17.32 N
- N = mg - Fy = 50 - 10 = 40 N
- f = μN = 0.2 × 40 = 8 N
- a = (17.32 - 8)/5 = 1.86 m/s²
2. Projectile: Find angle for range = 3 × max height.
- R = u² sin2θ/g, H = u² sin²θ/2g
- R = 3H → sin2θ = 1.5 sin²θ → 2 sinθ cosθ = 1.5 sin²θ → tanθ = 4/3 → θ ≈ 53°
3. Energy: 2 kg ball dropped from 10 m. Find velocity at 5 m height.
- mgh₁ = ½mv² + mgh₂ → v = √[2g(h₁-h₂)] = √[2×10×5] = 10 m/s
4. Heat: 2 kg ice at 0°C to water at 20°C. (Lf = 3.36×10⁵, cw = 4200)
- Q = mLf + mcΔT = 2×3.36×10⁵ + 2×4200×20 = 6.72×10⁵ + 1.68×10⁵ = 8.4×10⁵ J
3. Circular Motion: 0.5 kg stone whirled in 1m radius at 4 m/s. Tension?
- T = mv²/r = 0.5×16/1 = 8 N
Study Tips for NEB Physics#
- Derive all formulas - Don't just memorize, understand derivations
- Practice 5 numericals daily - Mix of easy, medium, hard
- Make formula sheet - One page per unit, carry everywhere
- Solve past 10 years papers - Pattern recognition is key
- Focus on units - Wrong unit = zero marks even if answer is right
- Draw diagrams - Free body diagrams, ray diagrams, vector diagrams
Recommended Resources#
- NEB Class 11 Physics Textbook (CDC)
- Numerical Physics by S.K. Pandey
- HC Verma Concepts of Physics Vol 1
- Past 10 Years NEB Question Papers
- YouTube: Physics Wallah, Science Simplified
Conclusion#
Class 11 Physics builds the conceptual foundation for all higher physics. Mechanics and Heat are conceptually rich and numerically heavy. Focus on understanding concepts rather than rote memorization. With consistent practice and clear concepts, 90%+ is achievable in NEB Physics.
Physics is not about memorizing formulas—it's about understanding nature's patterns.
Good luck with your NEB preparation!
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