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ICSE Class 11 Physics★ ISC Class 11 Physics · Internal assessment + foundation for ISC Class 12 · Board: ISC

Physics — Mechanics, Heat, Waves & Oscillations

ISC Class 11 Physics: UNITS and measurement. KINEMATICS — motion in 1D and 2D. NEWTON'S LAWS of motion. WORK, ENERGY, POWER. ROTATIONAL motion and GRAVITATION. PROPERTIES of matter. HEAT and THERMODYNAMICS. OSCILLATIONS and WAVES. ISC Class 11 Physics.

⏱ 22 min readHard difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Solve 1D and 2D kinematics problems using equations of motion and projectile motion formulas; interpret velocity-time and displacement-time graphs
2Apply Newton's three laws and free body diagram technique to solve problems involving friction, tension, normal force, and circular motion
3Use the work-energy theorem and conservation of mechanical energy to solve problems; calculate power and identify conservative vs non-conservative forces
4Apply moment of inertia, torque, and angular momentum conservation to rotational problems; use Newton's Law of Gravitation to calculate orbital and escape velocities
5Solve SHM problems using x = A sin(ωt + φ), T = 2π√(m/k) and T = 2π√(L/g); apply Doppler effect formula to find apparent frequency

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Why this chapter matters

ISC Class 11 Physics is the backbone of all quantitative physics. Kinematics and Newton's laws provide the mathematical language for every mechanical system. Work-Energy theorem and conservation principles appear in virtually every JEE/NEET numerical. Rotational motion (moment of inertia, torque, angular momentum conservation) and gravitation (orbital/escape velocity) form the core of Class 11 board long-answer questions. Thermodynamics (First Law, Carnot efficiency) directly feeds into Class 12 topics. Simple Harmonic Motion (SHM) and Doppler effect are among the most-tested ISC Class 11 topics in numerical problems.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Physics — Mechanics, Heat, Waves & Oscillations

1. Units and Measurement

Fundamental quantities: Length (m), Mass (kg), Time (s), Temperature (K), Electric Current (A), Amount (mol), Luminous Intensity (cd).
Dimensional Analysis: Checking correctness of equations. Deducing relationships.

2. Kinematics

Motion in 1D

Equations: v = u + at. s = ut + ½at². v² = u² + 2as.
Graphs: v-t graph: slope = acceleration. Area under = displacement.

Motion in 2D — Projectile Motion

Horizontal: uₓ = u cos θ (constant). Vertical: uᵧ = u sin θ (decelerates by g).
Time of flight: T = 2u sin θ/g. Range: R = u² sin 2θ/g. Max range at θ = 45°. Max height: H = u² sin²θ/2g.

Circular Motion

Centripetal acceleration: a = v²/r = ω²r. Centripetal force = mv²/r.

3. Newton's Laws of Motion

Law	Statement
First (Inertia)	Body continues in its state UNLESS acted upon by an external unbalanced force.
Second	F = ma (Force = mass × acceleration).
Third	Action and reaction are EQUAL and OPPOSITE. Act on DIFFERENT bodies.

Friction

Static (fₛ ≤ μₛN). Kinetic (fₖ = μₖN). μₛ > μₖ. Friction opposes RELATIVE motion.
Angle of repose: tan θ = μ.

Free Body Diagrams — Essential tool. Isolate the body. Draw ALL forces. Apply F=ma.

4. Work, Energy and Power

Work: W = Fd cos θ. Unit: Joule (J). Positive (θ<90°). Negative (θ>90°). Zero (θ=90°).
Kinetic Energy: K = ½mv². Potential Energy: U = mgh (gravitational).
Work-Energy Theorem: W_net = ΔK = K_f — K_i.
Conservation of Mechanical Energy: If only conservative forces act: K + U = CONSTANT.
Power: P = W/t. Unit: Watt (W). 1 HP = 746 W.

5. Rotational Motion & Centre of Mass

Angular velocity ω = dθ/dt. Angular acceleration α = dω/dt.
Equations for CONSTANT angular acceleration: ω = ω₀ + αt. θ = ω₀t + ½αt². ω² = ω₀² + 2αθ.
Torque: τ = r × F = Iα. Moment of Inertia I = Σmᵢrᵢ².
Angular Momentum: L = Iω. Conserved if NO external torque.
Centre of Mass: X_CM = Σmᵢxᵢ/Σmᵢ.

6. Gravitation

Newton's Law of Universal Gravitation

F = Gm₁m₂/r². G = 6.67 × 10⁻¹¹ Nm²/kg².

Acceleration due to Gravity

g = GM/R². g decreases with ALTITUDE and DEPTH. g varies with LATITUDE (Earth's rotation).

Satellites

Orbital velocity: v = √(GM/r). Escape velocity: vₑ = √(2GM/R) = √(2gR). Earth: ~11.2 km/s.

7. Properties of Bulk Matter

Elasticity

Stress = F/A. Strain = ΔL/L. Young's Modulus Y = Stress/Strain.
Hooke's Law: Within elastic limit, stress ∝ strain.

Fluid Pressure

P = hρg. Pascal's Law: Pressure applied to enclosed fluid transmitted UNDIMINISHED.
Archimedes' Principle: Upthrust = weight of fluid DISPLACED.
Bernoulli's Theorem: P/ρ + v²/2 + gh = constant. (Along a streamline, steady, incompressible, non-viscous flow).

Viscosity

Resistance of fluid to flow. η. Stokes' Law: F = 6πηrv.

Surface Tension

Force per unit length. Capillary rise: h = 2S cos θ/(ρgr).

8. Heat and Thermodynamics

Thermal Expansion

ΔL = L₀ α ΔT (linear). ΔA = A₀ β ΔT (area — β ≈ 2α). ΔV = V₀ γ ΔT (volume — γ ≈ 3α).

Specific Heat: Q = mcΔθ. Latent Heat: Q = mL. Calorimetry: Heat lost = Heat gained.

Kinetic Theory of Gases

PV = nRT. KE per molecule = (3/2)kT. Average speed: v̄ = √(8kT/πm).

First Law of Thermodynamics

ΔQ = ΔU + ΔW. 'Heat added = Change in internal energy + Work done BY the system.'

Second Law

Heat DOES NOT spontaneously flow from cold to hot body. No engine is 100% efficient.

Carnot Engine — Maximum theoretical efficiency: η = 1 − T_cold/T_hot.

9. Oscillations

Simple Harmonic Motion (SHM)

F = −kx. a = −(k/m)x = −ω²x. x = A sin(ωt + φ). Period T = 2π√(m/k) (spring). T = 2π√(L/g) (simple pendulum).

Energy in SHM: Total = ½kA². KE = ½mω²(A²−x²). PE = ½mω²x².

10. Waves

Types

Mechanical: Needs MEDIUM (sound, water waves). Electromagnetic: NO medium needed (light, radio).
Transverse: Particles vibrate PERPENDICULAR to wave direction (light, water). Longitudinal: Particles vibrate PARALLEL (sound).

Wave Equation

v = fλ (speed = frequency × wavelength).

Sound — Characteristics

Pitch (frequency). Loudness (amplitude). Timbre (waveform).

Doppler Effect

f′ = f × (v ± v_observer)/(v ∓ v_source). 'Sound changes pitch when source/observer moves.'

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Kinematics — Equations of Motion and Projectile

1D EQUATIONS (constant acceleration): v = u + at. s = ut + ½at². v² = u² + 2as. s_nth = u + a(2n−1)/2. PROJECTILE MOTION (θ from horizontal): Horizontal: x = u cos θ · t (constant velocity, no acceleration). Vertical: y = u sin θ · t − ½gt². Time of flight: T = 2u sin θ/g. Maximum height: H = u² sin²θ/2g. Range: R = u² sin 2θ/g. Maximum range at θ = 45°. CIRCULAR MOTION: Centripetal acceleration = v²/r = ω²r. Centripetal force = mv²/r (directed towards centre).

In projectile motion, horizontal velocity (uₓ = u cosθ) is CONSTANT throughout — no horizontal force. Vertical component decelerates at g = 9.8 m/s² going up and accelerates at g going down. At maximum height, vertical velocity = 0 (but horizontal velocity unchanged).

Newton's Laws, Friction and Work-Energy

NEWTON'S LAWS: F = ma (Second Law). For connected bodies: use Free Body Diagrams for each mass separately. FRICTION: Static: fs ≤ μsN. Kinetic: fk = μkN (constant). μs > μk always. Angle of repose: tan θ = μs. WORK: W = Fd cos θ. W > 0 if θ < 90°, W < 0 if θ > 90°, W = 0 if θ = 90°. KINETIC ENERGY: K = ½mv². POTENTIAL ENERGY: U = mgh. WORK-ENERGY THEOREM: W_net = ΔK = K_f − K_i. CONSERVATION: If no non-conservative forces: K + U = constant. POWER: P = W/t = Fv cos θ. 1 HP = 746 W.

For problems with strings/pulleys: tension T is the same throughout a massless, frictionless string. For an Atwood machine (two masses m₁, m₂): a = (m₁−m₂)g/(m₁+m₂). T = 2m₁m₂g/(m₁+m₂).

Rotation, Gravitation and Properties of Matter

ROTATIONAL EQUATIONS (constant α): ω = ω₀ + αt. θ = ω₀t + ½αt². ω² = ω₀² + 2αθ. TORQUE: τ = r × F = Iα. ANGULAR MOMENTUM: L = Iω. Conserved when external torque = 0 (ice skater pulling arms in). NEWTON'S GRAVITATION: F = Gm₁m₂/r². G = 6.67 × 10⁻¹¹ Nm²/kg². g = GM/R². ORBITAL VELOCITY: v₀ = √(GM/r). ESCAPE VELOCITY: vₑ = √(2GM/R) = √(2gR) ≈ 11.2 km/s (Earth). BERNOULLI: P + ½ρv² + ρgh = constant. SURFACE TENSION capillary rise: h = 2S cos θ/(ρgr). STOKES LAW: F = 6πηrv.

Geostationary satellite: orbital period = 24 hours (stays above same point on Earth). Orbital radius ≈ 42,000 km. Angular momentum conservation explains why stars spin faster as they collapse (L = Iω = constant; I decreases → ω increases).

Thermodynamics, SHM and Waves

THERMAL EXPANSION: ΔL = L₀αΔT. ΔV = V₀γΔT (γ ≈ 3α). Specific heat: Q = mcΔT. Latent heat: Q = mL. FIRST LAW: ΔQ = ΔU + ΔW. CARNOT EFFICIENCY: η = 1 − T_cold/T_hot (maximum possible for any heat engine). SHM: x = A sin(ωt + φ). v = Aω cos(ωt + φ). a = −Aω² sin(ωt + φ) = −ω²x. Spring: T = 2π√(m/k). Pendulum: T = 2π√(L/g). Energy in SHM: Total E = ½kA² = constant. KE = ½mω²(A²−x²). PE = ½mω²x². WAVES: v = fλ. Speed of sound in air ≈ 340 m/s at 0°C. DOPPLER: f′ = f(v ± v₀)/(v ∓ vₛ). (+v₀ and −vₛ when approaching; − v₀ and +vₛ when receding).

In SHM: at EQUILIBRIUM (x=0), velocity is MAXIMUM (v = Aω), acceleration = 0. At EXTREME positions (x = ±A), velocity = 0, acceleration is MAXIMUM (= Aω²). Total energy is conserved — KE converts to PE and back.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Not drawing free body diagrams before solving Newton's law problems

✓ ALWAYS draw a Free Body Diagram (FBD) for EACH body in the system before writing equations. An FBD shows all forces acting ON a single body: weight (mg downward), normal force (perpendicular to surface), tension (along string), friction (opposing motion), applied force. Once drawn, apply F_net = ma in each direction separately (horizontal and vertical). Without FBD, students consistently miss forces or apply Newton's third law pairs incorrectly.

WATCH OUT

✗ Confusing T = 2π√(m/k) (spring) with T = 2π√(L/g) (pendulum)

✓ Spring-mass system: T = 2π√(m/k) — period depends on MASS and SPRING CONSTANT. Increasing mass INCREASES T; increasing spring constant DECREASES T. Simple pendulum: T = 2π√(L/g) — period depends on LENGTH and g. Mass of bob does NOT affect period. Increasing length INCREASES T. On the Moon (g smaller), pendulum period INCREASES (pendulum swings slower). This is a classic ISC comparison question.

WATCH OUT

✗ Using the wrong sign convention in the Doppler effect formula

✓ Doppler formula: f′ = f × (v ± v_observer) / (v ∓ v_source). Memory aid: 'Use + in numerator (observer) and − in denominator (source) when APPROACHING; use − in numerator and + in denominator when RECEDING.' Why: when observer moves toward source, they intercept more wavefronts per second (higher apparent frequency). When source moves toward observer, wavefronts ahead are compressed (shorter wavelength → higher frequency). The opposite effects apply when moving away.

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· projectile

A ball is projected at 30° to the horizontal with an initial velocity of 20 m/s. Find the maximum height reached. (g = 10 m/s²)

▶ Show solution

Vertical component of initial velocity: uᵧ = u sin 30° = 20 × 0.5 = 10 m/s. At maximum height, vertical velocity = 0. Using v² = u² − 2gH: 0 = (10)² − 2 × 10 × H. H = 100/20 = 5 m. Alternatively, using formula: H = u² sin²θ / 2g = (20)² × (0.5)² / (2 × 10) = 400 × 0.25 / 20 = 100/20 = 5 m. Maximum height = 5 m.

Q2MEDIUM· SHM

A mass of 0.5 kg is attached to a spring of spring constant k = 200 N/m. Find (a) the angular frequency ω, (b) the time period T, and (c) the maximum velocity if amplitude A = 0.1 m.

▶ Show solution

(a) Angular frequency: ω = √(k/m) = √(200/0.5) = √400 = 20 rad/s. (b) Time period: T = 2π/ω = 2π/20 = π/10 ≈ 0.314 s. Alternatively, T = 2π√(m/k) = 2π√(0.5/200) = 2π × 0.05 = 0.314 s. (c) Maximum velocity occurs at the equilibrium position (x = 0): v_max = Aω = 0.1 × 20 = 2 m/s. At equilibrium, all energy is kinetic: KE_max = ½mv_max² = ½ × 0.5 × 4 = 1 J = Total Energy = ½kA² = ½ × 200 × 0.01 = 1 J ✓

Q3HARD· gravitation

Derive the expression for the escape velocity of a body from the surface of the Earth. Calculate its value. (G = 6.67 × 10⁻¹¹ Nm²/kg², M = 6 × 10²⁴ kg, R = 6.4 × 10⁶ m)

▶ Show solution

DERIVATION: Escape velocity is the minimum velocity needed to escape Earth's gravitational pull (reaching infinity with zero kinetic energy). Using energy conservation: KE at surface = PE to be overcome. ½mv² = GMm/R (energy needed to escape from r=R to r=∞). v² = 2GM/R. Therefore vₑ = √(2GM/R). Since g = GM/R²: vₑ = √(2gR). CALCULATION: vₑ = √(2 × 6.67 × 10⁻¹¹ × 6 × 10²⁴ / 6.4 × 10⁶). = √(2 × 6.67 × 6 × 10⁻¹¹⁺²⁴⁻⁶) = √(80.04 × 10⁷) = √(8.004 × 10⁸) = 2.83 × 10⁴ m/s ≈ 11.2 km/s. This is why rockets need to achieve ~11.2 km/s to leave Earth.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Equations of motion: v=u+at, s=ut+½at², v²=u²+2as. Projectile: R=u²sin2θ/g (max at 45°).
•Newton's 2nd: F=ma. 3rd: action-reaction on DIFFERENT bodies — they never cancel.
•Work W=Fd cosθ. Work-Energy Theorem: W_net = ΔKE. KE = ½mv². PE = mgh.
•Conservation of energy: K + U = constant (when only conservative forces act).
•Torque τ = Iα. Angular momentum L = Iω. L is conserved when external torque = 0.
•Escape velocity: vₑ = √(2gR) = √(2GM/R) ≈ 11.2 km/s from Earth.
•Bernoulli's theorem: P + ½ρv² + ρgh = constant along a streamline.
•Carnot efficiency: η = 1 − T_cold/T_hot. Second law: no engine is 100% efficient.
•SHM: T_spring = 2π√(m/k). T_pendulum = 2π√(L/g). v_max = Aω at x=0.
•Doppler: f′ = f(v±v₀)/(v∓vₛ). + numerator and − denominator when approaching.

CBSE marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Research Lagrangian and Hamiltonian Mechanics — reformulations of Newton's mechanics using energy methods (L = T − V) rather than forces. These approaches are more powerful for complex systems and form the foundation of quantum mechanics and field theory. Investigate why Lagrange's equations are invariant under coordinate transformations.
Investigate the Equivalence Principle in gravity — Einstein's insight that gravitational mass = inertial mass led to General Relativity (1915). The principle says that being in a uniform gravitational field is indistinguishable from being in an accelerating reference frame. This led to the idea that gravity is geometry — the curvature of spacetime.
Explore Carnot Cycle and the Second Law of Thermodynamics — Carnot (1824) proved that no heat engine can be more efficient than a reversible engine operating between two temperatures: η = 1 − T_cold/T_hot. This sets a fundamental limit on power plant efficiency and motivates the absolute Kelvin temperature scale.
Research Coupled Oscillators and Normal Modes — when two pendulums share a common support (or two springs are connected), their motions couple. The system has 'normal modes' — collective patterns of oscillation. This is the bridge from simple SHM to wave mechanics, to molecular vibrations, and ultimately to quantum field theory.

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Questions students ask

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The time period T = 2π√(L/g) contains only L (length of the pendulum) and g (acceleration due to gravity) — no mass term. This happens because the RESTORING FORCE for a pendulum is a component of GRAVITY (F = mg sin θ ≈ mg θ for small angles). Both the restoring force and the inertia (resistance to motion) are proportional to MASS — so mass cancels out in the equation of motion (F = ma → mg θ = ma → a = gθ). Since the acceleration is independent of mass, so is the period. This was first observed by Galileo — he noticed church chandeliers swinging with the same period regardless of their weight.

STATIC FRICTION: Acts when there is no relative motion between surfaces. It is a VARIABLE force — it adjusts itself to exactly oppose the applied force up to a maximum value (fₛ_max = μₛN). Until this maximum is exceeded, the body remains stationary. KINETIC (SLIDING) FRICTION: Acts when the surfaces are in RELATIVE MOTION. It is a CONSTANT force = μₖN (for given normal force N). Always μₛ > μₖ — it takes more force to start something moving than to keep it moving. This is why cars skid when brakes are applied too hard — once wheels lock, you transition from static to kinetic friction, losing steering control (hence ABS brakes are designed to stay in the static regime).