📘 PHYSICS NOTES

1. MECHANICS

1.1 PHYSICAL QUANTITIES, VECTOR AND KINEMATICS

Physical Quantities

Physical quantities are measurable properties of matter.

Types

Scalar Quantity
Vector Quantity

Dimensions

Dimensions represent physical quantities in terms of fundamental quantities.

Example:

$$[Force] = [MLT^{-2}]$$

Vector Algebra

Resolution of Vector

For vector (A):

$$A_x = A\cos\theta$$

$$A_y = A\sin\theta$$

Polygon Law of Vector

If several vectors acting simultaneously are represented in magnitude and direction by the sides of a polygon taken in order, then the closing side gives the resultant vector.

Equations of Motion

First Equation

$$v = u + at$$

Second Equation

$$s = ut + \frac{1}{2}at^2$$

Third Equation

$$v^2 = u^2 + 2as$$

Projectile Motion

Horizontal Range

$$R = \frac{u^2\sin2\theta}{g}$$

Relative Motion

Velocity of object A relative to B:

$$\vec{V}_{AB} = \vec{V}_A - \vec{V}_B$$

1.2 NEWTON’S LAWS OF MOTION AND FRICTION

Newton’s First Law

A body remains at rest or uniform motion unless acted upon by external force.

Newton’s Second Law

$$F = ma$$

Newton’s Third Law

Every action has equal and opposite reaction.

Conservation of Linear Momentum

$$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$$

Friction

Laws of Friction

Friction opposes motion
Friction is proportional to normal reaction

Frictional Force

$$F = \mu N$$

1.3 WORK, ENERGY AND POWER

Work

$$W = Fs\cos\theta$$

Kinetic Energy

$$KE = \frac{1}{2}mv^2$$

Potential Energy

$$PE = mgh$$

Power

$$P = \frac{W}{t}$$

Work-Energy Theorem

Work done equals change in kinetic energy.

Conservation of Energy

Energy can neither be created nor destroyed.

Collisions

Elastic Collision

Momentum and energy conserved.

Inelastic Collision

Only momentum conserved.

1.4 CIRCULAR MOTION, GRAVITATION AND SHM

Centripetal Force

$$F = \frac{mv^2}{r}$$

Banking of Road

$$\tan\theta = \frac{v^2}{rg}$$

Gravitational Force

$$F = \frac{GMm}{r^2}$$

Variation of g

Acceleration due to gravity decreases with height and depth.

Motion of Satellite

Satellite moves due to gravitational force.

Simple Harmonic Motion (SHM)

Equation

$$x = A\sin\omega t$$

Energy in SHM

Total energy:

$$E = \frac{1}{2}kA^2$$

Simple Pendulum

Time period:

$$T = 2\pi\sqrt{\frac{l}{g}}$$

Resonance

Maximum amplitude occurs when driving frequency equals natural frequency.

1.5 ROTATIONAL DYNAMICS

Torque

$$\tau = rF\sin\theta$$

Moment of Inertia

$$I = \sum mr^2$$

Rotational Kinetic Energy

$$KE = \frac{1}{2}I\omega^2$$

Angular Momentum

$$L = I\omega$$

Conservation of Angular Momentum

Angular momentum remains constant if no external torque acts.

1.6 ELASTICITY

Hooke’s Law

Stress is proportional to strain.

$$F = -kx$$

Young’s Modulus

$$Y = \frac{\text{Stress}}{\text{Strain}}$$

Bulk Modulus

$$K = \frac{\text{Pressure}}{\text{Volume Strain}}$$

Modulus of Rigidity

$$\eta = \frac{\text{Shear Stress}}{\text{Shear Strain}}$$

Poisson’s Ratio

Ratio of lateral strain to longitudinal strain.

1.7 FLUID MECHANICS

Archimedes’ Principle

Upthrust equals weight of displaced fluid.

Surface Tension

Force per unit length.

$$T = \frac{F}{l}$$

Viscosity

Internal friction between fluid layers.

Stoke’s Law

$$F = 6\pi \eta rv$$

Continuity Equation

$$Av = \text{constant}$$

Bernoulli’s Equation

$$P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$$

2. HEAT AND THERMODYNAMICS

2.1 TEMPERATURE AND QUANTITY OF HEAT

Thermal Equilibrium

Bodies in contact attain same temperature.

Specific Heat Capacity

$$Q = mc\Delta T$$

Latent Heat

$$Q = mL$$

Newton’s Law of Cooling

Rate of cooling proportional to temperature difference.

2.2 THERMAL EXPANSION

Linear Expansion

$$\Delta L = \alpha L\Delta T$$

Volume Expansion

$$\Delta V = \gamma V\Delta T$$

2.3 TRANSFER OF HEAT

Conduction

Transfer through solids.

Convection

Transfer through fluids.

Radiation

Transfer without medium.

Stefan-Boltzmann Law

$$E = \sigma T^4$$

2.4 KINETIC THEORY OF GASES

Gas Equation

$$PV = nRT$$

RMS Speed

$$v_{rms} = \sqrt{\frac{3RT}{M}}$$

2.5 LAWS OF THERMODYNAMICS

First Law

$$\Delta Q = \Delta U + W$$

Second Law

Heat cannot flow naturally from cold to hot body.

Carnot Efficiency

$$\eta = 1 - \frac{T_2}{T_1}$$

3. GEOMETRIC AND PHYSICAL OPTICS

3.1 REFLECTION

Mirror Formula

$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$

3.2 REFRACTION

Snell’s Law

$$\mu = \frac{\sin i}{\sin r}$$

Lens Formula

$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$

Lens Maker’s Formula

$$ \frac{1}{f}

(\mu -1) \left( \frac{1}{R_1}

\frac{1}{R_2} \right) $$

Optical Fiber

Works on Total Internal Reflection.

3.3 DISPERSION

White light splits into spectrum.

3.4 HUYGEN’S PRINCIPLE

Every point on wavefront acts as source of secondary wavelets.

3.5 INTERFERENCE

Young’s Double Slit Experiment demonstrates interference.

3.6 DIFFRACTION

Bending of light around obstacles.

3.7 POLARIZATION

Shows transverse nature of light.

4. WAVES AND SOUND

4.1 WAVE MOTION

Travelling Wave

Wave transfers energy.

Stationary Wave

No energy transfer.

4.2 VELOCITY OF SOUND

$$v = \sqrt{\frac{E}{\rho}}$$

4.3 WAVES IN PIPES

Open Pipe

$$f_n = \frac{nv}{2L}$$

Closed Pipe

$$f_n = \frac{nv}{4L}$$

4.4 DOPPLER EFFECT

Apparent change in frequency due to relative motion.

5. ELECTRICITY AND MAGNETISM

5.1 ELECTROSTATICS

Coulomb’s Law

$$F = \frac{kq_1q_2}{r^2}$$

Electric Field

$$E = \frac{F}{q}$$

Gauss Law

$$\phi = \frac{q}{\epsilon_0}$$

Capacitor

$$C = \frac{Q}{V}$$

Energy Stored

$$U = \frac{1}{2}CV^2$$

5.2 DC CIRCUITS

Ohm’s Law

$$V = IR$$

Joule’s Law

$$H = I^2Rt$$

Kirchhoff’s Law

Sum of currents entering junction equals leaving.

5.3 THERMOELECTRIC EFFECT

Seebeck Effect
Peltier Effect
Thomson Effect

5.4 MAGNETIC EFFECT

Force on Moving Charge

$$F = qvB\sin\theta$$

Biot-Savart Law

Magnetic field due to current element.

5.5 MAGNETIC PROPERTIES

Permeability
Susceptibility
Hysteresis

5.6 ELECTROMAGNETIC INDUCTION

Faraday’s Law

$$E = -\frac{d\phi}{dt}$$

Transformer Equation

$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$

5.7 ALTERNATING CURRENT

RMS Value

$$V_{rms} = \frac{V_0}{\sqrt{2}}$$

Power Factor

$$\cos\phi$$

6. MODERN PHYSICS

6.1 ELECTRONS

Millikan Experiment

Determined charge of electron.

6.2 PHOTOELECTRIC EFFECT

Einstein Equation

$$hf = \phi + KE$$

De Broglie Wavelength

$$\lambda = \frac{h}{p}$$

Uncertainty Principle

$$\Delta x \Delta p \geq \frac{h}{4\pi}$$

6.3 SEMICONDUCTORS

Intrinsic Semiconductor
Extrinsic Semiconductor
P-N Junction
Zener Diode
Transistor
Logic Gates

6.4 RADIOACTIVITY

Radioactive Decay

$$N = N_0e^{-\lambda t}$$

Einstein Mass Energy Relation

$$E = mc^2$$

Nuclear Reactions

Fission
Fusion

6.5 RECENT TRENDS IN PHYSICS

Particle Physics

Quarks
Leptons
Mesons
Higgs Boson

Universe

Big Bang Theory
Black Hole
Dark Matter
Gravitational Waves

Telecommunication

Radio
TV
Mobile Communication
GPS
Remote Sensing

Environment

Energy Crisis
Pollution
Ozone Layer Depletion

New Technologies

Nanotechnology
Superconductors
Perfect Conductors

EXAM TIPS

Learn formulas daily
Practice derivations
Solve numericals regularly
Focus on concepts
Revise short notes before exam

QUICK FORMULA REVISION

Work $$W = Fs \cos\theta$$ Kinetic Energy $$\frac{1}{2}mv^2$$ Ohm's Law $$V = IR$$ Lens Formula $$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$ Coulomb's Law $$F = \frac{k q_1 q_2}{r^2}$$ Gas Equation $$PV = nRT$$ Radioactive Decay $$N = N_0 e^{-\lambda t}$$

IOE Entrance notes