Comprehensive CIE IGCSE Physics Master Revision Notes

Physical Quantities and Measurement Techniques

• Scalars vs Vectors:     * Scalars: Physical quantities that have only magnitude (size) but no direction. Examples: Distance, speed, mass, energy, time, and temperature.     * Vectors: Physical quantities that have both magnitude and direction. Examples: Displacement, velocity, weight, force, acceleration, and momentum.
• SI Base Units and Derived Units:     * The International System of Units (SI) defines base units: length (meter, $m$), mass (kilogram, $kg$), time (second, $s$), temperature (kelvin, $K$), and electric current (ampere, $A$).     * Derived units are combinations of base units: speed ($m/s$), acceleration ($m/s^2$), force (newton, $N$ or $kg\,m/s^2$), and pressure (pascal, $Pa$).
• Standard Prefixes:     * Giga (G): $10^9$     * Mega (M): $10^6$     * Kilo (k): $10^3$     * Milli (m): $10^{-3}$     * Micro (\mu): $10^{-6}$     * Nano (n): $10^{-9}$
• Resultant Vectors at Right Angles:     * When two vectors act at right angles (perpendicularly), the resultant vector ($R$) can be calculated using the Pythagorean theorem and trigonometry.     * Example: If $F_x = 4.0\,N$ and $F_y = 3.0\,N$, then $R = \sqrt{F_x^2 + F_y^2} = \sqrt{4.0^2 + 3.0^2} = 5.0\,N$.
• Measurement and Uncertainty:     * Length: Measured using rulers (precision to $1\,mm$) or micrometers for very small thicknesses.     * Volume: Measured using a measuring cylinder (read the bottom of the meniscus at eye level to avoid parallax error).     * Time: For periodic events like a pendulum, measure the time for 10 oscillations and divide by 10 to find the period ($T$). Formula: $T = \frac{\text{Total Time}}{\text{Number of Oscillations}}$. Example: For 10 oscillations taking $12.5\,s$, $T = 12.5 / 10 = 1.25\,s$.     * Uncertainty/Precision: Always state measurements with the correct number of significant figures. Avoid parallax error by ensuring your line of sight is perpendicular to the scale.

Kinematics: Motion and Graphs

• Speed and Velocity:     * Speed: A scalar quantity; $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$.     * Velocity: A vector quantity; $v = \frac{\Delta s}{t}$, where $\Delta s$ is displacement.
• Acceleration:     * Acceleration ($a$) is the rate of change of velocity.     * Formula: $a = \frac{\Delta v}{\Delta t} = \frac{v - u}{t}$, where $v$ is final velocity and $u$ is initial velocity.     * Deceleration: Negative acceleration occurring when an object slows down.     * Velocity-Displacement Equation: $v^2 = u^2 + 2as$.
• Graph Analysis Rules:     * Distance-Time Graph: The gradient represents speed. A horizontal line means stationary; a straight sloped line means constant speed.     * Velocity-Time (v-t) Graph:         * The gradient represents acceleration.         * The area under the curve represents the total distance traveled.     * Worked Graph Example:         * Acceleration (Gradient): Calculate using $\frac{rise}{run}$.         * Distance (Area): Calculate using geometric shapes (triangles/rectangles) under the line.         * Average Speed: $\text{Avg Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$. Example result: $15.2\,m/s$.
• Free Fall and Terminal Velocity:     * Free Fall (Vacuum): Objects fall with constant acceleration $g$ (approx. $9.8\,m/s^2$ or $10\,m/s^2$ depending on syllabus version) regardless of mass.     * Air Resistance: As speed increases, air resistance increases.     * Terminal Velocity: When the upward air resistance equals the downward weight, the resultant force is zero. The object stops accelerating and falls at a constant terminal velocity.     * Skydiver Story:         1. Skydiver jumps: Acceleration is max as weight > air resistance.         2. Speed increases: Air resistance increases; acceleration decreases.         3. Terminal velocity reached: Weight = Air Resistance.         4. Parachute opens: Massive air resistance causes deceleration. New, lower terminal velocity is reached for safe landing.

Mass, Weight, and Density

• Mass vs Weight:     * Mass ($m$): The amount of matter in an object, measured in kilograms ($kg$). It is constant regardless of location.     * Weight ($W$): The gravitational force acting on a mass, measured in newtons ($N$).     * Gravitational Field Strength ($g$): The force per unit mass. Formula: $g = \frac{W}{m}$.     * On Earth, $g \approx 9.8\,N/kg$ (or $10\,N/kg$). Formula: $W = mg$.
• Density (\rho):     * Definition: Mass per unit volume. Formula: $\rho = \frac{m}{V}$. Units: $kg/m^3$ or $g/cm^3$.
• Experimental Methods for Density:     1. Regular Solid: Measure mass with a balance. Measure dimensions ($l, w, h$) with a ruler. Volume $V = l \times w \times h$.     2. Liquid: Measure mass of empty cylinder ($m_1$), fill with liquid, measure mass again ($m_2$). $m = m_2 - m_1$. Read volume ($V$) from the scale.     3. Irregular Solid (Displacement Method): Measure mass ($m$). Submerge solid in a displacement (eureka) can or measuring cylinder with water. The volume of displaced water equals the volume of the solid.
• Floating and Sinking: An object floats if its density is less than the density of the fluid it is in. Example: A density of $1.25\,g/cm^3$ will sink in water ($1.0\,g/cm^3$).

Forces, Momentum, and Pressure

• Effects of Forces:     * Forces can change the shape, speed, or direction of an object.     * Hooke's Law: The extension of a spring ($x$) is proportional to the applied load ($F$), provided the limit of proportionality is not exceeded. Formula: $F = kx$ (where $k$ is the spring constant in $N/m$ or $N/cm$).
• Newton's Laws:     1. Newton's 1st Law (Inertia): An object remains at rest or constant velocity unless acted upon by a resultant force.     2. Newton's 2nd Law: Force equals mass times acceleration ($F = ma$).     3. Newton's 3rd Law: For every action, there is an equal and opposite reaction.
• Circular Motion: A constant force acting perpendicular to the velocity (centripetal force) causes an object to move in a circle. The speed remains constant, but the velocity changes because the direction changes.
• Turning Effect (Moments):     * Moment: A measure of the turning effect of a force. Formula: $\text{Moment} = F \times d$, where $d$ is the perpendicular distance from the pivot.     * Equilibrium: For an object to be in equilibrium, the resultant force must be zero AND the principle of moments must apply: $\text{Sum of clockwise moments} = \text{Sum of anticlockwise moments}$.     * Example calculation: $F_1 \times d_1 = F_2 \times d_2$. If $5\,N \times 0.8\,m = F_2 \times 0.6\,m$, then $4.0 = 0.6 F_2$, so $F_2 = 6.67\,N$.
• Centre of Gravity and Stability:     * Centre of Gravity (CoG): The point through which all the weight of an object acts.     * Stability: An object remains stable as long as the vertical line of action from the CoG falls within its base. If it falls outside, the object topples.
• Momentum and Impulse:     * Momentum ($p$): $p = mv$. Units: $kg\,m/s$.     * Conservation of Momentum: In a closed system, the total momentum before a collision equals the total momentum after ($m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$).     * Impulse: The change in momentum. Formula: $\text{Impulse} = \Delta p = F \Delta t = m(v - u)$.     * Average Force: $F = \frac{\Delta p}{\Delta t}$.
• Pressure:     * Surfaces: $P = \frac{F}{A}$. Units: $Pa$ or $N/m^2$.     * Liquids: Pressure increases with depth. Formula: $\Delta p = \rho g \Delta h$.

Energy, Work, and Power

• Energy Stores: Chemical, kinetic ($KE$), gravitational potential ($GPE$), elastic, thermal, magnetic, electrostatic, and nuclear.
• Energy Transfers: Mechanically (force), electrically, by heating, or by radiation (waves).
• Key Equations:     * Kinetic Energy: $KE = \frac{1}{2}mv^2$     * Gravitational Potential Energy: $GPE = mgh$
• Conservation of Energy: Energy cannot be created or destroyed, only transferred from one store to another. Total energy remains constant.
• Work and Power:     * Work Done ($W$): Energy transferred by a force. Formula: $W = F \times d$.     * Power ($P$): The rate at which work is done. Formula: $P = \frac{W}{t} = \frac{\Delta E}{t}$. Units: Watts ($W$).
• Efficiency: $\text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100\%$.
• Energy Resources:     * The Sun: The primary source of energy for most processes on Earth (excluding tidal, geothermal, and nuclear). Energy is released in the Sun via Nuclear Fusion.

Thermal Physics

• Kinetic Particle Model:     * Solids: Particles in regular lattice; vibrate about fixed positions; strong intermolecular forces.     * Liquids: Randomly arranged; close together; slide past each other; intermediate forces.     * Gases: Far apart; move rapidly and randomly; negligible forces.     * Brownian Motion: The random movement of microscopic particles (e.g., smoke particles) resulting from collisions with invisible, fast-moving air molecules. This provides evidence for the kinetic particle model.
• Temperature:     * Temperature relates to the average kinetic energy of the particles.     * Absolute Zero: The coldest possible temperature ($-273\,^{\circ}C$ or $0\,K$), where particles have zero kinetic energy.     * Conversion: $T(K) = \theta(^{\circ}C) + 273$.
• Gases and Boyle's Law:     * For a fixed mass of gas at constant temperature: $pV = \text{constant}$ (or $p_1V_1 = p_2V_2$).
• Thermal Expansion:     * Gases expand the most, solids the least. Particles gain kinetic energy and vibrate/move more, increasing the average separation.     * Bimetal Strip: Used in thermostats; two metals bonded together expand at different rates, causing the strip to bend.
• Specific Heat Capacity (SHC):     * The energy required to raise the temperature of $1\,kg$ of a substance by $1\,^{\circ}C$.     * Formula: $c = \frac{\Delta E}{m \Delta \theta}$. Units: $J/(kg\,^{\circ}C)$.
• Phase Changes:     * Melting and Boiling: Occur at plateaus on a heating curve where temperature remains constant as energy is used to break intermolecular bonds.     * Evaporation vs Boiling:         * Boiling: Throughout the liquid; occurs at a specific boiling point; requires heat source.         * Evaporation: At the surface only; occurs at any temperature; uses internal energy of the liquid, causing cooling (e.g., sweating).
• Thermal Energy Transfer:     * Conduction: Lattice vibrations and free electron transfer (in metals).     * Convection: Circulation of density currents in fluids (liquids and gases).     * Radiation: Infrared (IR) radiation; travels as EM waves; needs no medium. Black/dull surfaces are the best emitters and absorbers; white/shiny surfaces are the best reflectors.

Properties of Waves

• Wave Terms:     * Wavelength (\lambda): Distance between two consecutive peaks.     * Frequency ($f$): Number of waves passing a point per second ($Hz$).     * Amplitude: Max displacement from rest position.     * Wave Equation: $v = f \lambda$.
• Wave Types:     * Transverse: Vibration perpendicular to energy transfer (e.g., Light, EM waves, water ripples).     * Longitudinal: Vibration parallel to energy transfer (e.g., Sound, seismic P-waves).
• Wave Behaviors:     * Reflection: $\text{Angle of incidence} (i) = \text{Angle of reflection} (r)$.     * Refraction: Change in speed and direction entering a different medium. When entering a slower, denser medium, waves bend towards the normal.     * Diffraction: Spreading of waves through a gap or around an obstacle. Maximum diffraction occurs when gap size $\approx \lambda$.
• Light:     * Snell's Law: $\text{Refractive index } (n) = \frac{\sin(i)}{\sin(r)} = \frac{c}{v}$.     * Total Internal Reflection (TIR): Occurs when moving from dense to less dense medium if the angle of incidence > critical angle ($c$). Formula: $n = \frac{1}{\sin(c)}$.     * Lenses: Converging (convex) lenses can produce real and virtual images. Diverging (concave) lenses produce only virtual images.     * Dispersion: Splitting of white light into the spectrum (ROYGBIV) due to different refractive indices for different wavelengths.

Electromagnetic (EM) Spectrum and Sound

• EM Spectrum Order (Increasing Frequency/Decreasing Wavelength):     1. Radio Waves (Broadcasting)     2. Microwaves (Heating, Satellite communication)     3. Infrared (Heating, Night vision, Remote controls)     4. Visible Light (Vision, Optical fibers)     5. Ultraviolet (Tanning, Sterilizing water)     6. X-rays (Medical imaging, Security)     7. Gamma Rays (Cancer treatment, Sterilizing equipment)
• Sound:     * Longitudinal mechanical waves. Human hearing range: $20\,Hz$ to $20,000\,Hz$.     * Ultrasound: Frequencies above $20,000\,Hz$; used in sonar and medical scans.     * Echo Calculation: $\text{Distance} = \frac{v \times t}{2}$.

Electricity and Magnetism

• Magnetism: Like poles repel, opposite poles attract. Magnetic field lines point from North to South.
• Electrical Quantities:     * Current ($I$): Rate of flow of charge ($I = Q/t$).     * Voltage ($V$): Energy per unit charge ($V = W/Q$).     * Ohm's Law: $V = IR$ (for an ohmic conductor).     * Resistance of a Wire: $R \propto \text{length}$ and $R \propto 1 / \text{cross-sectional area}$.
• Circuit Rules:     * Series: $I_{total} = I_1 = I_2$; $V_{supply} = V_1 + V_2$; $R_{total} = R_1 + R_2$.     * Parallel: $I_{total} = I_1 + I_2$; $V_{supply} = V_1 = V_2$; $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}$.
• Electromagnetic Induction:     * An EMF is induced when a conductor cuts magnetic field lines.     * Lenz's Law: The induced current acts to oppose the change that created it.     * Transformers: $\frac{V_p}{V_s} = \frac{N_p}{N_s}$ and for 100% efficiency $V_p I_p = V_s I_s$.

Nuclear Physics and Space

• Atomic Structure: Nucleus contains protons ($+1$ charge, $1\,u$ mass) and neutrons ($0$ charge, $1\,u$ mass). Electrons ($-1$ charge, negligible mass) orbit in shells.
• Radioactivity:     * Alpha (\alpha): Helium nucleus ($^4_2He$); high ionizing power; stopped by paper.     * Beta (\beta^-): Fast electron ($^0_{-1}e$); medium ionizing; stopped by aluminum.     * Gamma (\gamma): EM wave; low ionizing; reduced by thick lead.     * Half-Life: Time taken for the activity or number of nuclei to halve.
• Nuclear Reactions:     * Fission: Splitting a heavy nucleus (e.g., Uranium-235) into smaller nuclei and neutrons, releasing energy.     * Fusion: Joining light nuclei (e.g., Hydrogen) to form a heavier nucleus (Helium), releasing massive energy; powers stars.
• Space Physics:     * Orbital Speed: $v = \frac{2\pi r}{T}$.     * Stellar Life Cycle: Nebula $\rightarrow$ Protostar $\rightarrow$ Main Sequence $\rightarrow$ Red Giant/Supergiant $\rightarrow$ White Dwarf/Supernova/Black Hole.     * Hubble's Law: $\text{Recessional velocity} (v) = H_0 \times \text{distance} (d)$.     * Age of the Universe: Estimated as $\frac{1}{H_0} \approx 13.8 \text{ billion years}$.

Questions & Discussion

• Hard Exam-Style Question 1: Determine resultant force on a braking car on an incline. Use $F = ma$. Calculate distance via area under v-t graph and work done via $W = Fd$.
• Exam-Style Question (Nuclear decay): Balance a beta-minus decay equation for Carbon-14: $^{14}<em>6C \rightarrow ^{14}_7N + ^0</em>{-1}e$.
• Question (Space Distances): Convert Light-years to km. $1\,ly \approx 9.5 \times 10^{12}\,km$.