O Level Physics Topical Revision Notes

Topic 1: Physical Quantities, Units and Measurement

• Physical quantities consist of two parts: numerical magnitude and a unit.
  • Formally: a physical quantity = magnitude + unit. For example, a length of 5 meters consists of the magnitude 5 and the unit meter.
• Classification of quantities
  • Basic (fundamental) quantities and SI base units:
  • length → unit: metre (m)
  • mass → kilogram (kg)
  • time → second (s)
  • thermodynamic temperature → kelvin (K)
  • amount of substance → mole (mol)
  • current → ampere (A)
  • Derived quantities – defined in terms of base quantities via equations; their SI units are derived from the base units.
  • For example, speed is derived from length/time, with the unit m/s.
• Prefixes and orders of magnitude (SI prefixes)
  • Common prefixes and symbols (factor):
  • Tera (T) $10^{12}$
  • Giga (G) $10^{9}$
  • Mega (M) $10^{6}$
  • Kilo (k) $10^{3}$
  • Deci (d) $10^{-1}$
  • Centi (c) $10^{-2}$
  • Milli (m) $10^{-3}$
  • Micro (µ) $10^{-6}$
  • Nano (n) $10^{-9}$
  • Pico (p) $10^{-12}$
  • The syllabus highlights the bolded ones (the ones listed above).
  • Example: Converting 5 km to meters: $5 \text{ km} = 5 \times 10^3 \text{ m}$. Converting 200 mA to Amperes: $200 \text{ mA} = 200 \times 10^{-3} \text{ A} = 0.2 \text{ A}$.
• Orders of magnitude and estimation
  • Used to compare sizes from atomic scales to astronomical scales.
  • Examples:
  • Diameter of an atom: $10^{-10} \text{ m}$
  • Thickness of human hair: $10^{-5} \text{ m}$
  • Height of a human: $10^0 \text{ m}$ (or ~1 meter)
  • Diameter of Earth: $10^7 \text{ m}$
  • Distance to the Sun: $10^{11} \text{ m}$
• Scalars vs. vectors
  • Scalar: magnitude only (e.g., mass = 5 kg, distance = 10 m, time = 2 s, speed = 5 m/s, work = 10 J, energy = 50 J).
  • Vector: magnitude and direction (e.g., weight = 50 N downwards, displacement = 10 m East, velocity = 5 m/s North, acceleration = 2 m/s$^2$ upwards, force = 20 N at $30^\circ$ from horizontal).
• Addition of vectors (graphical and analytical)
  • Resultant R of two perpendicular vectors F1 and F2:
  • Magnitude: $R = \sqrt{F<em>1^2 + F</em>2^2}$
  • Direction: $\tan\theta = \frac{F<em>1}{F</em>2}$ (angle above the horizontal, for example)
  • Example: A force $F<em>1 = 3\text{ N}$ acting East and a force $F</em>2 = 4\text{ N}$ acting North.
  • The resultant magnitude $R = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\text{ N}$.
  • The direction $\theta = \tan^{-1}\left(\frac{4}{3}\right) \approx 53.1^\circ$ North of East.
  • Graphical method: parallel–parallelogram rule, scale drawing, then measure the resultant.
• Measurement of length and time
  • Instruments and accuracy:
  • Measuring tape, rule ($\pm 0.1\text{ cm}$). Used for lengths from a few cm to several meters.
  • Micrometers (typically $\pm 0.01\text{ mm}$) and vernier calipers (typically $\pm 0.01\text{ cm}$).
    • Micrometers measure very small dimensions like the thickness of a wire or a sheet of paper.
    • Vernier calipers measure external/internal diameters or depths of objects.
  • Time: stopwatches; accuracy depends on the instrument and procedure. Digital stopwatches can read to 0.01 s.
• Parallax errors and accuracy concepts
  • Parallax error arises from incorrect eye position or non-contact with the scale; correct positioning (eye level, perpendicular to scale) minimizes parallax.
  • Accuracy refers to how close a measurement is to the true value.
• Vernier calipers
  • Used to measure external diameter, thickness, etc., with precision $\pm 0.01\text{ cm}$.
  • Jaws: external jaws measure external dimensions; internal jaws measure internal dimensions; tail measures depth.
  • Zero error and correction procedures are important.
  • Positive Zero Error: When jaws are closed, the vernier zero mark is to the right of the main scale zero mark. Example: Vernier zero is at 0.04 cm. The reading will be (measured value - 0.04 cm).
  • Negative Zero Error: When jaws are closed, the vernier zero mark is to the left of the main scale zero mark. Example: Vernier zero is at -0.02 cm. The reading will be (measured value - (-0.02 cm) = measured value + 0.02 cm).
• Micrometer screw gauge
  • Measures very small lengths with precision; reading = main scale + circular (thimble) scale; zero error checks required.
  • Example reading: If the main scale reads 3.5 mm and the thimble scale aligns with 25 (meaning 0.25 mm), the reading is $3.5 \text{ mm} + 0.25 \text{ mm} = 3.75 \text{ mm}$. Apply zero correction if necessary.
• Period of oscillation of a simple pendulum
  • Definitions:
  • One oscillation: one complete to-and-fro movement from A to B to C and back to A.
  • Period T: time for one complete oscillation.
  • Amplitude: maximum displacement from rest position.
  • Period formula (near-earth gravity):
  • $T = 2\pi \sqrt{\frac{l}{g}}$
  • Note: This formula is for small angles of oscillation (<10^\circ).
  • Example: A pendulum with length $l = 0.99\text{ m}$ on Earth ($g \approx 9.81\text{ m s}^{-2}$) will have a period $T = 2\pi \sqrt{\frac{0.99}{9.81}} \approx 2.00\text{ s}$.

Topic 2: Kinematics

• Scalars and vectors: Distance vs. displacement; Speed vs. velocity.
  • Distance: scalar; total path length covered. E.g., walking 5m North then 3m South, distance = 8m.
  • Displacement: vector; straight-line distance from start to end, with direction. E.g., for the above, displacement = 2m North.
  • Speed: scalar; rate of change of distance. E.g., 10 m/s.
  • Velocity: vector; rate of change of displacement. E.g., 10 m/s East.
• Key definitions and equations
  • Speed: $\text{speed} = \frac{\text{distance travelled}}{t}$
  • Average speed: $v_{\text{avg}} = \frac{\text{Total distance travelled}}{\text{Total time taken}}$
  • Velocity: rate of change of displacement; average velocity: $v_{\text{avg}} = \frac{\Delta x}{\Delta t}$ (where $\Delta x$ is displacement and $\Delta t$ is time interval).
  • Example: A car travels 100 km in 2 hours. Its average speed is $100\text{ km} / 2\text{ h} = 50\text{ km/h}$.
• Acceleration
  • Acceleration: $a = \frac{\Delta v}{\Delta t}$ (rate of change of velocity).
  • Acceleration is a vector quantity (magnitude and direction). Positive for increasing velocity in a given direction, negative for decreasing velocity (deceleration) or increasing velocity in the opposite direction.
  • Example: A car increases its speed from 10 m/s to 20 m/s in 5 seconds. Its acceleration is $\frac{(20 - 10)\text{ m/s}}{5\text{ s}} = 2\text{ m s}^{-2}$.
• Graphical analysis of motion
  • Distance–time graph:
  • gradient = speed. A straight line indicates constant speed; a curved line indicates changing speed (acceleration).
  • Speed–time graph:
  • gradient = acceleration. A horizontal line means constant speed (zero acceleration).
  • area under the graph = displacement.
  • Example: A speed-time graph with a trapezoidal shape (initial speed u, final speed v, time t) has area = $\frac{1}{2}(u+v)t$, which is the displacement.
• Special results and concepts
  • Free-fall near the Earth's surface: acceleration due to gravity (g) is constant $\approx 10\text{ m s}^{-2}$ (approximate value used in the notes, more precisely $9.81\text{ m s}^{-2}$).
  • Terminal velocity: when air resistance equals weight, net force is zero and acceleration becomes zero; velocity becomes constant. This occurs for falling objects in a fluid (e.g., skydiver).
• Examples from the notes
  • Example 2.1 (car path O to D): Imagine a car travels along a semi-circular path from point O to point D. If the path length is 314 m, this is the distance. If the straight-line distance from O to D is 200 m directly East, this is the car's displacement ($200\text{ m East}$).
  • Example 2.4–2.6: These examples involve calculating displacement from velocity-time graphs. For instance, if a car accelerates uniformly from rest to 20 m/s in 10 s, the displacement is the area of the triangle: $\frac{1}{2} \times 10\text{ s} \times 20\text{ m/s} = 100\text{ m}$. If it then brakes to a stop, the negative gradient (deceleration) would be calculated, and the area under that part of the graph (a triangle or trapezium) would be the displacement during braking.

Topic 3: Dynamics

• Force and motion
  • A force is a push or pull, measured in newtons (N).
  • Contact force (normal force) upwards balances weight in contact with a surface. E.g., a book on a table experiences an upward normal force from the table.
  • Free body diagrams are used to represent forces on an object. All forces acting on the object are drawn as arrows from its center of mass.
• Newton’s Laws
  • First Law (equilibrium): A body at rest or moving with constant velocity experiences no resultant force.
  • Example: A book lying still on a table, or a satellite moving at constant velocity in space far from gravitational influences.
  • Second Law: Resultant force equals mass times acceleration:
  • $\mathbf{F}_{\text{net}} = m\mathbf{a}$
  • Example: A 10 kg block is pushed by a 20 N force. Its acceleration is $a = F/m = 20\text{ N} / 10\text{ kg} = 2\text{ m s}^{-2}$.
  • Third Law: For every action, there is an equal and opposite reaction.
  • Example: When you push against a wall (action force), the wall pushes back on you with an equal and opposite force (reaction force).
• Balanced vs. unbalanced forces
  • Balanced: net force = 0 N $\rightarrow$ no change in motion (object remains at rest or moves with constant velocity).
  • Example: A car cruising at a steady speed on a flat road, where engine thrust equals air resistance and friction.
  • Unbalanced: net force $\neq 0 \rightarrow$ acceleration occurs (velocity changes).
  • Example: A car accelerating from rest, where engine thrust is greater than resistive forces.
• Friction
  • Friction opposes motion between surfaces in contact. It depends on the nature of the surfaces and the normal force.
  • Advantages: enables walking, braking in vehicles, holding objects, starting a car (tires grip the road).
  • Disadvantages: causes wear and energy loss (e.g., heat in engine parts); requires more energy to move objects on rough surfaces.
  • Ways to overcome friction: lubricants (e.g., oil in engines), ball bearings (in wheels), smoother surfaces (polishing).
• Dynamics examples
  • Example 3.2: Pulling a block: A 50 N weight (mass $m = 50\text{ N} / 10\text{ m s}^{-2} = 5\text{ kg}$) is on a rough surface. A horizontal applied force $F_1 = 12\text{ N}$ pulls it, and friction $f = 2\text{ N}$ opposes it.
  • The horizontal resultant force = $F_1 - f = 12\text{ N} - 2\text{ N} = 10\text{ N}$.
  • The acceleration $a = F_{\text{net}}/m = 10\text{ N} / 5\text{ kg} = 2\text{ m s}^{-2}$.
  • Example 3.3: Circular motion: An object moving in a circle at constant speed experiences centripetal acceleration toward the center of the circle. This acceleration is caused by a resultant force (centripetal force) also directed toward the center. This force is often provided by tension in a string, gravity, or friction.
  • Example 3.4: Skydiver: A skydiver initially has weight Q greater than air resistance P, so they accelerate downwards. As their speed increases, P increases until eventually P = Q. At this point, the net force is zero, and the skydiver reaches terminal velocity.

Topic 4: Mass, Weight and Density

• Mass
  • A measure of the amount of substance in a body; SI unit: kg; scalar quantity; depends on size and constituent atoms.
  • Mass is an intrinsic property of an object and does not change with location.
• Inertia
  • The resistance of a body to changes in its state of rest or motion; proportional to mass. A more massive object has greater inertia and is harder to accelerate or decelerate.
• Gravitational field strength (g)
  • Defined as gravitational force per unit mass: $g = \frac{F}{m}$ (near the Earth’s surface $\approx 9.8\text{ N kg}^{-1}$, often approximated as $10\text{ N kg}^{-1}$ for calculations).
  • Example: On the Moon, $g \approx 1.6\text{ N kg}^{-1}$, so an object weighs less there.
• Weight (W)
  • Gravitational force on a body: $W = mg$.
  • Compared to mass: mass is intrinsic; weight depends on location (gravitational field). E.g., a person with a mass of 70 kg has a weight of $70\text{ kg} \times 9.8\text{ N kg}^{-1} = 686\text{ N}$ on Earth, but only $70\text{ kg} \times 1.6\text{ N kg}^{-1} = 112\text{ N}$ on the Moon.
• Density ($\rho$)
  • Defined as mass per unit volume: $\rho = \frac{m}{V}$; SI unit: kg m$^{-3}$. (Also commonly g cm$^{-3}$).
  • Example: A block of material has a mass of 500 g and a volume of 200 cm$^3$. Its density is $500\text{ g} / 200\text{ cm}^3 = 2.5\text{ g cm}^{-3}$.
• Buoyancy: an object floats if its density is less than the surrounding liquid (e.g., wood in water, since $\rho<em>{\text{wood}} < \rho</em>{\text{water}}$). An object sinks if more dense (e.g., a rock in water, since $\rho<em>{\text{rock}} > \rho</em>{\text{water}}$).

Topic 5: Turning Effect of Forces

• Moment of a force (torque)
  • Turning effect about a pivot: $\text{Moment} = F \times d$ where d is the perpendicular distance from pivot to line of action of the force.
  • SI unit of moment: N m.
  • Example: A 10 N force applied at the end of a 0.5 m spanner, perpendicular to the spanner, creates a moment of $10\text{ N} \times 0.5\text{ m} = 5\text{ N m}$.
• Equilibrium and the Principle of Moments
  • For an object in equilibrium (at rest or constant angular velocity):
  • The sum of clockwise moments about any point equals the sum of anticlockwise moments about that point: sum of moments = 0.
  • Example: A uniform plank of length 2 m and weight 20 N is pivoted at its center. If a 10 N weight is placed 0.5 m from the pivot on one side, a 10 N force needs to be applied 0.5 m from the pivot on the other side to keep it balanced ($10\text{ N} \times 0.5\text{ m}$ clockwise = $10\text{ N} \times 0.5\text{ m}$ anticlockwise).
• Centre of Gravity (C.G.)
  • The point where the whole weight appears to act.
  • The C.G. can lie outside the object, depending on shape.
  • Example: For a ring or a hollow cylinder, the C.G. is in the empty space at the center. For an L-shaped object, the C.G. is typically outside the material itself.
  • Its position influences stability.
• Stability
  • Stability is the ability of an object to return to its original position after a small displacement.
  • Stability criteria depend on base area, height of the centre of gravity, and contact area with the surface.
• Ways to improve stability
  • Lower the center of gravity. (e.g., racing cars have very low C.G.).
  • Increase the base area. (e.g., the wide base of a pyramid makes it very stable).

Topic 6: Pressure

• Pressure definition
  • Pressure = Force / Area; units: Pascal (Pa) = N m$^{-2}$.
  • Example: A 100 N force applied over an area of $0.1\text{ m}^2$ creates a pressure of $100\text{ N} / 0.1\text{ m}^2 = 1000\text{ Pa}$.
• Liquid pressure and hydrostatics
  • Pressure at depth in a liquid: $P = P<em>0 + \rho gh$, where $P</em>0$ is atmospheric pressure, $\rho$ is liquid density, $g$ is gravitational field strength, and $h$ is fluid depth.
  • In a liquid at rest, pressure is the same along any horizontal line (same depth). This is why water finds its own level.
  • Example: The pressure at a depth of 5 m in water ($\rho = 1000\text{ kg m}^{-3}$, $g = 10\text{ N kg}^{-1}$) is $P = P<em>0 + (1000 \times 10 \times 5) = P</em>0 + 50000\text{ Pa}$.
• Transmission of pressure in hydraulic systems
  • Incompressible fluid in a container transmits pressure in all directions (Pascal's Principle).
  • Basic hydraulic relation: $\frac{F<em>1}{A</em>1} = \frac{F<em>2}{A</em>2}$ when pistons areas are A1 and A2 and F1, F2 are the respective forces.
  • This principle allows lifting heavy loads using hydraulic systems (e.g., car jacks, hydraulic brakes).
  • Example: If $F<em>1 = 10\text{ N}$ is applied to a piston with area $A</em>1 = 0.01\text{ m}^2$, the pressure is $1000\text{ Pa}$. If this pressure acts on a larger piston with area $A<em>2 = 1\text{ m}^2$, the output force $F</em>2 = P \times A_2 = 1000\text{ Pa} \times 1\text{ m}^2 = 1000\text{ N}$, allowing a small force to generate a large force.
• Atmospheric pressure
  • Pressure exerted by the weight of air: measured with mercury barometer.
  • At sea level, standard atmosphere corresponds to 760 mm Hg ($\approx 1.01 \times 10^5\text{ Pa}$).
• Manometer
  • Instrument to measure gas pressure differences; uses height difference h and density $\rho$ of the manometer liquid: $P<em>1 = P</em>0 + \rho gh$ (if the gas pressure $P<em>1$ is greater than atmospheric pressure $P</em>0$ and pushes the liquid column down on its side).
  • Example: If a gas creates a height difference of 10 cm ($0.1\text{ m}$) in a mercury manometer ($\rho_{\text{Hg}} = 13600\text{ kg m}^{-3}$), the gauge pressure is $\rho gh = 13600 \times 10 \times 0.1 = 13600\text{ Pa}$.

Topic 7: Energy, Work and Power

• Forms of energy
  • Kinetic energy (KE), elastic potential energy, gravitational potential energy (GPE), chemical potential energy, thermal energy, electrical energy, nuclear energy, etc.
• Conservation of energy
  • The total energy in a closed system remains constant; energy converts between forms without net loss.
  • Example: A falling object converts GPE to KE; a pendulum converts GPE to KE and back.
• Kinetic energy and potential energy
  • KE: $K_E = \frac{1}{2} m v^2$
  • Example: A 2 kg object moving at 5 m/s has $K_E = \frac{1}{2} \times 2 \times 5^2 = 25\text{ J}$.
  • GPE (reference at Earth’s surface): $U = m g h$
  • Example: A 2 kg object raised 3 m above the ground ($g = 10\text{ N kg}^{-1}$) has $U = 2 \times 10 \times 3 = 60\text{ J}$.
• Work and power
  • Work done by a force: $W = F s$ (displacement in the direction of the force). If the force is not parallel to displacement, $W = Fs \cos\theta$.
  • Power: $P = \frac{W}{t}$; SI unit: W = J s$^{-1}$.
  • Example: A 50 N force pushes a box 10 m in 5 seconds. Work done = $50\text{ N} \times 10\text{ m} = 500\text{ J}$. Power = $500\text{ J} / 5\text{ s} = 100\text{ W}$.
• Efficiency
  • Efficiency of energy conversion: $\eta = \frac{\text{useful output energy}}{\text{total input energy}} \times 100\%$. Also, $\eta = \frac{\text{useful output power}}{\text{total input power}} \times 100\%$.
  • Example: A light bulb uses 100 J of electrical energy and produces 5 J of light energy. Its efficiency is $\frac{5\text{ J}}{100\text{ J}} \times 100\% = 5\%$.

Topic 8: Kinetic Model of Matter

• States of matter (qualitative comparison)
  • Solids: definite volume and shape; particles vibrate about fixed positions; densest (generally); strong inter-molecular forces.
  • Liquids: definite volume, take shape of container; particles can flow past each other; moderate forces; less dense than solids (generally).
  • Gases: no definite volume or shape; particles far apart; negligible intermolecular forces; compressible; move freely and randomly; least dense.
• Brownian motion
  • Random, irregular motion of microscopic particles suspended in fluids due to collisions with fast-moving, invisible fluid molecules.
  • Example: Smoke particles observed under a microscope moving erratically due to collisions with air molecules.
• Gas pressure and molecular model
  • Gas pressure arises from molecules colliding with container walls; increasing number of molecules, their speeds (related to temperature), or molecular mass increases pressure.
• Gas relationships (qualitative gas laws)
  • For a fixed amount of gas at constant volume, increasing temperature increases pressure (P $\propto$ T) (Gay-Lussac's Law).
  • For a fixed mass of gas at constant pressure, increasing temperature increases volume (V $\propto$ T) (Charles's Law).
  • For a fixed mass of gas at constant temperature, increasing volume decreases pressure (P $\propto$ 1/V) (Boyle's Law).
  • These lead to the relation $P<em>1V</em>1 = P<em>2V</em>2$ when T is constant, etc. (Combined Gas Law: $\frac{P<em>1V</em>1}{T<em>1} = \frac{P</em>2V<em>2}{T</em>2}$).
  • Example (Boyle's Law): A gas at 1 atm has a volume of 10 L. If its volume is compressed to 5 L at constant temperature, its new pressure will be 2 atm ($1 \times 10 = P2 \times 5 \implies P2 = 2$).

Topic 9: Transfer of Thermal Energy

• Three modes of heat transfer
  • Conduction: through direct contact; particles transfer energy by vibrating against neighbors. Metals are good conductors due to free electrons; liquids/gases are poor conductors.
  • Example: A metal spoon quickly gets hot when placed in hot soup.
  • Convection: in fluids (liquids and gases); warmer, less dense regions rise and cooler, denser regions sink, setting up currents.
  • Example: Boiling water in a pot (hot water rises, cool water sinks); sea breezes and land breezes created by differential heating of land and sea.
  • Radiation: transfer of energy by electromagnetic waves (infrared); does not require a medium and can travel through a vacuum; rate affected by colour/texture/area.
  • Example: Feeling the heat from a distant campfire; the Sun's energy reaching Earth.
• Applications
  • Greenhouses trap solar radiation; cooking utensils made of good conductors; insulating flasks minimize heat transfer.
• Vacuum flask
  • Optimally reduces heat transfer by all three modes:
  • Vacuum between double walls: eliminates conduction and convection.
  • Silvered/reflective inner surfaces: minimize heat transfer by radiation.
  • Stopper (cork/plastic): reduces heat loss by conduction and convection through the opening.

Topic 10: Temperature

• Temperature and scales
  • Temperature measured in Kelvin (K); relation to Celsius: $\theta<em>K = \theta</em>{{^{\circ}\text{C}}} + 273.15$. Absolute zero (0 K or $-273.15^{\circ}\text{C}$) is the lowest possible temperature.
  • Example: $20^{\circ}\text{C}$ is equivalent to $20 + 273.15 = 293.15\text{ K}$.
• Measurement and thermometric properties
  • Thermometric properties used for temperature scales include:
  • Volume changes of liquids, e.g., mercury/alcohol. These expand uniformly with temperature.
  • EMF between different metals (thermocouples). The voltage produced depends on the temperature difference.
  • Resistance of metals (e.g., platinum resistance thermometers). Resistance typically increases with temperature.
• Common thermometers and ranges
  • Mercury/alcohol thermometers (common for everyday use; alcohol used for lower temperatures);
  • Thermocouples (wide range, fast response, e.g., for furnaces or engines);
  • Fixed points (ice point $0^{\circ}\text{C}$, steam point $100^{\circ}\text{C}$ at standard atmospheric pressure) are used for calibration.
• Temperature calibration
  • Ice point ($0^{\circ}\text{C}$) and steam point ($100^{\circ}\text{C}$) serve as fixed points; the range between these points is subdivided into 100 equal divisions for the Celsius scale.
• Thermocouples
  • Two junctions of dissimilar metals at different temperatures; voltages produced depend on temperature difference.
  • Advantages: wide range, robustness, small size, fast response, measurement at a point.
  • Example: Used to measure very high temperatures in industrial ovens where liquid-in-glass thermometers would melt.

Topic 11: Thermal Properties of Matter

• Internal energy
  • Sum of kinetic and potential energies of molecules within a substance; increases with temperature rise.
  • For an ideal gas, internal energy is purely kinetic.
• Heat capacity and specific heat capacity
  • Heat capacity: the energy required to raise the temperature of the substance by $1^{\circ}\text{C}$ (or 1 K): $C$ with units J $^{\circ}\text{C}^{-1}$ or J K$^{-1}$.
  • Specific heat capacity: energy required to raise the temperature of 1 kg of substance by $1^{\circ}\text{C}$ (or 1 K): $c$ with units J kg$^{-1} {^{\circ}\text{C}^{-1}}$ or J kg$^{-1}\text{ K}^{-1}$.
  • Formulas:
  • $Q = C \Delta \theta$
  • $Q = m c \Delta \theta$
  • Example: To raise the temperature of 2 kg of water ($c_{\text{water}} = 4200\text{ J kg}^{-1} {^{\circ}\text{C}^{-1}}$) by $10^{\circ}\text{C}$ requires $Q = 2 \times 4200 \times 10 = 84000\text{ J}$.
• Latent heat and phase changes
  • Latent heat is the energy absorbed or released during a phase change (e.g., melting, boiling) without a change in temperature.
  • Latent heat of fusion (melting/solidification): $Q = m L<em>f$ ($L</em>f$ is specific latent heat of fusion).
  • Latent heat of vaporisation (boiling/condensation): $Q = m L<em>v$ ($L</em>v$ is specific latent heat of vaporisation).
  • Melting/solidification and boiling/condensation occur at constant temperature (plateaus on heating/cooling curves) while energy is absorbed or released to break/form intermolecular bonds.
  • Example: To melt 1 kg of ice at $0^{\circ}\text{C}$ ($L_f = 3.34 \times 10^5\text{ J kg}^{-1})$) requires $Q = 1 \times 3.34 \times 10^5 = 334000\text{ J}$. The temperature remains $0^{\circ}\text{C}$ during this process.
• Types of internal energy by state
  • Solid: mainly vibrational kinetic + potential energy (due to fixed positions in a lattice).
  • Liquid: translational kinetic + potential energy (particles can move past each other).
  • Gas: mainly translational kinetic energy (particles are far apart, so potential energy due to intermolecular forces is negligible).
• Cooling curves
  • Illustrate temperature vs. time during cooling/heating, showing plateaus during phase changes. For a pure substance, the phase change occurs at a sharp, constant temperature. For a mixture, the phase change occurs over a range of temperatures.

Topic 12: General Wave Properties

• Wave motion and energy transfer
  • Waves involve oscillations that transfer energy without transferring matter.
  • Mechanical waves require a medium (e.g., sound waves, water waves); electromagnetic waves do not require a medium and can travel in vacuum (e.g., light waves).
  • Transverse waves (e.g., light) have oscillations perpendicular to wave propagation. Longitudinal waves (e.g., sound) have oscillations parallel to wave propagation.
• Key quantities
  • Speed (v): how fast the wave travels through the medium.
  • Frequency (f): number of oscillations per second (Hz).
  • Wavelength ($\lambda$): distance between two consecutive identical points on a wave.
  • Period (T): time for one complete oscillation ($T = 1/f$).
  • Amplitude (a): maximum displacement of a particle from its rest position.
  • Relationship: $v = f \lambda$
  • Data is often represented as wavefronts (plane or circular) and as sine curves for displacement vs. time or vs. distance.
  • Example: A sound wave with frequency 100 Hz in air (where $v \approx 330\text{ m/s}$) has a wavelength $\lambda = v/f = 330/100 = 3.3\text{ m}$.
• Wavefronts
  • A wavefront is a locus of points in phase; circular (near a point source) and plane (far from the source).

Topic 13: Light

• Reflection
  • Law: angle of incidence i equals angle of reflection r, with the incident ray, reflected ray, and normal all in the same plane.
  • Normal: imaginary line perpendicular to the reflecting surface at the point of incidence.
  • Example: If a light ray hits a plane mirror at an angle of $30^\circ$ to the normal, it will reflect at $30^\circ$ to the normal.
• Refraction
  • Snell’s Law: $n<em>1 \sin i = n</em>2 \sin r$ where n is the refractive index of the medium.
  • Refractive index definition: $n = \frac{c}{v}$ where c is the speed of light in vacuum ($\approx 3 \times 10^8\text{ m s}^{-1}$) and v is the speed in the medium.
  • Critical angle and total internal reflection: when light travels from a denser to a less dense medium, if the angle of incidence exceeds the critical angle (i > c), refraction ceases and total internal reflection occurs.
  • Example: Light entering water ($n<em>{\text{water}} = 1.33$) from air ($n</em>{\text{air}} = 1$) with an angle of incidence of $45^\circ$. $(1) \sin 45^\circ = (1.33) \sin r \implies \sin r = (\sin 45^\circ) / 1.33 \approx 0.5317 \implies r \approx 32.1^\circ$.
• Lenses and ray diagrams
  • Thin lenses: converging (convex, thicker in middle, focuses parallel rays to a focal point) and diverging (concave, thinner in middle, spreads parallel rays as if from a focal point).
  • Focal length f, optical centre C, principal axis, ray diagrams show how rays refract.
  • Real images (can be projected on a screen) and virtual images (cannot be projected, seen through the lens), magnification, and applications (e.g., telescope, camera, projector, magnifying glass).
  • Example: A converging lens can form a real, inverted image when the object is placed beyond the focal point, or a virtual, upright, magnified image (like a magnifying glass) when the object is within the focal point.
• Optical fibres
  • Utilize total internal reflection to transmit light with advantages: high data capacity, low interference, secure transmission, and flexibility.

Topic 14: Electromagnetic Spectrum

• Electromagnetic waves (EM waves)
  • All EM waves are transverse and travel at the speed of light in vacuum: $c \approx 3 \times 10^8 \text{ m s}^{-1}$.
  • Propagation does not require a medium; can travel in vacuum.
• Spectrum components (order of magnitude of wavelength and basic uses)
  • Organized by decreasing wavelength (increasing frequency/energy):
  • Radio waves: Longest wavelength ($\sim 10^3\text{ m}$-$10^{-1}\text{ m}$). Uses: broadcasting, communication, radar.
  • Microwaves: ($\sim 10^{-1}\text{ m}$-$10^{-3}\text{ m}$). Uses: cooking (microwave ovens), satellite communication, mobile phones.
  • Infrared (IR): ($\sim 10^{-3}\text{ m}$-$7 \times 10^{-7}\text{ m}$). Uses: remote controls, thermal imaging, optical fibres (heat), night vision, heating.
  • Visible light: ($\sim 7 \times 10^{-7}\text{ m}$-(red) to $4 \times 10^{-7}\text{ m}$(violet)). Uses: human vision, optical fibres, lasers, photography.
  • Ultraviolet (UV): ($\sim 4 \times 10^{-7}\text{ m}$-$10^{-8}\text{ m}$). Uses: sterilisation, sunbeds, fluorescent lamps, detecting forged currency.
  • X-rays: ($\sim 10^{-8}\text{ m}$-$10^{-12}\text{ m}$). Uses: medical imaging (radiography), security scans, crystallography.
  • Gamma rays ($\gamma$): Shortest wavelength (\sim <10^{-12}\text{ m}). Uses: sterilisation of medical equipment/food, cancer treatment (radiotherapy).
• Effects and hazards of EM radiation
  • Heating (IR, microwaves) and ionisation effects (UV, X-rays, gamma rays).
  • Higher frequency waves tend to be more energetic and potentially hazardous (e.g., ionising radiation can cause cell damage and cancer).

Topic 15: Sound

• Production and nature
  • Sound is produced by vibrating sources (e.g., vocal cords, guitar strings, speakers).
  • Longitudinal waves that require a medium for propagation (cannot travel in a vacuum).
• Medium and speed of sound
  • Speed of sound depends on the medium and its temperature/density:
  • Solids > Liquids > Gases (sound travels fastest in solids, slowest in gases).
  • Example: Speed of sound in air $\approx 330-340\text{ m/s}$, in water $\approx 1500\text{ m/s}$, in steel $\approx 5000\text{ m/s}$.
• Amplitude and frequency
  • Loudness is related to amplitude (larger amplitude means louder sound).
  • Pitch is related to frequency (higher frequency means higher pitch).
  • ($v = f \lambda$); for a constant speed, higher frequency means shorter wavelength and higher pitch.
• Determining the speed of sound in air
  • A basic method uses a timing apparatus and a known distance (e.g., firing a starting pistol at one end of a field, and a timer at the other end measures the time delay between seeing the flash and hearing the sound, then $v = \text{distance/time}$).
• Echoes
  • Sound waves reflecting off a surface. Distance measurement using echoes: time delay corresponds to twice the distance to the reflecting surface.
  • $2d = v \Delta t \implies d = \frac{v \Delta t}{2}$
  • Example: If an echo from a cliff is heard 4 seconds after a shout, and the speed of sound in air is 340 m/s, the distance to the cliff is $d = (340 \times 4) / 2 = 680\text{ m}$.
• Ultrasound
  • Frequencies above 20 kHz (beyond human hearing range).
  • Uses include prenatal scanning (imaging unborn babies), detecting flaws in materials (e.g., cracks in metal pipes), medical therapeutic uses, sonar (imaging underwater objects).

Topic 16: Static Electricity

• Electric charges
  • Charges are either positive (+) or negative (-); like charges repel, unlike charges attract.
  • Charge magnitude is measured in coulombs (C).
  • The total charge Q relates to number of electrons N via: $Q = N e$ where e is the elementary charge ($e = 1.6 \times 10^{-19} \text{ C}$ for a single electron).
• Charge transfer and rubbing
  • Rubbing (charging by friction) transfers electrons from one material to another, resulting in both objects becoming oppositely charged; nuclei do not move.
  • Insulators (e.g., plastic, glass) tend to retain charges on surfaces where they are generated.
  • Conductors (e.g., metals) allow charge redistribution across their surface.
  • Example: Rubbing a plastic rod with a cloth transfers electrons from the cloth to the rod, making the rod negatively charged and the cloth positively charged.
• Electric field
  • An electric field is a region in which a unit positive charge experiences a force. It is a force field.
  • Field is a vector quantity; electric field lines indicate the direction of force on a positive test charge. Field lines originate from positive charges and terminate on negative charges.
• Electric field patterns
  • Field patterns around isolated point charges (radial, outwards from positive, inwards to negative).
  • Field patterns between two point charges (like charges repel, field lines push away; opposite charges attract, field lines connect).
  • Uniform fields exist between parallel charged plates (parallel, equally spaced field lines).
• Hazards and applications
  • Hazards: lightning (large-scale static discharge), electric shocks from charged objects.
  • Applications: induction charging (charging without contact), photocopying processes (toner particles attracted to charged drum), electrostatic spray painting (charged paint particles are attracted to the object being painted).

Topic 17: Current of Electricity

• Conventional current vs electron flow
  • Conventional current: positive charge flow direction (from positive terminal to negative terminal, historical convention).
  • Electron flow: actual charge carriers are electrons moving opposite to the conventional current (from negative terminal to positive terminal).
• Charge, current and time
  • Charge: $Q = I t$, with current I (in Amperes, A) and time t (in seconds, s).
  • Example: A current of 2 A flows for 10 s. The total charge passed is $Q = 2\text{ A} \times 10\text{ s} = 20\text{ C}$.
• Electromotive force (e.m.f., emf)
  • The work done by a source (e.g., battery) to move unit charge around a complete circuit: $W = QV$
  • V is emf (in volts, V). Unit: J/C.
  • For a series of sources, total emf adds; for parallel, it depends on configuration.
• Potential difference (p.d.)
  • PD across a component is the work done to move unit charge across that component: $V = \frac{W}{Q}$ or simply the potential drop across the component in a circuit.
  • It is the energy converted from electrical to other forms (heat, light) per unit charge.
• Resistance and Ohm’s Law
  • Resistance: $R = \frac{V}{I}$ (Unit: Ohm, $\Omega$).
  • Ohm’s Law: a linear conductor at constant temperature obeys V $\propto$ I (current is directly proportional to potential difference); plot of I–V is a straight line for ohmic conductors.
  • Non-ohmic: filament lamp has increasing resistance with increasing current due to temperature rise (it gets hotter, resistance increases, so I-V graph curves).
  • Example: A resistor with 12 V across it draws 2 A of current. Its resistance is $R = 12\text{ V} / 2\text{ A} = 6 \Omega$.
• Components: diodes and LDR
  • Diode: semiconductor device that allows current to flow in one direction only (forward bias) and blocks it in the reverse direction (rectification); nonlinear I–V characteristic.
  • LDR (Light-Dependent Resistor / photoresistor): resistance decreases with increasing light intensity; used in automatic lighting circuits (e.g., street lights, night lights).

Topic 18: D.C. Circuits

• Basic circuit rules
  • Current in a series circuit is the same at all points.
  • The sum of the potential differences in a series circuit equals the emf of the source: $V = V<em>1 + V</em>2 + \cdots$ (Kirchhoff's Voltage Law).
  • In parallel circuits, the current splits (total current is sum of branch currents); the potential difference across each branch is the same.
• Resistance in series and parallel
  • Series: Effective Resistance $R<em>{\text{eff}} = R</em>1 + R_2 + \cdots$
  • Example: Two resistors, $3 \Omega$ and $5 \Omega$, in series have $R_{\text{eff}} = 3 + 5 = 8 \Omega$.
  • Parallel: $1/R<em>{\text{eff}} = 1/R</em>1 + 1/R_2 + \cdots$
  • Example: Two resistors, $3 \Omega$ and $6 \Omega$, in parallel have $1/R<em>{\text{eff}} = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 \implies R</em>{\text{eff}} = 2 \Omega$.
• Circuit symbols
  • Familiar symbols: fuse, lamp (bulb), battery (DC source), switch, voltmeter (connected in parallel), ammeter (connected in series), thermistor, LDR, resistor, variable resistor.
• Potential divider concept
  • A uniform wire (or series of resistors) connected to a voltage source can act as a variable resistor to provide a fraction of the supply voltage; $V_{PW}$ (voltage across part of the wire/resistor) depends on the position along the resistor.
  • The output voltage is given by $V<em>{\text{out}} = V</em>{\text{in}} \left(\frac{R<em>2}{R</em>1 + R_2}\right)$.
  • Example: A 12 V supply across two series resistors, $R<em>1 = 200 \Omega$ and $R</em>2 = 100 \Omega$. The voltage across $R<em>2$ is $V</em>{R2} = 12\text{ V} \left(\frac{100}{200 + 100}\right) = 12\text{ V} \times \frac{1}{3} = 4\text{ V}$.
• Thermistors and LDRs as inputs
  • Temperature-dependent (thermistors) or light-dependent (LDRs) resistance changes used in potential dividers for sensing.
  • Example: In a temperature sensor, a thermistor's resistance decreases with increasing temperature. If placed as $R<em>2$ in a potential divider, the output voltage ($V</em>{R2}$) would decrease as temperature rises, triggering a fan or alarm.

Topic 19: Practical Electricity

• Heating effects of electricity
  • Electrical energy can be converted to heat in resistors (heating elements).
  • Common materials: Nichrome due to high resistivity and high melting point. Used in toaster elements, electric kettles, hair dryers.
• Energy and power relations for appliances
  • Work/energy: $W = VI t$ (electrical energy converted).
  • Power: $P = VI$ (rate of energy conversion); alternative forms: $P = I^2 R$; $P = V^2 / R$.
  • Example: A 240 V heater draws 10 A of current. Its power is $P = 240 \times 10 = 2400\text{ W}$. In 1 hour ($3600\text{ s}$), it uses $W = 2400 \times 3600 = 8.64 \times 10^6\text{ J}$.
• Cost of electricity
  • Cost = energy used (kWh) $\times$ price per kWh; 1 kWh = $3.6 \times 10^6\text{ J}$.
  • Example: If electricity costs $0.20 per kWh, and an appliance uses 2.4 kWh, the cost is$2.4 \times 0.20 = $0.48$.
• Hazards and safety
  • Damp conditions increase conductivity and risk of shock.
  • Damaged insulation exposes live wires.
  • Overheating cables can cause fires (due to too much current, I$^2$R heating).
  • Multiple plug outlets can overload circuits, leading to overheating.
• Fuses and circuit breakers protect circuits; earthing provides safety for metal casings.
  • Live, neutral, and earth wires: live is dangerous (carries fluctuating voltage); neutral is at/near earth potential (completes circuit); earth provides a low-resistance path to ground for fault currents, preventing electrocution.
• Electrical wiring and safety devices
  • Switches are always placed on the live wire to break the circuit fully when turned off.
  • Fuses are rated for expected current; they melt and break the circuit if current exceeds safe limits.
  • Double insulation (plastic casing) provides protection without needing an earth wire for appliances.
  • Earthing connects metal casings of appliances to the ground, so if the live wire touches the casing, current flows to earth and blows the fuse.

Topic 20: Magnetism

• Properties of magnets
  • Two poles (North and South); magnets do not exist as monopoles (if cut, new poles form).
  • Like poles repel; unlike poles attract.
  • Magnetic dipoles can be represented by arrows indicating orientation.
• Induced magnetism
  • A magnetic material (e.g., iron, steel) becomes magnetised when placed in a magnetic field; domains (regions of aligned atomic magnets) within the material align to produce induced magnetisation.
  • Example: A paper clip becomes temporarily magnetic when held near a strong magnet and can then pick up other paper clips.
• Magnetisation using electricity
  • A steel bar can be magnetised by placing it in a solenoid connected to a DC source (electromagnetism); the direction of current determines the pole orientation (use right-hand grip rule).
• Magnetic materials and magnets
  • Common magnetic materials: iron, steel, nickel, cobalt (ferromagnetic materials).
  • Temporary (soft) magnets (e.g., soft iron): easily magnetised and demagnetised. Used in electromagnets, relays.
  • Permanent magnets (e.g., steel, alnico): hard to magnetise but retain magnetism strongly. Used in compasses, speakers, motors.
• Electromagnets vs permanent magnets
  • Electromagnet: coil of wire with soft iron core; magnetism is temporary and requires current to sustain (can be turned on/off).
  • Permanent magnets: magnetism persists without current; used in compasses, motors, dynamos, door catches, speakers.
• Magnetic field and field lines
  • Magnetic field lines show the direction of the magnetic force (from N to S outside the magnet, S to N inside); strength is indicated by line density (closer lines mean stronger field).
• Field patterns and effects
  • Field patterns between bar magnets show attraction/repulsion interactions depending on pole orientation.
  • Example: Two North poles facing each other will have field lines pushing away from each other, illustrating repulsion.

Topic 21: Electromagnetism

• Magnetic fields around currents
  • A current-carrying wire produces a magnetic field; the pattern depends on the geometry of the conductor.
  • Straight Wire: Concentric circles around the wire. Direction using Right-Hand Grip Rule (thumb in current direction, fingers show field direction).
  • Coil/Solenoid: Magnetic field similar