Physics Matters GCE 'O' Level Comprehensive Study Notes

CHAPTER 1: MEASUREMENTS

1.1 What Is Physics?

• Physics is the study of the natural world, ranging from the very large (e.g., the solar system) to the very small (e.g., the atom).

• Core Concepts: Matter and energy.

• Disciplinary Ideas:     * Matter and energy make up the Universe.     * Matter interacts through forces and fields.     * Forces help us understand motion.     * Waves can transfer energy without transferring matter.     * Conservation laws constrain the changes in systems.     * Microscopic models can explain macroscopic phenomena.

1.2 What Are Physical Quantities?

• Definition: A physical quantity is a quantity that can be measured. It typically consists of a numerical magnitude and a unit (e.g., "4.5 m").

• Base Quantities and SI Units:     * Length: metre ($m$)     * Mass: kilogram ($kg$)     * Time: second ($s$)     * Electric current: ampere ($A$)     * Thermodynamic temperature: kelvin ($K$)     * Amount of substance: mole ($mol$)     * Luminous intensity: candela ($cd$) (Standardized as SI units).

• Temperature Conversion:     * Temperature in kelvin = Temperature in degree Celsius + $273$

• Chemistry Link: 1 mole contains $6.02 \times 10^{23}$ particles (Avogadro's constant).

Prefixes for SI Units

• Multiples:     * Tera (T): $10^{12}$     * Giga (G): $10^{9}$     * Mega (M): $10^{6}$     * Kilo (k): $10^{3}$

• Sub-multiples:     * Deci (d): $10^{-1}$     * Centi (c): $10^{-2}$     * Milli (m): $10^{-3}$     * Micro ($\mu$): $10^{-6}$     * Nano (n): $10^{-9}$

Standard Form

• Numbers expressed as a value between 1 and 10 multiplied by a power of 10.

• Example: $16\,800 = 1.68 \times 10^4$.

1.3 How Do We Measure Physical Quantities?

Measurement of Length

• Instruments and Precision:     * Measuring Tape: Used for straight or curved distances longer than a metre. Precision: $0.1\,cm$ or $1\,mm$.     * Metre Rule: Measures up to $1\,m$. Precision: $0.1\,cm$ or $1\,mm$.     * Digital Calipers: Measures internal/external diameters and depth. Precision: $0.01\,mm$ (recorded to $0.1\,mm$ to account for error).     * Digital Micrometer Screw Gauge: Measures diameter/thickness of tiny objects. Precision: $0.001\,mm$ (recorded to $0.01\,mm$).

• Common Errors:     * Parallax Error: Caused by the eye position not being perpendicular to the scale.     * Zero Error: Caused by worn ends or misaligned scales.     * Random Error: Varies unpredictably from one measurement to another.     * Systematic Error: Constant error across all measurements (e.g., zero error).

Measurement of Time

• Units: SI unit is the second ($s$).

• Periodic Motion: Regular intervals of events (seasons, moon phases).

• Simple Pendulum:     * Oscillation: One complete to-and-fro motion.     * Period ($T$): Time taken for one complete oscillation.     * Relationship: $T^2 \propto l$ (Square of period is directly proportional to length).     * Human Reaction Time: Typically $0.3\text{--}0.5\,s$, introduces random error in manual timing.

• Atomic Clocks: Used as primary standards for time (accuracy of $1\,s$ in two million years).

1.4 What Are Scalars and Vectors?

• Scalars: Physical quantities with magnitude only (e.g., distance, speed, mass, energy, time).

• Vectors: Physical quantities with both magnitude and direction (e.g., displacement, velocity, acceleration, force, weight).

Comparisons

• Distance vs. Displacement:     * Distance: Total length covered regardless of direction (scalar).     * Displacement: Straight-line distance in a specified direction from a fixed reference point (vector).

• Speed vs. Velocity:     * $\text{Speed} = \frac{\text{distance}}{\text{time taken}}$ (scalar).     * $\text{Velocity} = \frac{\text{displacement}}{\text{time taken}}$ (vector).

Vector Addition (Graphical Method)

• Parallel Vectors: Add arithmetically if in the same direction; subtract if opposite.

• Non-parallel Vectors: Use the Head-to-Tail Method.     1. Choose an appropriate scale.     2. Draw the first vector.     3. Draw the second vector starting from the head of the first.     4. The Resultant Vector is the arrow from the tail of the first to the head of the last.     5. Resultant force = zero if the arrows form a closed triangle (equilibrium).

CHAPTER 2: KINEMATICS

2.1 Speed, Velocity, and Acceleration

• Instantaneous Speed: Speed of an object at a particular instant.

• Uniform Speed: Constant change in distance per unit time.

• Uniform Acceleration: Constant rate of change of velocity.

• Equation for Uniform Acceleration ($a$):     $a = \frac{v - u}{t}$     Where $v$ = final velocity, $u$ = initial velocity, $t$ = time interval.

• Acceleration of Free Fall: Constant near Earth's surface ($g \approx 10\,m/s^2$).

2.2 Graphical Analysis of Motion

Displacement-Time ($s\text{-}t$) Graphs

• Gradient: Represents velocity ($v$).

• Flat line: Object is at rest ($v = 0$).

• Straight sloping line: Constant/uniform velocity.

• Curve (Increasing gradient): Increasing velocity (acceleration).

• Curve (Decreasing gradient): Decreasing velocity (deceleration).

Velocity-Time ($v\text{-}t$) Graphs

• Gradient: Represents acceleration ($a$).

• Area under graph: Represents displacement ($s$).

• Horizontal line: Constant velocity ($a = 0$).

• Straight sloping line: Uniform acceleration/deceleration.

• Curved line: Non-uniform acceleration.

2.3 Acceleration of Free Fall

• Galileo's Discovery: All objects fall with the same acceleration ($g$) regardless of mass, assuming negligible air resistance.

• In a vacuum, a feather and a hammer fall at the same rate ($10\,m/s^2$).

CHAPTER 3: DYNAMICS I: MASS AND WEIGHT

3.1 Types of Forces

• Force: A push or a pull due to interaction between objects.

• Contact Forces: Friction, air resistance, normal force, tension.

• Non-contact Forces: Gravitational force (weight), electrostatic force, magnetic force.

3.2 Mass and Weight

• Mass ($m$): Measure of the amount of matter in a body. SI unit: $kg$. Constant regardless of location.

• Weight ($W$): Gravitational force acting on an object. SI unit: $N$. Varies with location.

• Equation: $W = m \times g$

• Gravitational Field: A region where a mass experiences a force due to gravitational attraction.

• Gravitational Field Strength ($g$): Gravitational force per unit mass. On Earth, $g \approx 10\,N/kg$.

CHAPTER 4: DYNAMICS II: FORCES

4.1 Newton's Laws of Motion

• First Law (Law of Inertia): Every object continues in a state of rest or uniform motion in a straight line unless a resultant force acts on it.

• Inertia: Reluctance of an object to change its state of rest or motion. Mass is the property that resists change.

• Second Law: When a resultant force acts on an object of constant mass, the object accelerates in the direction of the resultant force. Equation: $F_{\text{net}} = m \times a$.

• Third Law: If body A exerts a force on body B, body B exerts an equal and opposite force on body A (Action-Reaction pairs). Note: They act on different bodies.

4.3 Resistive Forces and Terminal Velocity

• Friction: Opposes motion between surfaces. Can be reduced (lubricants, ball bearings, air cushions) or enhanced (treads, chalk).

• Terminal Velocity: Reached when air resistance ($R$) equals the weight ($W$) of a falling object. Resultant force = $0$, acceleration = $0$, velocity is constant.

CHAPTER 5: TURNING EFFECTS OF FORCES

5.1 Moment of a Force

• Moment ($M$): The turning effect of a force about a pivot.

• Equation: $M = F \times d$     Where $d$ = perpendicular distance from the pivot to the line of action of the force.

• SI Unit: Newton metre ($N\,m$).

• Principle of Moments: For a body in equilibrium, the sum of clockwise moments = sum of anticlockwise moments.

5.2 Center of Gravity and Stability

• Center of Gravity (CG): The imaginary point where the entire weight of the object seems to act.

• Stability: Ability of an object to return to its original position.     * Higher stability achieved by: Lowering the CG or increasing the base area.

CHAPTER 6: PRESSURE

6.1 Pressure in Solids

• Definition: Force acting per unit area.

• Equation: $P = \frac{F}{A}$

• SI Unit: Pascal ($1\,Pa = 1\,N/m^2$).

6.2 Pressure in Liquids

• Pascal's Principle: Pressure applied to an enclosed liquid is transmitted undiminished to all parts of the liquid.

• Hydraulic Press Equation: $\frac{F_1}{A_1} = \frac{F_2}{A_2}$

• Pressure Due to a Liquid Column: $P = h \times \rho \times g$     Where $h$ = depth, $\rho$ = density, $g$ = gravitational field strength.

6.3 Measuring Pressure

• Barometer: Measures atmospheric pressure ($P_{\text{atm}}$). Standard height of mercury is $760\,mm\,Hg$.

• Manometer: Measures gas pressure difference (gauge pressure).

CHAPTER 7: ENERGY

7.1 Energy Stores and Transfers

• Stores: Kinetic (KE), Gravitational Potential (GPE), Elastic Potential, Chemical Potential, Nuclear, Internal (store of moving particles).

• Equations:     * $E_k = \frac{1}{2} m v^2$     * $E_p = mgh$

• Pathways: Mechanical (work done), Heating, Waves (EM/sound), Electrical.

• Conservation of Energy: Energy cannot be created or destroyed, only transferred. Total energy in a system remains constant.

7.2 Work Done and Power

• Work Done ($W$): $W = F \times s$ (Product of force and distance moved in the direction of force).

• Power ($P$): $\text{Power} = \frac{\text{Energy Transferred}}{\text{Time Taken}}$. Unit: Watt ($W = 1\,J/s$).

• Efficiency: $\frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \times 100\%$.

CHAPTERS 8-10: THERMAL PHYSICS

8.1 Kinetic Particle Model

• States of Matter:     * Solids: Fixed shape/volume, high density, particles vibrate about fixed positions.     * Liquids: Fixed volume, no fixed shape, particles slide over each other.     * Gases: No fixed shape/volume, compressible, particles move randomly at high speeds.

• Brownian Motion: Evidence of random movement of molecules in fluids.

10.1 Heat Capacity and Specific Heat Capacity

• Specific Heat Capacity ($c$): Change in internal energy per unit mass per unit change in temperature.

• Equation: $Q = mc\Delta\theta$

• Latent Heat: Energy needed for change of state without temperature change ($Q = mL$).     * Fusion ($L_f$): Solid to liquid.     * Vaporization ($L_v$): Liquid to gas.

CHAPTERS 11-14: WAVES AND LIGHT

11.2 Wave Characteristics

• Transverse Waves: Vibration perpendicular to wave direction (e.g., light, water waves).

• Longitudinal Waves: Vibration parallel to wave direction (e.g., sound).

• Wave Equation: $v = f \times \lambda$

12.1 Sound

• Produced by vibrating sources; requires a medium.

• Pitch: Determined by frequency.

• Loudness: Determined by amplitude.

• Audible Range: $20\,Hz\text{--}20\,000\,Hz$.

13.1 Electromagnetic (EM) Spectrum

• All travel at $3 \times 10^8\,m/s$ in a vacuum. Transverse waves.

• Order (Long to Short Wavelength): Radio waves, Microwaves, Infrared, Visible light, Ultraviolet, X-rays, Gamma rays.

14.1 Reflection

• Law of Reflection: Angle of incidence ($i$) = Angle of reflection ($r$).

• Plane Mirror Images: Virtual, upright, same size, laterally inverted, same distance behind mirror as object in front.

14.2 Refraction

• Refractive Index ($n$): $n = \frac{\sin(i)}{\sin(r)} = \frac{c}{v}$.

• Total Internal Reflection: Occurs when light travels from a denser to less dense medium and the angle of incidence > Critical Angle ($c$) ($\sin(c) = \frac{1}{n}$).

CHAPTERS 15-18: ELECTRICITY AND MAGNETISM

15.1 Static Electricity

• Charging: Involves transfer of electrons (rubbing or induction).

• Electric Field: Direction points the way a positive test charge would move.

16.1 Current Electricity

• Current ($I$): $I = \frac{Q}{t}$. SI unit: Ampere ($A$).

• Resistance ($R$): $R = \frac{V}{I}$. Depends on length ($l$) and area ($A$): $R = \rho \frac{l}{A}$.

17.1 D.C. Circuits

• Series: Total resistance $R_{\text{tot}} = R_1 + R_2$; Current is constant throughout.

• Parallel: $\frac{1}{R_{\text{tot}}} = \frac{1}{R_1} + \frac{1}{R_2}$; Voltage is constant across branches.

18.2 Electrical Safety

• Wires: Live (brown), Neutral (blue), Earth (yellow/green).

• Fuse: Breaks circuit if current exceeds rating. Must be placed in the Live wire.

CHAPTERS 19-21: ELECTROMAGNETISM

19.1 Magnetism

• Interaction of magnetic fields. Domain theory explains magnetisation.

20.2 Motor Effect

• Fleming's Left-Hand Rule: Used to find force direction ($F$) on a current ($I$) in a magnetic field ($B$).

21.2 Electromagnetic Induction

• Faraday's Law: Magnitude of induced e.m.f. is proportional to rate of change of magnetic flux.

• Lenz's Law: Direction of induced current opposes the change creating it.

• Transformers: $\frac{V_p}{V_s} = \frac{N_p}{N_s}$. Ideal: $V_p I_p = V_s I_s$.

CHAPTER 22: RADIOACTIVITY

• Atom Structure: Protons ($Z$) and Neutrons in nucleus, Electrons in orbits.

• Nucleon Equation: $x = A - Z$.

• Isotopes: Same protons ($Z$), different neutrons.

• Radiation Types:     * Alpha ($\alpha$): Helium nucleus ($^4_2He$), high ionisation.     * Beta ($\beta$): Fast electron ($^0_{-1}e$), medium penetration.     * Gamma ($\gamma$): High-frequency EM wave, deep penetration.

• Half-life: Time for half the radioactive nuclei to decay.