Physics Notes for End-of-Year Examination 2025 (Year 3)

Chapter 1: Key Concepts of Measurement

Since 1948, the SI (Système International d’Unités) is the preferred language of science and technology; reflects current best measurement practice.
When numbers are approximated and quoted to the nearest power of 10, this is an order of magnitude estimate.
Wherever possible, use SI units.
Base SI units: kilogram (kg), metre (m), second (s), ampere (A), mole (mol), kelvin (K).
Derived quantities: combinations of base units (e.g., density with the unit kg/m³). Some derived units have names, e.g., the pascal (Pa) = N/m².
Values in science are commonly expressed in standard form (scientific notation): $3.9820 \times 10^{4}$ instead of 39 820.
Units use prefixes for decimal sub- and multiples (e.g., kilo-): nano (n, 10⁻⁹), micro (µ, 10⁻⁶), milli (m, 10⁻³), centi (c, 10⁻²), deci (d, 10⁻¹), kilo (k, 10³), mega (M, 10⁶), giga (G, 10⁹), tera (T, 10¹²).
Random errors (uncertainties) occur in all experiments and cause values to scatter around the true value.
Random errors can be reduced by averaging repeated readings and by taking a range of readings.
Systematic errors occur if the same error affects every measurement (e.g., zero error on a measuring instrument) and are not reduced by repeating measurements.
An accurate measurement has low systematic error; precise measurements have low random errors.
The number of significant figures expresses precision; a calculated result should not have more significant figures than the least precise data used.
Vectors vs. scalars:
- Vector: magnitude and direction (e.g., force, velocity, acceleration). Represented in diagrams by arrows; a vector quantity has both magnitude and direction.
- Scalar: only magnitude (e.g., mass, energy, time).
Recall base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol).
Recall SI prefixes and their symbols and powers of ten as listed above.
Convert between different units of quantities; perform arithmetic in scientific notation.
Distinguish between precision and accuracy of a measurement.
Describe how to measure volume of a liquid or solid with appropriate precision/accuracy (e.g., measuring cylinder or calculation).
Define scalar and vector quantities and give common examples.
Recall vectors: displacement, force, weight, velocity, acceleration, gravitational field strength; Scalars: distance, speed, time, mass, energy, temperature.

Chapter 2: Kinematics

Motion can be described with motion graphs and algebraic equations.
Displacement (s): distance in a given direction from a fixed reference point. SI unit: m. (Displacement is a vector quantity.)
Speed: rate of change of distance with time. SI unit: m s⁻¹. (Speed is a scalar.)
Velocity (v): rate of change of displacement with time (speed in a given direction). (Vector quantity; SI unit: m s⁻¹.)
Acceleration (a): rate of change of velocity with respect to time; vector quantity; SI unit: m s⁻².
Instantaneous values: instantaneous velocity/acceleration can be found from very short time intervals or from the gradients of tangents to displacement-time graphs.
Displacement-time graphs: slope = velocity; velocity-time graphs: slope = acceleration; area under a velocity-time graph = displacement.
Uniform acceleration: equations of motion (one-dimensional, constant acceleration):
- First equation (velocity-time): $v = u + a t$
- Second equation (displacement from velocity): $s = ut + \tfrac{1}{2} a t^{2}$
- Third equation (velocity-squared): $v^{2} = u^{2} + 2 a s$
Symbols:
- Initial velocity: u; final velocity: v; time interval: t; displacement: s; acceleration: a.
For uniform motion: velocity constant; gradient of s-t graph is zero; distance equals speed × time.
The gradient of a displacement-time graph at any point equals the instantaneous velocity at that time (slope = v).
The gradient of a velocity-time graph at any interval equals the instantaneous acceleration (slope = a).
The area under a velocity-time graph between t₁ and t₂ equals the displacement during that interval.
The simplest motion: uniform velocity (v constant) has v = constant; uniform acceleration: v changes linearly with time; area under v-t graph corresponds to distance.
Important note: initial velocity u and final velocity v refer to the start and end of the time interval considered, not necessarily the entire motion.

Chapter 3: Mass and Weight

Two interpretations of mass:
- A measure of the amount of substance in a body.
- A property of a body that resists changes in motion (inertia).
Gravitational field (g): a region in which a mass experiences a force due to gravitational attraction; g is the acceleration due to gravity near the Earth’s surface.
Weight (W): a force exerted by Earth’s mass on an object; W = mg, with g ≈ 9.8 N kg⁻¹ (m s⁻²).
Mass vs. weight: mass is the amount of matter; weight is the force due to gravity on that mass.
Free-body diagrams (FBDs): arrows represent forces acting on an object; used to analyze forces and predict motion.
Gravitational field strength (g) is the force per unit mass; equivalent to the acceleration of free fall.
Measuring mass and weight: using an electronic balance (mass) or a force meter (weight).
Near-Earth gravity: g ≈ 9.8 m s⁻²; weight is a force; mass is invariant (in classical mechanics).

Chapter 4: Forces and Motion

Force is a vector quantity and can be represented by arrows with magnitude proportional to force.
Common forces:
- Weight (gravity)
- Normal contact force (from a surface)
- Tension
- Friction (opposes motion between surfaces)
- Air resistance (opposes motion through air)
- Non-contact forces: gravitational, electrical, magnetic.
Weight is the gravitational force; W = mg; measured in newtons (N).
Free-body diagrams show all forces acting on the object, drawn separately from the problem’s surroundings.
Resultant (net) force is the combined effect of all forces; can be zero (equilibrium) or non-zero (causes acceleration).
Newton’s laws of motion:
- 1st law (equilibrium): an object at rest stays at rest, or moves with constant velocity, unless acted on by a resultant force; translational equilibrium occurs when resultant force is zero.
- 2nd law: F_net = m a (net force produces acceleration).
- 3rd law: action-reaction pairs: when A exerts a force on B, B exerts an equal and opposite force on A; these forces act on different objects.
Resistance to motion: air resistance increases with speed; as air resistance grows, resultant force and acceleration decrease; at terminal velocity, air resistance balances weight.
Net force and acceleration direction: acceleration is in the same direction as the resultant force.
The Newton’s laws can be applied to describe balanced vs unbalanced forces and to predict motion.
For a single force scenario: if the pushing force equals friction, the object is at rest or moving with constant velocity (net force zero).
Free-body diagram guidelines include labeling forces, drawing vectors from the object outward, and using scale for vector lengths.

Chapter 5: Turning Effect of Forces

Centre of gravity: the single point where the weight of a body acts.
Moment of a force: a measure of its turning effect; defined as the product of the force and the perpendicular distance to the pivot: $\text{Moment} = F \times d_{\perp}$
Principle of moments: for equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments; a body in equilibrium has no resultant moment.
If there is no resultant force and no resultant moment, the system is in equilibrium (translational and rotational).
Apply the principle of moments to solve problems involving levers and turning forces.

Chapter 6: Pressure (Key Concepts)

Pressure is force per unit area: $P = \frac{F}{A}$ with SI unit Pa (Pascal) = N/m².
Atmospheric pressure at sea level ~ $1.0 \times 10^{5} \text{ Pa}$ ; acts in all directions (upwards, sideways, downwards).
Hydrostatic pressure varies with depth and density of the liquid: $P = h \rho g$ where h is depth, ρ is density, g is gravitational field strength.
The height of a liquid column can be used to measure atmospheric pressure (hydrostatic pressure reference).
The chapter also covers: density concepts, changes in pressure with depth, and how atmospheric pressure relates to fluid statics.

Chapter 7: Work, Energy and Power

Energy stores (types):
- Gravitational potential store
- Chemical potential store
- Nuclear potential store
- Elastic potential store
- Internal store (sum of kinetic and potential energies of particles in a substance)
Energy transfers (pathways): mechanical work, heating, electrical work, waves (electromagnetic and mechanical).
Energy is measured in joules (J).
Transfer of energy between stores can be illustrated with a LOL diagram (Laws of Logic/LoL not elaborated here; for study, think of energy flow between stores).
Examples of energy transfer events:
- Collision changes kinetic energy
- Heating increases internal energy
- Deforming a body changes elastic potential energy
- Lifting increases gravitational potential energy
- Burning reduces chemical energy
- Thermal energy transfer between objects in contact
Near Earth surface: gravitational potential energy change is $\Delta E_p = m g \Delta h$ .
Kinetic energy: $E_k = \tfrac{1}{2} m v^2$ .
The principle of conservation of energy: total energy of a closed system remains constant; energy can transfer between stores but the sum remains the same.
Dissipation: energy becomes less useful over time; some energy is lost to the surroundings and cannot be fully recovered to do useful work.
Efficiency: $\eta = \frac{\text{useful energy out}}{\text{total energy input}} \times 100\%$ , typically expressed as a percentage.
Work is the transfer of energy when a force moves a point of application: $W = F \times s$ (where s is displacement in the line of action).
Power: rate of energy transfer: $P = \frac{W}{\Delta t} = \frac{\Delta E}{\Delta t}$ ; for motion with constant velocity, $P = F \times v$ .
Practical use of energy concepts includes analyzing resources (food, fuels) and devices (bulbs, machines) in terms of energy transfer and efficiency.
Applications of energy relationships to new situations: use energy conservation and work/energy theorems to solve problems.

Chapter 8–10: Thermal Concepts

Macroscopic observations can be explained by microscopic particle behavior; all substances contain particles (molecules) with kinetic energy; solids/ liquids also have potential energy due to interparticle forces; total internal energy is the sum of kinetic and potential energies.
Thermal energy transfer occurs from hotter to cooler bodies; thermal equilibrium occurs when temperatures equalize; if insulated, no net transfer.
Temperature scales:
- Celsius: fixed points of water (0°C = ice point; 100°C = steam point); Celsius has no true zero.
- Kelvin (K): absolute temperature scale with true zero at 0 K (absolute zero). Relationship: $T\,(K) = \theta\,(°C) + 273$ .
Kinetic model of matter:
- Solids: strong interparticle forces; particles vibrate around fixed positions.
- Liquids: weaker forces; particles can move relative to each other but remain close.
- Gases: very weak intermolecular forces; particles move freely in random directions and collide frequently.
Brownian motion provides indirect evidence of molecular motion; visible effects occur due to collisions of many molecules with suspended particles.
Ideal gas model relates macroscopic properties (mass, volume, temperature, pressure) to microscopic behavior of particles.
Pressure in gases arises from collisions of molecules with container walls: pressure is the average normal force per unit area.
Temperature measures average kinetic energy of molecules; a higher temperature means higher molecular motion.
Thermal properties:
- Heat capacity (C): energy needed to raise the temperature of a system by 1 K; $C = \frac{E}{\Delta T}$ .
- Specific heat capacity (c): energy needed to raise the temperature of 1 kg by 1 K; $c = \frac{E}{m\Delta T}$ .
Energy transfer and temperature change:
- Relationship between kinetic energy decrease and internal energy increase (or vice versa): $\Delta K = m c \Delta T$ in certain contexts; similarly, near Earth’s surface: $m g \Delta h = m c \Delta T$ when gravitational potential energy converts to internal energy.
Phase changes and latent heat:
- Melting (solid to liquid) and freezing (liquid to solid) occur at a characteristic temperature; during phase changes, temperature remains constant while latent heat is absorbed or released.
- Boiling (liquid to gas) and condensation (gas to liquid) likewise involve latent heat with no temperature change during the phase change.
- Latent heats:
- Specific latent heat of fusion: $E = m L_f$ for solid-liquid phase change at constant temperature.
- Specific latent heat of vaporisation: $E = m L_v$ for liquid-gas phase change at constant temperature.
Thermal energy transfer mechanisms:
- Conduction: transfer through solids by lattice vibrations and, in metals, free electrons.
- Convection: transfer through fluids due to density differences (hotter, less dense fluid rises; cooler fluid sinks), creating convection currents.
- Thermal radiation: transfer by infrared electromagnetic waves; does not require a medium; dull black surfaces are good absorbers and emitters of radiation; surface color and texture affect emission/absorption/reflectivity; rate of emission depends on surface temperature and surface area.
Calibration and temperature measurement:
- Liquid-in-glass thermometers require fixed points (ice point, steam point) for calibration; temperatures are converted between Kelvin and Celsius as needed.
Gas law relationships (kinetic model context):
- For gases, relationships among pressure, volume, and temperature can be expressed as often-stated form: $PV = nRT$ , and for a fixed amount of gas, $\frac{P V}{T} = \text{constant}$ when n and R are constant.
In all chapters, students are assessed on:
- Defining key terms (distance, displacement, speed, velocity, acceleration).
- Distinguishing between speed vs velocity and distance vs displacement.
- Calculations of average speed and average velocity.
- Reading and interpreting position-time and velocity-time graphs; instantaneous values; determining displacements and times; gradients and areas under graphs.
- Knowledge and application of kinematic equations for one-dimensional motion with constant acceleration: $a = \frac{v-u}{t}, \quad s = ut + \tfrac{1}{2} a t^{2}, \quad v^{2} = u^{2} + 2 a s, \quad v = u + a t$ .
- Understanding force, motion, and energy concepts; solving problems using F = ma; understanding Newton’s laws; free-body diagrams; action-reaction pairs; equilibrium; terminal velocity; energy conservation; work and power; efficiency.
- Grasping thermal concepts: internal energy, temperature, heat transfer, phase changes, latent heat, calibration of thermometers, and gas laws.

Key equations recap (for quick study):

Displacement and motion
- $v = u + a t$
- $s = ut + \tfrac{1}{2} a t^{2}$
- $v^{2} = u^{2} + 2 a s$
- $v_{\text{avg}} = \frac{u+v}{2}$
Kinematics graph relations
- Displacement-time: slope = velocity; Velocity-time: slope = acceleration; Area under v-t = displacement.
Forces and motion
- Newton’s laws: (F{\text{net}} = ma); (F{1} \rightleftharpoons F_{2}) third-law pairs; weight $W = mg$ ; Free-body diagrams.
Work and power
- $W = F s$
- $P = \frac{W}{\Delta t} = \frac{\Delta E}{\Delta t}$
Efficiency
- $\eta = \frac{\text{useful energy out}}{\text{total energy input}} \times 100\%$
Heat and temperature
- Heat transfer: $Q = m c \Delta T$ ; Heat capacity: $C = \frac{E}{\Delta T}$ ; Specific heat: $c = \frac{E}{m \Delta T}$
Phase changes and latent heat
- $E = m L_f$ (fusion)
- $E = m L_v$ (vaporisation)
Gas laws (kinetic model context)
- $P V = n R T$ ; for fixed n, $\frac{P V}{T} = \text{constant}$
Pressure
- $P = \frac{F}{A}$ ; Atmospheric pressure ~ $1.0 \times 10^{5} \text{ Pa}$ ; Hydrostatic pressure: $P = h \rho g$ ; Change in pressure beneath a liquid surface: $\Delta p = \rho g \Delta h$
Temperature scales
- $T(K) = \theta(^{\circ}C) + 273$ ; 0 K is absolute zero.

Notes for exam preparation:

Be able to identify and label forces in free-body diagrams, including static and dynamic cases, and recognize when a system is in translational or rotational equilibrium.
Be comfortable with interpreting and deriving from graphs (s-t, v-t) and applying the equations of motion for constant acceleration.
Distinguish between energy stores, energy transfer pathways, and the concept of efficiency and dissipation in real-world systems.
Understand the differences between conduction, convection, and radiation as mechanisms of heat transfer, and relate surface properties to absorption/emission of infrared radiation.
Be able to apply the kinetic model to gases to explain macroscopic properties like pressure, temperature, and volume, and use the related equations to solve problems.