Comprehensive University Physics Study Guide

1. GENERAL PHYSICS

• 1.1. Quantity and Unit

• Physical quantities: These are divided into two types:     - Base quantity: These have only one SI unit. Examples include Mass, Length, Time, Current, and Temperature.     - Derived quantity: These can be expressed by combining suitable base quantities. Examples include Speed, Volume, Area, and Force.

• SI units (International System of Units):     - Length: metre ($m$)     - Mass: kilogram ($kg$)     - Time: second ($s$)     - Current: Ampere ($A$)     - Temperature: Kelvin ($K$)

• Prefixes: Used for very large or small quantities as multiples or decimals of ten:     - Mega ($M$): $10^{6}$ ($1,000,000$)     - kilo ($K$): $10^{3}$ ($1,000$)     - centi ($C$): $10^{-2}$ ($0.01$)     - Milli ($m$): $10^{-3}$ ($0.001$)     - Micro ($μ$): $10^{-6}$ ($0.000001$)

• Scalars and Vectors:     - Definition (Scalar): A quantity having magnitude only. Examples: mass, length, area, volume, density, time, distance, speed, energy, temperature, current, voltage.     - Definition (Vector): A quantity having both magnitude and direction. Examples: weight, displacement, velocity, acceleration, force, moment.

• 1.2. Length and Time

• Length: Defined as the measurement of something from one end to the other ($SI$ unit: metre, $m$).

• Instruments for measuring length:     - Measuring tape: Used for long lengths (accuracy $1\,mm$). Examples: Length of classroom, height of building.     - Ruler: Used for medium lengths (accuracy $1\,mm$). Examples: Width of paper, length of pen.     - Vernier calipers: Used for short lengths (accuracy $0.1\,mm$). Examples: Diameter of pen, internal diameter of tube.     - Micrometer screw gauge: Used for very short lengths (accuracy $0.01\,mm$). Examples: Diameter of hair, thickness of razor blade.

• Vernier Calipers Procedure:   1. Put object between jaws.   2. Read main scale before the $0$ mark of vernier scale.   3. Find vernier scale marking in line with main scale.   4. Reading = Main scale reading + Vernier scale reading ($cm$).

• Micrometer Screw Gauge Procedure:   1. Turn thimble gently until object is gripped.   2. Read main scale on sleeve before thimble edge.   3. Find circular scale marking in line with the horizontal line of the main scale.   4. Reading = Main scale reading + Circular scale reading ($mm$).

• Time: $SI$ unit is the second ($s$).   - Conversion: $1\,day = 24\,hours = 1440\,minutes = 86400\,s$.   - $1\,year = 31,536,000\,s$.

• Simple Pendulum:   - Definition (Period, T): The time taken for one complete oscillation.   - Formula: $T = \frac{t}{n}$ where $t$ is time and $n$ is the number of oscillations.   - Factors affecting period: Length of the pendulum ($l$) and acceleration due to gravity ($g$). Period does not depend on the mass of the bob or the size of the arc (if small).

• 1.3. Speed, Velocity and Acceleration

• Distance and Displacement:     - Definition (Distance): Total length taken between two points (scalar).     - Definition (Displacement): Change of position in a particular direction (vector).

• Speed: Rate of change of distance traveled with time ($m/s$).     - Formula: $\text{Speed} = \frac{\text{Distance traveled}}{\text{Time taken}}$     - $\text{Average Speed} = \frac{\text{Total distance}}{\text{Total time}}$

• Velocity: Rate of change of displacement with time (vector).

• Acceleration: Rate of change of velocity with time ($m/s^{2}$, vector).     - Formula: $a = \frac{v - u}{t}$ ($v$: final velocity, $u$: initial velocity).     - Deceleration (Retardation): Indicated by a negative acceleration value.

• Uniformly Accelerated Linear Motion Equations:     - $v = u + at$     - $x = ut + \frac{1}{2}at^{2}$     - $v^{2} = u^{2} + 2ax$

• Acceleration due to Gravity ($g$): Approx. $10\,m/s^{2}$.     - Free fall: $u = 0\,m/s$, $a = g = 10\,m/s^{2}$.     - Throwing up: $v = 0\,m/s$ at the top, $a = -g = -10\,m/s^{2}$.

• Speed-Time Graphs:     - Gradient = Acceleration.     - Area under graph = Distance traveled.     - Constant speed = horizontal line; Uniform acceleration = straight line sloping up.

• 1.4. Mass and Weight

• Mass: Quantity of matter in a substance (measured in $kg$ via beam balance; stays constant everywhere).

• Weight: Attractive force exerted by gravity (measured in $N$ via spring balance; varies by location).     - Formula: $w = mg$     - Gravity on the moon is approx. $1/6$ of earth ($g \approx 1.67\,m/s^{2}$).

• Centre of Gravity: The point through which the whole weight appears to act.

• Stability: Ability to regain original position.     - To increase stability: Lower the centre of gravity and increase the base area.

• 1.5. Volume and Density

• Volume: Amount of space occupied ($m^{3}$). Cuboid formula: $l \times b \times h$.

• Density: Mass per unit volume.     - Formula: $D = \frac{m}{V}$     - Units: $kg/m^{3}$ or $g/cm^{3}$.

• 1.6. Force

• Force: A push or a pull (vector, measured in Newtons, $N$).

• Newton's First Law: If forces are balanced, a body at rest stays at rest, and a moving body stays at constant speed.

• Inertia: Property resisting change to motion; depends on mass.

• Newton's Second Law: Unbalanced forces produce acceleration.     - Formula: $F = ma$

• Friction: Force acting to stop motion of touching surfaces; acts in opposite direction.

• Centripetal Force: Force in circular motion directed toward the center.

• Hooke's Law: Extension of a loaded spring is directly proportional to the applied load provided the elastic limit is not exceeded: $\frac{\text{Extension}}{\text{Load}} = \text{Constant}$.

• 1.7. Moment

• Definition: Product of the force and the perpendicular distance from the pivot ($M = Fd$, unit: $Nm$).

• Principle of Moments: For equilibrium, $\sum \text{Clockwise Moments} = \sum \text{Anticlockwise Moments}$.

• 1.8. Work, Energy and Power

• Work: Product of force and distance moved in the direction of the force.     - Formula: $W = Fd$ (unit: Joule, $J$).

• Energy: Ability to do work.     - Potential Energy (Gravitational): $PE = mgh$     - Kinetic Energy: $KE = \frac{1}{2}mv^{2}$

• Conservation of Energy: Energy cannot be created or destroyed, only changed from one form to another.

• Power: Rate of doing work.     - Formula: $P = \frac{W}{t} = \frac{E}{t}$ (unit: Watt, $W$).

• 1.9. Simple Machines

• Mechanical Advantage (M.A.): $\frac{\text{Load}}{\text{Effort}}$

• Velocity Ratio (V.R.): $\frac{\text{Distance moved by effort}}{\text{Distance moved by load}}$

• Efficiency: $\frac{\text{Useful work done}}{\text{Total work put in}} \times 100\% = \frac{M.A.}{V.R.} \times 100\%$

2. THERMAL PHYSICS

• 2.1. Kinetic Theory

• States of Matter:     - Solid: Fixed shape/volume, high density, particles vibrate in fixed positions, strong cohesive forces.     - Liquid: Fixed volume, no fixed shape, particles move vigorously and can change positions.     - Gas: No fixed shape/volume, low density, particles move randomly at high speeds.

• Brownian Motion: Continuous random motion of particles (e.g., smoke particles in air) due to collisions with invisible air molecules.

• Diffusion: Process of mixing by random molecular motion; moves from high to low concentration.

• Evaporation: Change of liquid to gas at the surface (occurs at any temperature). Boiling occurs within the liquid at a fixed boiling point.

• 2.2. Thermal Properties

• Thermal Expansion: Bodies increase in size when heated. Application: Bimetallic strips (copper expands more than iron) used in thermostats.

• Thermometers: Use physical properties like volume, e.m.f., or resistance.     - Clinical thermometer: Sensitive, narrow bore, includes a constriction to prevent mercury backflow.     - Fixed points: Lower ($0^{\circ}C$; melting ice) and Upper ($100^{\circ}C$; boiling water steam).

• Thermocouple: Two different metal wires; electric current flows when junctions are at different temperatures.

• 2.3. Gas Laws

• Pressure: $P = \frac{F}{A}$.

• Boyle's Law: $P_{1}V_{1} = P_{2}V_{2}$ (at constant temperature).

• Temperature Conversion: $T_{K} = T_{C} + 273$.

• Charles' Law: $\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$ (at constant pressure, temperatures in Kelvin).

• General Gas Equation: $\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}$.

• 2.4. Transfer of thermal energy

• Conduction: Heat transmission through a medium (Hotter vibrating molecules collide with neighbors). Metals are good conductors.

• Convection: Heat transfer by movement of heated particles in fluids (liquids/gases). Creates convection currents.

• Radiation: Heat flow via electromagnetic waves (infra-red); requires no medium. Black surfaces are good emitters and absorbers; silvered surfaces prevent radiation.

3. PROPERTIES OF WAVES

• 3.1. General Waves

• Transverse Wave: Vibrations are at right angles to travel direction (e.g., light).

• Longitudinal Wave: Vibrations are parallel to travel direction (e.g., sound).

• Terms:     - Amplitude ($A$, unit: $m$): max displacement.     - Wavelength ($\lambda$, unit: $m$): distance between repetitions.     - Frequency ($f$, unit: $Hz$ or $s^{-1}$): $\text{waves per second}$.     - Period ($T$, unit: $s$): $\text{time for one complete vibration}$.     - Formulas: $f = \frac{1}{T}$ and $v = f\lambda$.

• 3.2. Sound

• Nature: Longitudinal wave requiring a medium. Cannot travel through a vacuum.

• Speed: Faster in solids, slowest in gases ($\text{air} \approx 340\,m/s$).

• Pitch: Depends on frequency (high pitch = high frequency).

• Loudness: Depends on amplitude.

• Echos: Echo method calculate sound speed via $v = \frac{2s}{t}$.

• 3.3. Light

• Reflection: Law 1: $i = r$. Law 2: Incident ray, reflected ray, and normal all lie in the same plane.

• Virtual Images: Formed in plane mirrors; same size as object, laterally inverted, same distance behind as object is in front.

• Refraction: Bending of light between media due to speed changes.     - Snell's Law: $n = \frac{\sin(i)}{\sin(r)}$ where $n$ is the refractive index.

• Critical Angle: The angle of incidence resulting in refraction at $90^{\circ}$.     - If $i > \text{Critical Angle}$, Total Internal Reflection occurs.

• Lenses: Converging (convex) lens. Images can be real/virtual, upright/inverted, magnified/diminished depending on object position relative to focal length ($f$).

• Electromagnetic Spectrum: Radio, Microwaves, IR, Visible (Red to Violet), UV, X-rays, Gamma rays. All travel at $3 \times 10^{8}\,m/s$ in vacuum.

4. ELECTRICITY

• 4.1. Static Electricity

• Charge: Rubbing causes electron transfer. 'Like charges repel', 'Unlike charges attract'.

• Induced Charge: Charged objects attract uncharged ones by separating original charges.

• Lightning: Large scale discharge of electrons from clouds to earth.

• 4.2. Electric Circuit

• Current ($I$): Rate of flow of charge ($I = \frac{Q}{t}$, unit: Ampere).

• Electromotive Force (e.m.f.): Energy supplied per coulomb within a cell ($V = \frac{E}{Q}$, unit: Volt).

• Potential Difference (p.d.): Energy converted per unit charge passing through a component ($V = \frac{E}{Q}$).

• Resistance ($R$): Opposition to current ($R = \frac{V}{I}$, unit: Ohm, $\Omega$).

• Circuits:     - Series: $I$ same everywhere; $R_{\text{total}} = R_{1} + R_{2}$; $V_{\text{total}} = V_{1} + V_{2}$.     - Parallel: $V$ same across branches; $I_{\text{total}} = I_{1} + I_{2}$; $\frac{1}{R_{\text{total}}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$.

• 4.3. Practical Electricity Circuit

• Power: $P = VI$ (unit: Watt).

• Energy Cost: Calculated in kilowatt-hours ($kWh$). $E = Pt$. $\text{Cost} = \text{Energy} \times \text{Unit Price}$.

• Safety:     - Wires: Live (brown), Neutral (blue), Earth (green/yellow).     - Safety devices: Fuses (installed on live wire, wire melts on high current), switches (on live wire), earthing, and double insulation.

5. MAGNETISM

• 5.1. Simple phenomenon of magnetism

• Poles: North and South. Like poles repel; unlike poles attract.

• Magnetic Materials: Iron (soft - easily magnetized/demagnetized), Steel (hard - retains magnetism).

• Magnetization Methods: Stroking with a magnet or electrical method using a solenoid and Direct Current ($D.C.$).

• Demagnetization Methods: Heating, hammering, or using Alternating Current ($A.C.$) solenoid.

• 5.2. Electromagnetic Effect

• Fleming's Left-hand Rule: Relates Force (thumb), Magnetic field (first finger), and Current (second finger).

• Electromagnetic Induction: Inducing e.m.f. by moving a conductor through magnetic flux (Faraday's Law).

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

• A.C. Generator: Rotating coil in magnetic field uses slip rings and carbon brushes to produce alternating current.

• Transformers: Change $A.C.$ voltage levels.     - Formula: $\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}$     - Ideal ($100\%$ efficiency): $V_{s}I_{s} = V_{p}I_{p}$.

6. INTRODUCTORY ELECTRONICS

• 6.1. Electron

• Thermionic Emission: Emission of electrons from a hot surface (e.g., cathode).

• Cathode Rays: Streams of electrons traveling in straight lines; affected by magnetic and electric fields.

• 6.2. C.R.O. (Cathode Ray Oscilloscope)

• Parts: Electron gun (filament, cathode, grid, anode), deflection system (X and Y plates), and fluorescent screen.

• Function: Y-plates deflect vertically (Y-gain in $V/cm$) for voltage; X-plates deflect horizontally (Time base in $ms/cm$) for timing/frequency.

7. ATOMIC PHYSICS

• 7.1. Nuclear Atom

• Composition: Nucleus contains protons ($+$, atomic number $Z$) and neutrons (neutral). Nucleons ($A$) = protons + neutrons. Electrons ($-$) orbit the nucleus.

• Symbol Notation: $^{A}_{Z}X$.

• Isotopes: Atoms with same $Z$ (atomic number) but different $A$ (mass number).

• 7.2. Radioactivity

• Types of Radiation:     - Alpha ($\alpha$): Helium nucleus ($^{4}_{2}He$); high ionizing, short range, deflected by fields.     - Beta ($\beta$): Electron ($^{0}_{-1}e$); medium ionizing/range.     - Gamma ($\gamma$): Electromagnetic wave; high penetration, low ionizing.

• Radioactive Decay Equations:     - Alpha decay: $^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}He$     - Beta decay: $^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + ^{0}_{-1}e$

• Half-life: Time taken for half of the unstable nuclei in a sample to decay.

• Safety: Stored in lead boxes, minimized exposure, protective clothing, and badges.