Cambridge O Level Physics Quick Revision Summary

Motion, Forces and Energy

• Physical Quantities & Measurement Techniques:

  • Base SI units: metre ($\text{m}$), kilogram ($\text{kg}$), second ($\text{s}$).
  • Scalars: Quantities with magnitude only (e.g., distance, speed, time, mass, energy, temperature).
  • Vectors: Quantities with magnitude and direction (e.g., displacement, velocity, acceleration, force, weight, momentum).
  • Resultant of two perpendicular vectors $F_X$ and $F_Y$:     $F = \sqrt{F_X^2 + F_Y^2}$$\tan(\theta) = \frac{F_Y}{F_X}$

• Motion:

  • Speed: Distance travelled per unit time:     $v = \frac{s}{t}$
  • Average Speed:$\text{Average speed} = \frac{\text{total distance travelled}}{\text{total time taken}}$
  • Velocity: Change in displacement per unit time.
  • Acceleration: Change in velocity per unit time:     $a = \frac{\Delta v}{\Delta t} = \frac{v - u}{t}$
  • Equations of Constant Acceleration:$v = u + at$$s = \frac{(u + v)t}{2}$
  • Acceleration of Free Fall ($g$): Approximately $9.8\,m/s^2$ near Earth's surface.
  • Graphical Analysis:
  • Gradient of a distance–time graph represents speed.
  • Gradient of a speed–time graph represents acceleration.
  • Area under a speed–time graph represents total distance travelled.

• Mass, Weight and Density:

  • Mass ($m$): Measure of the quantity of matter in an object at rest; resists change in motion (inertia). Measured in kilograms ($\text{kg}$).
  • Weight ($W$): Gravitational force acting on an object:     $W = mg$
  • Gravitational Field Strength ($g$): Force per unit mass ($g = \frac{W}{m} = 9.8\,N/kg$ on Earth).
  • Density ($\rho$): Mass per unit volume:     $\rho = \frac{m}{V}$

• Forces & Momentum:

  • Hooke's Law & Spring Constant ($k$):$F = kx$     where $k$ is the force per unit extension up to the limit of proportionality.
  • Newton's First Law: An object remains at rest or continues at constant speed in a straight line unless acted upon by a resultant force.
  • Newton's Second Law:$F = ma$
  • Newton's Third Law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A.
  • Momentum ($p$):$p = mv$
  • Impulse & Resultant Force:$\text{Impulse} = F\Delta t = \Delta(mv)$$F = \frac{\Delta p}{\Delta t}$
  • Conservation of Momentum: Total momentum remains constant in a closed system provided no external forces act.
  • Terminal Velocity: Reached when upward drag force equals downward weight ($F_{\text{net}} = 0$).
  • Centripetal Force: Inward force perpendicular to velocity required to maintain circular motion.

• Turning Effect & Centre of Gravity:

  • Moment of a Force:$\text{Moment} = \text{force} \times \text{perpendicular distance from pivot}$
  • Principle of Moments: For an object in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
  • Equilibrium: Achieved when there is no resultant force and no resultant moment.
  • Centre of Gravity: The point through which all of an object's weight acts.

• Energy, Work, Power & Pressure:

  • Work Done ($W$):$W = Fd = \Delta E$
  • Kinetic Energy ($E_k$):$E_k = \frac{1}{2}mv^2$
  • Gravitational Potential Energy Change ($\Delta E_p$):$\Delta E_p = mg\Delta h$
  • Principle of Conservation of Energy: Energy cannot be created or destroyed; it is always conserved.
  • Efficiency:$\text{Efficiency} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\% = \frac{\text{useful power output}}{\text{total power input}} \times 100\%$
  • Power ($P$): Work done or energy transferred per unit time:     $P = \frac{W}{t} = \frac{\Delta E}{t}$
  • Pressure ($p$): Force per unit area:     $p = \frac{F}{A}$
  • Liquid Pressure Change ($\Delta p$):$\Delta p = \rho g \Delta h$

Thermal Physics

• Kinetic Particle Model of Matter:

  • States of Matter:
  • Solids: Fixed lattice structure, particles vibrate about fixed positions.
  • Liquids: Particles close together, can slide over one another.
  • Gases: Particles far apart, rapid and random motion.
  • Absolute Zero: $0\,\text{K} = -273\,^\circ\text{C}$, the temperature at which particle motion stops.
  • Temperature Scale Conversion:$T(\text{K}) = \theta(^\circ\text{C}) + 273$
  • Boyle's Law (at constant temperature):$p_1 V_1 = p_2 V_2$

• Thermal Properties & Temperature:

  • Internal Energy: Total energy stored inside an object due to the motion and arrangement of its particles.
  • Specific Heat Capacity ($c$): Energy required per unit mass per unit temperature increase:     $c = \frac{\Delta E}{m \Delta \theta}$$\Delta E = mc\Delta \theta$
  • Latent Heat: Energy transferred during a change of state at constant temperature (fusion for solid-liquid; vaporisation for liquid-gas).
  • Evaporation: Escape of energetic particles from the surface of a liquid, causing the average kinetic energy of remaining particles to drop (cooling effect).

• Transfer of Thermal Energy:

  • Conduction: Thermal energy transfer in solids through particle lattice vibrations and free delocalised electrons (in metals).
  • Convection: Thermal energy transfer in fluids due to density changes (warmed fluid expands, becomes less dense, and rises).
  • Radiation: Thermal transfer via infrared electromagnetic waves without requiring a medium. Dull black surfaces are the best emitters and absorbers; shiny white surfaces are the best reflectors.

Waves

• General Wave Properties:

  • Waves transfer energy without transferring matter.
  • Transverse Waves: Vibration perpendicular to the direction of wave travel (e.g., light, water waves).
  • Longitudinal Waves: Vibration parallel to the direction of wave travel, forming compressions and rarefactions (e.g., sound).
  • Wave Equation:$v = f\lambda$
  • Reflection: Angle of incidence equals angle of reflection ($i = r$).
  • Refraction: Change in wave speed and wavelength when crossing a boundary between media.
  • Diffraction: Spreading of waves through a gap or around an edge; greatest when gap size is comparable to wavelength $\lambda$.

• Light:

  • Refractive Index ($n$):$n = \frac{\sin(i)}{\sin(r)}$
  • Critical Angle ($c$): Angle of incidence in an optically denser medium resulting in an angle of refraction of $90^\circ$:     $\sin(c) = \frac{1}{n}$
  • Total Internal Reflection: Occurs when angle of incidence $i > c$ travelling from a denser to a less dense medium.
  • Thin Lenses: Converging lenses focus parallel rays to a real principal focus $F$; diverging lenses cause parallel rays to diverge from a virtual focus.
  • Linear Magnification:$\text{Linear magnification} = \frac{\text{image length}}{\text{object length}}$
  • Dispersion: Separation of white light into spectrum colors (red, orange, yellow, green, blue, indigo, violet) by a prism due to varying refractive indices.

• Electromagnetic Spectrum:

  • Regions in order of increasing frequency / decreasing wavelength: Radio waves, Microwaves, Infrared, Visible light, Ultraviolet, X-rays, Gamma rays.
  • All electromagnetic waves travel at speed $c \approx 3.0 \times 10^8\,m/s$ in a vacuum (and approximately the same in air).

• Sound:

  • Longitudinal waves requiring a medium for transmission.
  • Speed of sound in air: \approx 330\text{--}350\,m/s$.\n - Audible range for healthy human ear: 20\,Hz$to$20000\,Hz$.
  • Pitch increases with frequency; loudness increases with amplitude.
  • Ultrasound: Sound waves with frequency greater than 20\,kHz$.\n\n# Electricity and Magnetism\n\n- **Magnetism:**\n - Like magnetic poles repel; unlike poles attract.\n - Hard magnetic materials (e.g., steel) retain permanent magnetism; soft magnetic materials (e.g., soft iron) lose magnetism easily.\n - Magnetic field lines point from North to South poles.\n\n- **Electrical Quantities:**\n - **Electric Charge (Q$):** Measured in Coulombs ($\text{C}). Like charges repel, unlike attract.\n - **Electric Current (I):** Rate of flow of charge:\n    I = \frac{Q}{t}\n - **Conventional Current:** Flows from positive to negative terminal; electron flow is from negative to positive.\n - **Electromotive Force (e.m.f., E):** Electrical work done by a source per unit charge moving around a complete circuit:\n    E = \frac{W}{Q}\n - **Potential Difference (p.d., V):** Work done per unit charge passing through a component:\n    V = \frac{W}{Q}\n - **Resistance (R):**\n    R = \frac{V}{I}\n - **Resistance of a Wire:** Directly proportional to length l$and inversely proportional to cross-sectional area$A:\n    R \propto \frac{l}{A}\n - **Electrical Power & Energy:**\n    P = IV = I^2 R = \frac{V^2}{R}\n    E = IVt\n - **Kilowatt-Hour (\text{kWh}$):**$1\,\text{kWh} = 3.6 \times 10^6\,\text{J}.\n\n- **Electric Circuits:**\n - **Series Circuit:** Current is identical at all points. Total resistance R = R_1 + R_2 + R_3$; total voltage$V = V_1 + V_2 + V_3$.
  • Parallel Circuit: Potential difference across each parallel branch is equal. Total current $I = I_1 + I_2 + \dots$. Combined resistance for two resistors:     $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \implies R = \frac{R_1 R_2}{R_1 + R_2}$
  • Potential Divider:$\frac{V_1}{V_2} = \frac{R_1}{R_2}$$V_1 = V \times \frac{R_1}{R_1 + R_2}$

• Electromagnetic Effects:

  • Magnetic field forms around current-carrying wires and solenoids.
  • Fleming's Left-Hand Rule (Motor Rule): Thumb = Thrust/Force, First finger = Field, Second finger = Current.
  • Fleming's Right-Hand Rule (Dynamo Rule): Thumb = Motion/Force, First finger = Field, Second finger = Induced Current.
  • Transformer Equations:$\frac{V_P}{V_S} = \frac{N_P}{N_S}$$I_P V_P = I_S V_S \quad (\text{for an ideal } 100\% \text{ efficient transformer})$
  • High-Voltage Transmission: Stepping up voltage lowers current, reducing $I^2 R$ thermal energy losses in transmission cables.

Nuclear Physics

• Nuclear Model of the Atom:
  • Atom consists of a dense positively charged nucleus (protons and neutrons) surrounded by orbiting electrons.
  • Proton Number ($Z$): Number of protons in the nucleus.
  • Nucleon Number ($A$): Total number of protons and neutrons in the nucleus.
  • Isotopes: Atoms of the same element with the same proton number $Z$ but different nucleon number A$.\n - **Nuclide Notation:**\n    _{Z}^{A}\text{X}\n\n- **Radioactivity:**\n - **Alpha (\alpha$) Particles:** Helium nucleus ($_2^4\text{He}), strongly ionising, stopped by paper, range of a few cm in air.\n - **Beta (\beta^-) Particles:** High-speed electron ($_{-1}^0 e), moderately ionising, stopped by a few mm of aluminium.
  • Gamma ($\gamma$) Rays: High-frequency electromagnetic radiation, weakly ionising, stopped by thick lead.
  • Radioactive Decay: Spontaneous, random disintegration of an unstable nucleus into a different nucleus/element.
  • Half-Life: Time taken for half the unstable nuclei in a given sample of an isotope to decay.

Space Physics

• Earth and the Solar System:

  • Average Orbital Speed:$v = \frac{2\pi r}{T}$
  • Solar System: Consists of the Sun (a medium-sized star containing over $99\%$ of the Solar System's mass), 8 planets, dwarf planets, moons, asteroids, and comets.
  • Gravitational attraction of the Sun keeps planets, asteroids, and comets in elliptical orbits.
  • Light-Year: Distance travelled by light in a vacuum in 1 year ($1\,\text{light-year} \approx 9.5 \times 10^{15}\,m$).

• Stars and the Universe:

  • Powered by Fusion: Stable stars are powered by the nuclear fusion of hydrogen into helium in their hot, dense cores.
  • Life Cycle of Low Mass Stars (e.g. Sun): Protostar $\rightarrow$ Stable Main Sequence Star $\rightarrow$ Red Giant $\rightarrow$ Planetary Nebula with White Dwarf $\rightarrow$ Black Dwarf.
  • Life Cycle of High Mass Stars: Protostar $\rightarrow$ Stable Star $\rightarrow$ Red Supergiant $\rightarrow$ Supernova $\rightarrow$ Neutron Star or Black Hole.
  • Redshift: Increase in wavelength of light from distant galaxies due to their motion away from Earth; provides evidence that the Universe is expanding and supports the Big Bang theory.
  • Hubble Constant ($H_0$): Ratio of the speed of recession $v$ of a galaxy to its distance $d$:     $H_0 = \frac{v}{d} \approx 2.2 \times 10^{-18}\,s^{-1}$
  • Age of the Universe:$\text{Age} \approx \frac{1}{H_0} \approx 14\text{ billion years}$