M1.1-Mathematical models in mechanics

Topic 1 : Mathematical Models IAL M1 NOTES In Edexcel Mechanics 1 (M1),various assumptions are made in order to simplify the mathematical models and calculations in mechanics problems. These assumptions allow for the application of idealized laws and principles. Below are some of the key assumptions commonly encountered: 1.Particles Assumption:Objects are modeled as particles. Implication:The object’s size is negligible, so its rotation, shape, and internal structure are ignored. All the mass of the object is considered to be concentrated at a single point, which simplifies the analysis of motion and forces. 2.Rods Assumption:Objects such as beams or bars are modeled as rods. Implication:A rod is assumed to be one-dimensional (has length but no width or depth) and rigid, meaning it cannot bend or stretch. This allows for simpler force analysis without considering deformation. 3.Smooth Surfaces Assumption:Surfaces in contact are smooth. Implication:There is no friction between the object and the surface, which eliminates the need to account for frictional forces in calculations. 4.Rough Surfaces Assumption:When a surface is described as rough, friction is present. Implication:Frictional forces need to be considered, usually modeled using the coefficient of friction, μ, and calculated with the formula F=μR, where R is the normal reaction force. 5.Light Objects Assumption:Objects such as strings or pulleys are often assumed to be light. Implication:The object’s mass is considered negligible, so it does not affect the system’s dynamics. For example, the tension in a light string is the same throughout its length. 6.Inextensible Strings Assumption:Strings are inextensible. Implication:The string does not stretch, meaning the objects connected by the string move with the same speed and acceleration. This assumption simplifies the analysis of systems involving pulleys and connected particles. 7.Smooth Pulleys Assumption:Pulleys are often considered smooth. Implication:There is no friction in the pulley, meaning the tension in the string remains constant on both sides of the pulley. 8.Uniform Gravitational Field Assumption:Gravity is constant and acts vertically downward with acceleration g=9.8 m/s2 Implication:The weight of an object can be calculated as W=mg, where m is the mass of the object and g is the acceleration due to gravity. 9.Neglecting Air Resistance Assumption:Air resistance is often ignored in many mechanics problems. Implication:This simplifies motion analysis, as no drag forces are considered, and objects are treated as moving freely under the influence of gravity or other forces. 10.Rigid Bodies Assumption:Objects that are not particles may be assumed to be rigid bodies. Implication:These objects do not deform under applied forces, which means that the distances between any two points on the object remain constant, allowing for simpler force and moment calculations. 11.Laminar Objects Assumption:Some objects are assumed to be laminar (thin and flat). Implication:The object has area but negligible thickness, which allows simplified calculations, especially in problems involving moments and centers of mass. These assumptions allow for the creation of idealized models, which makes the mathematical analysis more manageable. However, real-world scenarios may require adjustments or additional factors when these assumptions no longer hold. Modelling Assumptions Assumptions made·   motion takes place in a straight line·   acceleration is constant·   air resistance can be ignored·   objects are modelled as masses concentrated at a single point (no rotation)·   g is assumed to be 9.8m/s2  everywhere at or near the Earths surface TOPIC Menu M1.1-Mathematical models in mechanics M1.2-Vectors in Mechanics M1.3-Kinematics of a particle moving in a straight line M1.4-Dynamics of a particle moving in a straight line or plane M1.5-Statics of a particle M1.6-Moments PRACTISE EXTRAS

TOPIC 24-MEDICAL PHYSICS

Topic 24 : Medical Physics Menu CHANGE TOPIC YR 13 PHYSICS START PAGE TOPIC 12-MOTION IN A CIRCLE TOPIC 14-TEMPERATURE TOPIC 15-16-IDEAL GASES & THERMODYNAMICS TOPIC 18-ELECTRIC FIELDS TOPIC 19-CAPACITANCE TOPIC 20-MAGNETIC FIELDS TOPIC 21-ALTERNATING CURRENTS TOPIC 22-QUANTUM PHYSICS TOPIC 23-NUCLEAR PHYSICS TOPIC 24-MEDICAL PHYSICS NOTES TOPIC 24 MEDICAL PHYSICS.pdf Ultrasound X Rays https://youtu.be/hTz_rGP4v9Yhttps://youtu.be/IsaTx5-KLT8 PET Scan https://youtu.be/oySvkmezdo0https://youtu.be/GHLBcCv4rqk PRACTISE TOPIC 24 MEDICAL PHYSICS – WORKSHEET 1.pdf Extra support content EXTRAS Piezoelectric Effect Image Formation with Ultrasound X-Ray Production Piezoelectric Effect   The piezoelectric effect is the ability of certain materials to generate an electric charge when subjected to mechanical stress (reverse effect) or to deform when an electric field is applied (forward effect). Forward Piezoelectric Effect: When an alternating current (AC) electric signal is applied to the piezoelectric material, it causes the material to deform (expand or contract). This is because the electric field from the AC signal causes a shift in the internal charges of the material, resulting in mechanical strain. This is the principle used to create ultrasound waves. Reverse Piezoelectric Effect: When a mechanical force (such as compression or tension) is applied to the piezoelectric material, it causes the material to generate an electric signal (EMF). The mechanical deformation causes a redistribution of charges within the material, generating an electrical response. This is used in ultrasound to detect the sound waves reflected from tissue or objects. Image Formation with Ultrasound The process of image generation from the detected sound waves in ultrasound involves several steps: Sound Wave Emission: The piezoelectric transducer emits high-frequency sound waves (ultrasound) into the body or material being examined. Wave Reflection: As the ultrasound waves travel through the medium, they encounter different tissues or structures with varying densities. These cause the sound waves to reflect back to the transducer. Detection of Echoes: The same piezoelectric transducer detects the reflected sound waves (echoes) as they return. The time it takes for the sound waves to travel to and from the tissue gives information about the distance to the reflecting surfaces. Signal Conversion: The reflected sound waves cause the transducer to vibrate, generating an electric signal (via the reverse piezoelectric effect). The strength and time delay of the echoes are measured. Image Construction: The electric signals are then processed by a computer, which calculates the depth and location of the reflecting surfaces based on the speed of sound in the medium. These signals are used to create a visual image of the internal structures, with different tissues appearing in varying shades of grey or color depending on the density and composition of the tissue. Summary: The image is formed by processing the time delay and intensity of the reflected sound waves, with denser materials reflecting more strongly and at different speeds, allowing for a detailed internal view. X-Ray Production X-rays are produced when high-speed electrons collide with a metal target. Here’s a simplified breakdown: 1. Electron Acceleration: Cathode: A filament (similar to a light bulb filament) is heated, releasing electrons through a process called thermionic emission. Voltage: A high voltage is applied between the cathode (negative) and the anode (positive). This accelerates the electrons towards the anode at extremely high speeds. 2. Collision and X-ray Production: Anode: The accelerated electrons collide with a metal target (usually tungsten) on the anode. Two primary mechanisms: Bremsstrahlung Radiation: Most common. Electrons are slowed down or deflected by the strong electric field of the target’s nucleus. This sudden deceleration results in the release of energy in the form of X-rays. Characteristic Radiation: Less common. An incoming electron collides with an inner-shell electron of a target atom, knocking it out. An electron from a higher energy level fills the vacancy, releasing energy as an X-ray photon with a specific energy characteristic of the target material. 3. X-ray Beam: The resulting X-rays are emitted from the target in all directions. A window in the X-ray tube allows a specific beam of X-rays to pass through and be directed towards the patient or object being imaged. Key Points: Voltage (kVp): Controls the energy (penetrating power) of the X-rays. Higher kVp results in higher energy X-rays. Current (mA): Controls the number of electrons emitted from the cathode, thus influencing the intensity of the X-ray beam. In summary: X-ray production involves accelerating electrons to high speeds and then abruptly stopping them. This interaction results in the release of energy in the form of X-rays, which can be used for medical imaging and other applications.

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NOTABLE PHYSICISTS AND MATHEMATICIANS

Luminary Physicists and Mathematicians LUMINARY LIST Isaac Newton (1642–1727)​ Michael Faraday (1791–1867) Sir John Ambrose Fleming FRS (1849 – 1945) ​ Henri Becquerel (1852–1908)​ Albert Einstein (1879–1955) Albert Einstein (1879–1955) Albert Einstein Introduction Albert Einstein (1879–1955) was a German-born theoretical physicist renowned for developing the theories of relativity, which revolutionized our understanding of space, time, and gravity. His contributions to quantum mechanics, statistical physics, and cosmology have had a lasting impact on modern science. Early Life and Education Albert Einstein was born on March 14, 1879, in Ulm, Germany, to a Jewish family. As a child, he showed an early fascination with mathematics and science. However, he struggled with the rigid structure of the German education system. In 1895, Einstein failed the entrance exam to the Swiss Federal Polytechnic School (ETH Zurich) but later passed on his second attempt in 1896. He graduated in 1900 with a degree in physics and mathematics but struggled to find a teaching position. In 1902, he secured a job as a clerk at the Swiss Patent Office in Bern, where he had time to develop his scientific theories. Scientific Achievements 1. The Miracle Year (1905) In 1905, often called Einstein’s “Annus Mirabilis” (Miracle Year), he published four groundbreaking papers that changed physics forever: Special Theory of Relativity – Introduced the concept that time and space are relative, leading to the famous equation E = mc² (energy equals mass times the speed of light squared). Photoelectric Effect – Explained how light behaves as both a particle and a wave, laying the foundation for quantum mechanics. This work won him the Nobel Prize in Physics in 1921. Brownian Motion – Provided mathematical proof for the existence of atoms by explaining the random movement of particles in a liquid. Mass-Energy Equivalence – Demonstrated that a small amount of mass could be converted into a large amount of energy, a concept later used in nuclear energy. 2. General Theory of Relativity (1915) In 1915, Einstein introduced the General Theory of Relativity, which described gravity as the bending of spacetime by massive objects. This theory was confirmed in 1919 when British astronomer Sir Arthur Eddington observed the bending of starlight during a solar eclipse. 3. Quantum Mechanics and the Einstein-Podolsky-Rosen (EPR) Paradox Although Einstein contributed significantly to quantum mechanics, he was skeptical of some of its interpretations. In 1935, he co-authored the EPR Paradox, which questioned quantum entanglement, a phenomenon that is now crucial to modern physics. 4. Later Years and the Atomic Bomb In 1933, Einstein fled Nazi Germany and moved to the United States, joining Princeton University. In 1939, he signed a letter to President Franklin D. Roosevelt, warning that Germany might develop nuclear weapons. This led to the Manhattan Project, though Einstein himself was not directly involved in building the bomb. Later Life and Legacy After World War II, Einstein became an advocate for nuclear disarmament, world peace, and civil rights. He declined an offer to become the President of Israel in 1952 and continued his research until his death on April 18, 1955, in Princeton, New Jersey. Impact on Science and Technology Einstein’s work continues to influence various fields, including: Modern GPS technology, which relies on relativity to ensure accuracy. Space exploration and black hole research, supported by his theories. Quantum computing and cryptography, based on principles he helped establish. Conclusion Albert Einstein was not only a scientific genius but also a humanitarian and advocate for peace. His theories remain fundamental to physics, shaping our understanding of the universe and leading to technological advancements that benefit society today Henri Becquerel (1852–1908) Henri Becquerel was a French physicist who is best known for his discovery of radioactivity. This groundbreaking discovery earned him the Nobel Prize in Physics in 1903, which he shared with Marie Curie and Pierre Curie. Key Contributions: Discovery of Radioactivity (1896):Becquerel was studying phosphorescence in uranium salts and their ability to emit light after exposure to sunlight. During his experiments, he accidentally discovered that uranium compounds could emit radiation spontaneously, without any external energy source like sunlight. This radiation could expose photographic plates, even if the uranium was wrapped in black paper. This observation led him to conclude that the emission was a new, unknown type of radiation — what we now call radioactivity. The Path to Discovery: Inspired by Wilhelm Roentgen’s discovery of X-rays in 1895, Becquerel hypothesized that phosphorescent materials, such as uranium salts, might emit similar rays. He placed uranium salts on a photographic plate wrapped in black paper and left them in sunlight. Due to cloudy weather, he stored the experimental setup in a dark drawer but later found that the photographic plate was still exposed. This proved that uranium emitted radiation spontaneously, without any need for external light or energy. Impact on Science: Becquerel’s discovery of radioactivity laid the foundation for: Nuclear physics and the study of radioactive elements. The work of the Curies, who discovered polonium and radium. The development of technologies such as nuclear power, medical imaging, and cancer treatments using radiation. Legacy: The unit of radioactivity, the becquerel (Bq), is named in his honor. 1 Bq = 1 decay per second, representing the rate at which a radioactive substance undergoes decay. Henri Becquerel’s contributions changed our understanding of atomic and nuclear science, making him one of the pioneers of modern physics. Sir.Isaac Newton (1642–1727) Isaac Newton (1642–1727) was an English mathematician, physicist, astronomer, and one of the most influential scientists in history. He played a critical role in the development of modern science through his groundbreaking discoveries and theories. Below is a summary of his key contributions and achievements: Early Life Born: January 4, 1643 (December 25, 1642, Old Style calendar) in Woolsthorpe, England. He was a premature child, and his father died before he was born. His mother remarried, leaving him to be raised by his grandparents. He showed an early interest in mechanics and mathematics. Major Contributions 1. Laws of Motion Newton formulated the three laws of motion, which form the foundation of classical mechanics: First Law (Law of Inertia):An object remains at rest or in uniform motion in a straight line unless acted upon by an external force. Second Law (F = ma):The force acting on

TOPIC 12-MOTION IN A CIRCLE

Topic 12 : Motion in a Circle Menu CHANGE TOPIC PHYSICS START PAGE TOPIC 14: TEMPERATURE TOPIC 15-16 : IDEAL GASES & THERMODYNAMICS TOPIC 18-ELECTRIC FIELDS TOPIC 19-CAPACITANCE TOPIC 20-MAGNETIC FIELDS TOPIC 21-ALTERNATING CURRENTS TOPIC 22-QUANTUM PHYSICS REVISION KITS NOTES CIRCULAR MOTION-INTRO.pdfCIRCULAR MOTION-Centripetal Acceleration.pdfCIRCULAR MOTION-DERIVING a.pdfCIRCULAR MOTION-FORMULA-SUMMARY.pdf Uniform Circular Motion Uniform Circular Motion 1. Radian and Angular Displacement in Radians • Radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.• Angular Displacement (θ) is the angle through which an object moves along the circular path. It is measured in radians.• Formula: θ = s / r  Where:    – s is the arc length.    – r is the radius of the circle. 2. Angular Speed (ω) • Angular Speed (ω) is the rate at which an object’s angular displacement changes with respect to time.• It is expressed in radians per second (rad/s).• Formula:  ω = Δθ / Δt  Where:    – Δθ is the change in angular displacement (in radians).    – Δt is the time interval over which the change occurs. 3. Relationships between Angular and Linear Quantities • ω = 2π / T  – T is the period (the time taken for one complete revolution).  – This shows that the angular speed is inversely proportional to the period.• v = rω  Where:    – v is the linear speed (tangential speed) of the object moving in the circular path.    – r is the radius of the circular path.    – ω is the angular speed.   PRACTISE EXTRAS

TOPIC 23-NUCLEAR PHYSICS

Topic 23 : Nuclear Physics Menu CHANGE TOPIC PHYSICS START PAGE TOPIC 12-MOTION IN A CIRCLE TOPIC 14: TEMPERATURE TOPIC 15-16 : IDEAL GASES & THERMODYNAMICS TOPIC 18-ELECTRIC FIELDS TOPIC 19-CAPACITANCE TOPIC 20-MAGNETIC FIELDS TOPIC 21-ALTERNATING CURRENTS TOPIC 22-QUANTUM PHYSICS TOPIC 23-NUCLEAR PHYSICS NOTES TOPIC 23 NUCLEAR PHYSICS.pdf Why Eb Reduces for larger Nuclei Origin of Nuclear Force Pions and Mesons Fundamental Particles Energy Release Why Eb Reduces for larger Nuclei For heavier nuclei (with mass number A>56), the binding energy per nucleon gradually decreases as the nucleon number increases. This trend indicates that heavier nuclei are less stable compared to intermediate-sized nuclei, and this can be explained by the following factors: 1. Nuclear Forces and Distance Between Nucleons In a nucleus, protons and neutrons are bound together by the strong nuclear force, which is a short-range force. As the number of nucleons increases, the effective range of the strong nuclear force becomes less significant for the nucleons at the edge of the nucleus. These nucleons experience weaker attraction compared to those near the center. For larger nuclei, the strong force can’t efficiently hold the outer nucleons together, leading to a lower binding energy per nucleon. 2. Coulomb Repulsion Between Protons Larger nuclei contain more protons, which repel each other due to the Coulomb (electrostatic) force. This repulsion increases with the number of protons in the nucleus, and it becomes harder to keep the nucleus together as the repulsive force overcomes the attractive strong nuclear force. This effect reduces the binding energy per nucleon for heavier nuclei. 3. Nuclear Saturation The nuclear force is saturating, meaning it only affects nucleons that are in close proximity to each other. As a result, when the number of nucleons increases, the additional nucleons contribute less to the overall binding energy. In lighter nuclei, each nucleon is able to interact strongly with many other nucleons, leading to a higher binding energy per nucleon. In contrast, heavier nuclei have more nucleons that are not as effectively bound, lowering the average binding energy per nucleon. 4. Shell Effects and Nuclear Structure In nuclei with intermediate mass (around A≈56, such as iron), nucleons fill nuclear energy levels in a manner that optimizes the strong nuclear force. This results in a relatively high binding energy per nucleon. For heavier nuclei, the shell effects (where nucleons fill discrete energy levels) become less pronounced, and the added nucleons do not contribute as effectively to the overall binding, further reducing the binding energy per nucleon. Conclusion: The decrease in binding energy per nucleon in heavier nuclei is primarily due to the combination of weaker nuclear forces acting on the outer nucleons, increased Coulomb repulsion between protons, and the saturation of the nuclear force. These factors make it harder to bind additional nucleons, which explains why nuclei with higher atomic numbers (especially beyond iron) become less stable and have a lower binding energy per nucleon.   Origin of Nuclear Force The nuclear force originates from the fundamental interactions between the constituent particles of nucleons (protons and neutrons), which are quarks and gluons. The nuclear force, also known as the strong nuclear force, is a residual effect of the strong interaction, one of the four fundamental forces in nature. Here’s a breakdown: 1. The Strong Interaction and Quantum Chromodynamics (QCD) At the most fundamental level, protons and neutrons are composed of quarks (up and down quarks), bound together by the exchange of particles called gluons. The gluons mediate the strong interaction, described by the theory of Quantum Chromodynamics (QCD). This interaction is responsible for keeping quarks tightly confined within protons and neutrons. 2. Residual Strong Force Between Nucleons While the strong interaction primarily binds quarks within individual nucleons, a residual effect of this force extends beyond individual nucleons, binding protons and neutrons together in the nucleus. This residual strong force is what we refer to as the nuclear force. It acts between nucleons and has the following characteristics: Attractive at medium distances (1–3 femtometers): This attraction binds protons and neutrons together in the nucleus. Repulsive at very short distances (<1 femtometer): This prevents nucleons from collapsing into each other. Short-ranged: It diminishes rapidly beyond about 3 femtometers, which is why it cannot bind nuclei with extremely large numbers of nucleons effectively. 3. Mediators of the Nuclear Force: Pions The nuclear force can be described as mediated by the exchange of mesons, particularly pions (particles composed of a quark and an antiquark). The exchange of pions between nucleons creates the attractive and repulsive forces that hold the nucleus together. Summary The origin of the nuclear force lies in the strong interaction between quarks, mediated by gluons, as described by Quantum Chromodynamics (QCD). The nuclear force is a residual effect of this interaction, manifesting as the force that binds nucleons together within atomic nuclei.   Pions and Mesons 1. Mesons Definition: Mesons are a class of subatomic particles composed of one quark and one antiquark, bound together by the strong interaction mediated by gluons. Characteristics: Intermediate mass: Mesons are heavier than electrons but lighter than protons and neutrons. Force mediators: Mesons play a key role in the residual strong force that binds protons and neutrons in the nucleus. Unstable: Mesons are highly unstable and decay quickly into other particles (e.g., electrons, photons, or neutrinos). Examples: Pions (π+pi^+π+, π−pi^-π−, π0pi^0π0) and kaons (K+K^+K+, K−K^-K−, K0K^0K0). 2. Pions Definition: Pions (πpiπ) are the lightest and most well-known mesons. They play a central role in mediating the nuclear force between nucleons (protons and neutrons) in an atomic nucleus. Types of Pions: Charged Pions: π+pi^+π+: Composed of an up quark (uuu) and an anti-down quark (dˉbar{d}dˉ). π−pi^-π−: Composed of a down quark (ddd) and an anti-up quark (uˉbar{u}uˉ). Neutral Pion (π0pi^0π0): Composed of a quark-antiquark pair, such as a mixture of uuˉubar{u}uuˉ and ddˉdbar{d}ddˉ. Role in the Nuclear Force: Pions are exchanged between protons and neutrons in the nucleus, creating an attractive force that binds these nucleons together. This exchange is analogous to how photons mediate the electromagnetic force,

IGCSE PHYC-2026 CLASS REVISION KITS

REVISION KITS & MASTERIES MASTERIES MASTERY 1.pdfMASTERY 1-ANSWERS.pdfMASTERY 2.pdfMASTERY 2-SCHEME.pdf Energy Work and Power Easy.pdfEnergy Work and Power Easy-markScheme.pdfEnergy Work and Power Hard.pdfEnergy Work and Power Hard-markScheme.pdfEnergy Work and Power Water 2.pdfEnergy Work and Power Water 2-markScheme.pdf REVISION KITS OTHER RESOURCES Menu GO TO IG START PAGE UNIT1:MOTION,FORCES,ENERGY TOPIC 1 MEASUREMENT TECHNIQUES TOPIC 2 MOTION TOPIC 3 MASS,WEIGHT AND DENSITY TOPIC 4 EFFECTS OF A FORCE TOPIC 5 MOMENTS TOPIC 6 MOMENTUM TOPIC 7 PRESSURE TOPIC 8 ENERY,WORK & POWER TOPIC 9 ENERGY RESOURCES UNIT 2:THERMAL PHYSICS TOPIC 10 KINETIC PARTICLE MODEL TOPIC 11 THERMAL PROPERTIES TOPIC 12 THERMAL TRANSFERS UNIT 3: WAVES TOPIC 13 WAVES-PROPERTIES MULTICHOICE REVISION UNIT 1 MULTICHOICE REVISION UNIT 2 REVISION KITS

TOPIC 22-QUANTUM PHYSICS

Topic 22 : Quantum Physics Menu CHANGE TOPIC PHYSICS START PAGE TOPIC 14: TEMPERATURE TOPIC 15-16 : IDEAL GASES & THERMODYNAMICS TOPIC 18-ELECTRIC FIELDS TOPIC 19-CAPACITANCE TOPIC 20-MAGNETIC FIELDS TOPIC 21-ALTERNATING CURRENTS TOPIC 22-QUANTUM PHYSICS REVISION KITS NOTES TOPIC 22 QUANTUM PHYSICS.pdfTOPIC 22 QUANTUM PHYSICS.pptx Emission & Absorption Quantum Physics Summary Emission & Absorption Emission and Absorption Line Spectra (using Photon Absorption and Emission with Hydrogen as an Example): Emission Line Spectrum of Hydrogen: When hydrogen atoms are energized, electrons jump to higher energy levels. As they return to lower levels, they emit photons with specific energies. Each photon corresponds to a particular wavelength, creating bright emission lines at those wavelengths. For example, when an electron drops from the third to the second energy level, it emits a photon with the H-alpha wavelength in the red part of the visible spectrum. Absorption Line Spectrum of Hydrogen: When continuous light passes through a cooler hydrogen gas, electrons in the hydrogen atoms absorb photons of specific energies. This absorption excites electrons to higher energy levels, removing photons of specific wavelengths from the continuous spectrum. This produces dark lines in the spectrum, matching the wavelengths of the emission lines, like H-alpha, H-beta, and others in the Balmer series. Using photon absorption and emission, hydrogen’s line spectra reveal its presence and help determine conditions in stars and interstellar gas.   Quantum Physics Summary Summary of Quantum Physics Quantum physics is the branch of science that deals with the behavior of matter and energy on the smallest scales, such as atoms and subatomic particles. It departs significantly from classical physics by introducing concepts that are non-intuitive but experimentally verified. Key Principles: Wave-Particle Duality: Particles, like electrons and photons, exhibit both wave-like and particle-like behavior depending on the experiment. Quantization: Energy levels in atoms and systems are discrete, not continuous. Electrons in atoms, for example, can only occupy certain allowed energy states. Uncertainty Principle: Heisenberg’s Uncertainty Principle states that it is impossible to precisely measure both the position and momentum of a particle simultaneously. Superposition: Particles can exist in multiple states simultaneously until measured, as described by Schrödinger’s wave function. Entanglement: When particles interact, their states can become linked, such that the state of one instantly affects the other, even over large distances. Probability and Measurement: Quantum systems are governed by probabilities. The outcome of an event is described by a wave function, which gives the likelihood of different results. Applications: Semiconductors: Basis for modern electronics like transistors and microchips. Lasers: Used in medicine, communication, and data storage. Quantum Computing: Exploits superposition and entanglement for vastly more powerful computation. Medical Imaging: Techniques like MRI rely on quantum principles. Nanotechnology: Manipulates materials at atomic scales for advanced technologies. Quantum physics revolutionized our understanding of nature, laying the foundation for modern technology and bridging the gap between the macroscopic classical world and the microscopic quantum realm.   PRACTISE TOPIC 22 QUANTUM PHYSICS -WORKSHEET1.pdfTOPIC 22 QUANTUM PHYSICS -WORKSHEET1 -MARKSCHEME.pdfTOPIC 22 QUANTUM PHYSICS -WORKSHEET2.pdfTOPIC 22 QUANTUM PHYSICS -WORKSHEET2 -MARKSCHEME.pdf EXTRAS

Year 13 Physics-TOPIC 21-ALTERNATING CURRENTS

Topic 21 : Alternating Currents Menu CHANGE TOPIC PHYSICS START PAGE TOPIC 14: TEMPERATURE TOPIC 15-16 : IDEAL GASES & THERMODYNAMICS TOPIC 18-ELECTRIC FIELDS TOPIC 19-CAPACITANCE TOPIC 20-MAGNETIC FIELDS TOPIC 21-ALTERNATING CURRENTS TOPIC 22-QUANTUM PHYSICS NOTES TOPIC 21 ALTERNATING CURRENTS.pdf Why DC Square Waves Modulation Why DC Why most Electronic Devices use DC Most electronics use direct current (DC) for several reasons: Stable Voltage and Current: DC provides a constant voltage and current, which is essential for sensitive electronic components that require a steady power supply to operate correctly. Fluctuations in AC could cause inconsistent performance or even damage to components. Compatibility with Electronic Components: Many components in electronic devices, such as transistors, diodes, and integrated circuits (ICs), are designed to operate on DC. These components rely on a consistent polarity, which DC provides, whereas AC continuously changes direction. Ease of Storage: DC can be easily stored in batteries, which provide portable and reliable power sources for devices like laptops, smartphones, and other portable electronics. Batteries inherently produce DC, making them compatible with DC-powered devices without conversion. Lower Risk of Electromagnetic Interference (EMI): DC power does not create electromagnetic interference in the same way AC does, which is beneficial for devices with delicate circuits that could malfunction due to interference. Simple Conversion for Small-Scale Electronics: Although AC power is used for large-scale transmission due to its efficiency over long distances, it can be converted to DC using rectifiers when it reaches homes or devices. This allows electronics to benefit from AC distribution while still using DC internally. In short, DC power provides the stable, consistent, and compatible power source required by most electronic devices for reliable operation. Square Waves Square Waves A square wave graph for current or voltage occurs when the waveform alternates directly between two fixed values (e.g., maximum positive and maximum negative) without gradual transitions, creating a sharp “on-off” pattern. Square waves are commonly used in the following contexts: Digital Electronics: Digital signals in computers and other digital systems are typically represented by square waves, where “high” (e.g., +5V) represents a binary 1, and “low” (e.g., 0V or ground) represents a binary 0. These square waves are essential for clock signals in digital circuits, helping synchronize operations by switching between high and low states at a regular frequency. Pulse Width Modulation (PWM): PWM signals, which are square waves with varying duty cycles, are used to control the power delivered to devices. By changing the “on” versus “off” time in each cycle, PWM controls the average power sent to devices such as LEDs, motors, or audio amplifiers. PWM is widely used in applications where fine control over power or speed is required, such as in dimming lights or controlling motor speed. Switching Power Supplies: In switching power supplies, square waves are used to convert high-frequency AC to DC. The switching action allows for more efficient power conversion and reduced heat loss compared to traditional linear power supplies. Square waves at high frequencies help to reduce the size of components like transformers and capacitors in power supply circuits. Signal Generation and Testing: Square waves are used as test signals in electronics for evaluating the response of circuits and systems, especially for testing the behavior of amplifiers, filters, and oscilloscopes. They allow engineers to see how circuits respond to rapid transitions, which can reveal performance issues or limitations. Communication Systems: Some communication systems, especially in low-frequency or binary data transmission, use square waves to transmit data, as the sharp transitions between levels make it easier to detect the presence of signals. In summary, square waves are prominent in applications that involve digital signals, precise control over power, and efficient power conversion. Their rapid switching capability is ideal for systems requiring distinct “on” and “off” states. Modulation A demodulator is an electronic device or circuit used to extract the original information signal from a modulated carrier wave in communication systems. This process, known as demodulation, is essential in wireless and wired communications, including radio, television, and digital data transmission, where information is transmitted over distances by embedding it within high-frequency carrier waves. How Demodulation Works In communication systems, information (such as audio, video, or data) is often embedded or encoded onto a carrier wave—a process called modulation. Demodulation reverses this process by separating the information from the carrier wave, recovering the original message. Types of Modulation and Corresponding Demodulators Different modulation methods require specific demodulators: Amplitude Modulation (AM) Demodulator: Extracts the original signal by detecting variations in the amplitude (height) of the carrier wave. Commonly used in AM radio receivers to recover audio signals. Frequency Modulation (FM) Demodulator: Detects frequency changes in the carrier wave to retrieve the information signal. Used in FM radio receivers, where audio is encoded as frequency variations. Phase Modulation (PM) Demodulator: Recovers information by detecting phase shifts in the carrier wave. Employed in certain digital communication systems. Applications of Demodulators Radio Broadcasting: Demodulates radio signals for audio playback. Television: Extracts audio and video signals from broadcast or cable signals. Data Communications: Used in modems to convert internet data into usable digital signals. Cellular and Satellite Communication: Recovers voice, data, or multimedia signals for mobile and satellite devices. Importance of Demodulation Demodulation enables effective communication by allowing receivers to retrieve the information signal originally embedded in the carrier. Without demodulation, it would be impossible to interpret transmitted data accurately, as the information would remain embedded within the high-frequency carrier wave.   PRACTISE TOPIC 21-ALTERNATING CURRENTS-WORKSHEET 1.pdfTOPIC 21-ALTERNATING CURRENTS-WORKSHEET 1 SCHEME.pdf EXTRAS

IG MATH-TOPIC 2: Fractions, percentages, and standard form

FRACTIONS & PERCENTAGES Menu CHOOSE ANOTHER TOPIC MAIN PAGE Unit 1:Number 2: Fractions, percentages, and standard form 3: Sequences, surds, and sets 4: Understanding measurement 5: Making Sense of Algebra 6: Equations, Factors & Formulae 7: Straight line graphs and Quadratic Equations​ 8: Lines, Angles & Shapes IGCSE MATH-PAST PAPERS & REVISION TESTS Worked_Examples_Fractions_and_Percentages.pdf PRACTICE The four rules 2-markScheme.pdfThe four rules 1-markScheme.pdfThe four rules 2.pdfThe four rules 3.pdfThe four rules 3-markScheme.pdfUse directed numbers.pdfUse directed numbers-markScheme.pdfOrder quantities.pdfOrder quantities-markScheme.pdfConvert between equivalent forms of fractions, decimals and percentages.pdfConvert between equivalent forms of fractions, decimals and percentages-markScheme.pdfRatio and proportion 1.pdfThe four rules 1.pdfRatio and proportion 1-markScheme.pdfRatio and proportion 2.pdfRatio and proportion 2-markScheme.pdf Pick a Topic Menu Unit 1: Number IG MATH-TOPIC1-NUMBER IG MATH-TOPIC 2: Fractions, percentages, and standard form IG MATH-TOPIC 3: Sequences, surds, and sets Unit 2:Algebra and graphs IG MATH-TOPIC 5: Making Sense of Algebra IG MATH-TOPIC 6: Equations, Factors & Formulae Unit 3:Coordinate geometry TOPIC 7: Straight line graphs and Quadratic Equations​ Unit 4:Geometry TOPIC 8: Lines, Angles & Shapes Unit 5:Mensuration CAIE IGCSE MATH-UNIT 5 MENSURATION IG MATH-TOPIC 4: Understanding measurement