Ultrasound is a longitudinal wave with a frequency greater than 20kHz. It is non-ionising, non-invasive and quick. Ultrasound used in medical imaging typically has frequencies of 1-15MHz, arriving in pulses with a frequency of 5kHz. It is generated and detected by...

# Notes

## Diagnostic Methods in MedicineDiagnostic Methods in Medicine

Medical tracers such as technetium-99m and fluorine-18 can be used as diagnostic tools. Inject tracer (into bloodstream) Taken up by organ or shows blockage By emitting radiation detected by camera More specifically, tracers may be used to: Monitor blood flow in...

## Using X-raysUsing X-rays

X-rays are high energy photons with short wavelengths, range 10-8 to 10-13m. They are produced in X-ray tubes: Evacuated tube containing two electrodes (evacuated so electrons pass through without interacting with gas atoms) An external power supply is used to create...

## Nuclear Fission and FusionNuclear Fission and Fusion

Einstein’s mass-energy equation describes how mass and energy are interchangeable quantities. Conservation of mass-energy can also be used to explain radioactivity phenomena: when energy is released in the KE of an alpha or beta particle (or the energy of a gamma...

## RadioactivityRadioactivity

Radioactive decay is random and spontaneous. Random: cannot be predicted; each atom has the same chance of decaying in a given time interval 2. Spontaneous: not affected by external factors like pressure or the presence of other nuclei in the sample 3 types of...

## Fundamental ParticlesFundamental Particles

Each particle has a corresponding antiparticle with the same mass but opposite values for all other properties (e.g. strangeness, charge). Examples of particle-antiparticle pairs include: electron-positron, proton-antiproton, neutronantineutron,...

## The Nuclear AtomThe Nuclear Atom

Rutherford’s alpha-scattering experiment provided evidence of a small, charged nucleus. A narrow beam of alpha particles, all of the same kinetic energy from a radioactive source were targeted at a thin piece of gold foil which was only a few atomic layers thick. The...

## ElectromagnetismElectromagnetism

When a conducting rod moves in a field, the electrons experience a force so accumulate at one end. This induces an emf across the ends of the rod. An emf can be induced in a flat coil or solenoid by moving he coil towards or away from the magnet’s poles, or moving a...

## Motion of Charged ParticlesMotion of Charged Particles

The force on a charged particle travelling at right angles to a uniform magnetic field is given by: According to Fleming’s left hand rule, the force experienced by the particle is always perpendicular to its direction of motion. This is the condition for circular...

## Magnetic fieldsMagnetic fields

Magnetic fields are regions where a force is exerted on magnetic materials. They are created by moving charges and permanent magnets. Magnetic fields can be mapped by magnetic field lines, which pass from north to south, The closer the lines, the stronger the field....

## Electric Potential and EnergyElectric Potential and Energy

Electric potential energy is given by the formula This result is obtained by integrating the force-distance graph because work done is equal to the area under the graph. Electric potential is the electric potential energy experienced per unit charge. Therefore, it...

## Uniform Electric FieldsUniform Electric Fields

The electric field strength of a uniform electric field is given by: Derivation: The units of electric field strength can therefore be given as This also yields some equations of capacitance: Where is the permittivity of free space and ε is the relative...

## Coulomb’s LawCoulomb’s Law

Coulomb’s law can be applied to any point charges. It is given by: Since , it follows that, for a point charge, the electric field strength is given by: Gravitational and electric fields show some similarities and differences: ...

## Point and Spherical ChargesPoint and Spherical Charges

Fields are regions in which an object will experience a force at a distance (non-contact force). An electric field is created by charged objects. A uniformly charged sphere can be modelled can be modelled as a point charge at its centre. Electric field lines map...

## Uniform Electric FieldUniform Electric Field

The capacitance of a parallel plate capacitor depends on the separation between the plates and the area of overlap between them. Where is the permittivity of the dielectric, given by = 0 (where 0 is the permittivity of free space and is the relative permittivity of...

## Charging and Discharging CapacitorsCharging and Discharging Capacitors

Capacitors can be charged and discharged through a resistor. Meters with a data logger can be used to plot a graph of charge, p.d. or current against time. When a capacitor charges: Electrons flow onto the plate connected to the negative terminal of the power supply...

## EnergyEnergy

Capacitors store small amounts of energy that can be accessed quickly. The energy stored by a capacitor is equal to the work done by the battery. This is given by the area under a p.d.-charge graph. Capacitors are found in electronic devices that don’t need to store...

## CapacitorsCapacitors

Capacitors are electrical components that can store charge. They consist of two conducting plates separated by a dielectric. When connected to a power source, positive and negative charge build up on opposite plates by removal and addition of electrons. The insulating...

## CosmologyCosmology

Astronomical distances are expressed using three specialist units: Astronomical unit: average distance between the Earth and the Sun Light-year: distance travelled by light in a vacuum in a time of one year Parsec: the distance from which a base length (radius) of 1...

## Electromagnetic Radiation From StarsElectromagnetic Radiation From Stars

When electrons are bound to their atoms in a gas, they can only exist in one of a discrete set of energies referred to as energy levels. Energy levels are negative because energy is required to remove an electron from the atom; an electron with zero energy is free...

## StarsStars

Astrophysics definitions: Planets: an object in orbit around a star which has 3 characteristics: Mass large enough for its gravitational attraction to give it a round shape No fusion reactions Has cleared its orbit of most other objects, e.g. asteroids Planetary...

## Gravitational Potential and EnergyGravitational Potential and Energy

Gravitational potential energy is the work done in bringing a mass from infinity to the point. It is found by integration – it’s equal to the area under a force-distance graph. For a point or spherical mass, it’s given by Gravitational potential is the GPE per unit...

## Planetary MotionPlanetary Motion

Kepler devised three laws of planetary motion: The orbit of a planet is an ellipse with the Sun at one focus A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time (planets move faster closer to the Sun Most planets in the...

## Newton’s Law of GravitationNewton’s Law of Gravitation

This describes the forces between any objects that have mass. It states that the force between two point masses is: Directly proportional to the product of the masses, Inversely proportional to the square of their separation, These can be combined into a single...

## Point and Spherical MassesPoint and Spherical Masses

Gravitational fields are due to objects having mass. The field extends to infinity, but becomes gets weaker as the distance from the centre of mass of the object increases. It becomes negligible at long distances. The mass of a spherical object can be modelled as a...

## DampingDamping

An oscillation is damped when an external force that acts on the oscillator has the effect of decreasing the amplitude of its oscillations. Light damping causes the amplitude of the oscillator to gradually decrease with time. The period is unchanged. Heavy damping...

## Energy of a Simple Harmonic OscillatorEnergy of a Simple Harmonic Oscillator

During simple harmonic motion, energy is interchanged between kinetic and potential energy. As long as there are no energy losses due to frictional forces, the total (mechanical) energy remains constant. When the kinetic energy is at a maximum, the oscillator is at...

## Simple Harmonic OscillationsSimple Harmonic Oscillations

SHM definitions: Displacement: distance from the equilibrium position Amplitude: the maximum displacement from the equilibrium position Period: the time taken to complete one full oscillation Frequency: the number of complete oscillations per unit time Angular...

## Centripetal ForceCentripetal Force

A constant net force perpendicular to the velocity of an object causes it to travel in a circular path. Such a force can be described as a centripetal force. For an object moving at a constant speed in a circle: Centripetal acceleration is given by: and = yields: =...

## Kinematics of Circular MotionKinematics of Circular Motion

The radian is a measure of an angle. It is defined as the angle subtended by a circular arc with a length equal to the radius of the circle. 2 radians is equal to 360°. The period of an object in circular motion is the time taken for one revolution, whereas the...

## Ideal GasesIdeal Gases

One mole is defined as the amount of substance that contains as many elementary entities as there are atoms in 12g of carbon-12. This number is called the Avogadro constant, NA, and has been measured as 6.02 × 1023. The kinetic theory of gases is a model used to...

## Thermal Properties of MaterialThermal Properties of Material

The specific heat capacity of a substance is how much energy is needed to raise the temperature of 1kg of that substance by 1° You can determine the specific heat capacity of substances in the laboratory: For a metal, use an electric heater to heat a metal cylinder....

## TemperatureTemperature

Bodies are in thermal equilibrium if there is no net flow of energy. This happens when they are at the same temperature. Thermal energy is always transferred from regions of higher temperature to regions of lower temperature. According to the zeroth law of...

## Solid, Liquid and GasSolid, Liquid and Gas

According to the simple kinetic model, solids, liquids and gases are made up of tiny moving or vibrating particles. solid liquid Gas are held tightly and packed fairly close together - they are strongly attracted to each other o are in fixed positions but they do...

## Wave-particle DualityWave-particle Duality

Wave-particle duality is a model used to describe how all matter has both wave and particle properties. For example, under certain conditions, electrons can be made to diffract. They spread out like waves as they pass through a tiny gap (thin slice of polycrystalline...

## The Photoelectric EffectThe Photoelectric Effect

The photoelectric effect is the process by which photons of electromagnetic radiation shone onto a metal cause photoelectric emission of electrons from its surface. This is demonstrated by the gold leaf electroscope. The top plate is charged by briefly touching it...

## PhotonsPhotons

Electromagnetic radiation has particulate, as well as wave, nature. A photon is the quantum pf energy of this EM radiation (quantised describes something that takes discrete values). Energy of a photon is given by the equation = ℎ and therefore is Planck’s constant,...

## Stationary WavesStationary Waves

A stationary wave forms when two progressive waves with the same frequency travelling in opposite directions are superposed. As they have same frequency, at certain point the are interphase (node) and at other points they are in phase (antinode). The separation...

## SuperpositionSuperposition

The principle of superposition of waves states that when two waves meet at a point the resultant displacement at that point is equal to the vector sum of the displacements of the individual waves. If two progressive waves are in phase then the maximum positive...

## Electromagnetic WavesElectromagnetic Waves

Electromagnetic waves are transverse waves comprising of electric and magnetic fields oscillating at right angles to each other. Different types of EM waves are classified by wavelength. Type of EM wave Wavelength Radio waves Microwaves Infrared Visible Ultraviolet...

## Wave MotionWave Motion

Progressive waves are oscillations that travel through matter (or vacuum), transferring energy from one place to another, but not matter. In a transverse wave the oscillations are perpendicular to the direction of energy transfer (e.g. electromagnetic waves, waves on...

## Potential DividersPotential Dividers

Potential dividers are electric circuits that divide the potential difference across two or more components (often two resistors) in order to produce a specific output. Potential dividers function by the fact that the p.d. across each resistor depends on its...

## Circuit SymbolsCircuit Symbols

Consult the textbook or the internet.

## Internal ResistanceInternal Resistance

When current flows through a power source, some energy is lost and not all energy transferred to the charge is available for the circuit. The terminal p.d. is the measured at the terminals of the power source is therefore less than the actual e.m.f., and this...

## Series and Parallel CircuitsSeries and Parallel Circuits

In series circuits, there is only one possible path for the current. The current is the same in every position and the sum of the e.m.f.s equals the sum of the IR products. In parallel circuits, there is more than one possible path for the current. How much charge...

## PowerPower

Power is the rate of energy transfer by each electrical component. This equation can be combined with = × to give two additional equations for power: Since = , this equation also yields:

## ResistivityResistivity

Resistivity is a property of a material, measured in Ωm, defined as the product of the resistance of a component made of the material and its cross sectional area divided by its length at a given temperature. Good conductors have a very low resistivity (in the order...

## ResistanceResistance

The resistance of a component is defined as the ratio between V and I. Its unit is the ohm, where Ohm’s law states that, for metallic conductor kept at a constant temperature, the current in a wire is directly proportional to the p.d. across its ends. Resistance...

## Electromotive Force and Potential DifferenceElectromotive Force and Potential Difference

Potential difference is a measure of the transfer of energy by charge carriers; its unit is the volt where one volt is the p.d. across a component when 1J of energy is transferred per unit charge passing through the component. In this equation, V is the p.d. measured...

## Mean Drift VelocityMean Drift Velocity

Mean drift velocity is the average velocity of electrons as they move through a wire. Its symbol is v and its unit is ms-1. Charge carriers actually move slowly as free electrons repeatedly collide with the positive metal ions as they drift through the wire towards...

## ChargeCharge

Electric current is defined as the rate of flow of charge, and it is measured in amperes. It is the amount of current passing a point in the circuit per unit time. Electric charge is measured in coulombs, where one coulomb is the electric charge flowing past a point...

## CollisionsCollisions

The principle of conservation of momentum is that, for a system of interacting objects, the total momentum in a specified direction remains constant, as long as no external forces act on the system. So, when two objects collide, the total momentum before and after the...

## 1 Newton’s Laws of Motion1 Newton’s Laws of Motion

Newton developed three laws of motion: An object will remain at rest or continue to move at a constant velocity unless acted upon by a resultant force. The net (resultant) force acting on an object is directly proportional to the rate of change of its momentum, and is...

## Mechanical Properties of MatterMechanical Properties of Matter

The area under a force-extension (or compression) graph gives the work done. This is transferred to elastic potential energy within the material. Elastic potential energy is given by: Tensile stress is defined as the force applied per unit cross sectional area of the...

## SpringsSprings

A pair of equal and opposite forces is required to alter the shape of an object. Forces that produce an extension (tensile deformation) are called tensile forces and forces that shorten an object (compressive deformation) are called compressive forces. Hooke’s Law...

## Kinetic and Potential EnergiesKinetic and Potential Energies

The kinetic energy of an object is given by: The gravitational potential energy of an object in a uniform gravitational field is given by: When an object falls through a gravitational field, GPE is converted to KE. When it reaches the ground, its GPE is 0 and its KE...

## Work and Conservation of EnergyWork and Conservation of Energy

Work done is equivalent to the product of the force and the direction moved in the direction of the force. W=Fx Work done has the unit Nm or joule. It is also equivalent to energy transferred (energy is the capacity to do work). If the force is applied at an angle to...

## Density and PressureDensity and Pressure

The density of an object is defined as its mass per unit volume. Mass is measured directly using a digital balance. Volume is measured either using measurements taken with a ruler, digital calliper of micrometer (for regular solids), or by displacement (for irregular...

## Linear MotionLinear Motion

There are five SUVAT equations involving motion in a straight line at a constant acceleration. When an object is accelerating under gravity with no other force acting on it, it is said to be in free fall. The acceleration of free fall is denoted by g, whose value is...

## Projectile MotionProjectile Motion

The vertical and horizontal motions of a projectile are independent of one another. The vertical velocity changes due to acceleration of free fall, whereas horizontal velocity remains constant. This means that a projectile has a constant velocity in one direction and...

## DynamicsDynamics

Net force is the product of mass and acceleration. The unit of force is newtons (N). f = m × a. The mass of an object is absolute – it is constant for a specific object or particle. However, the magnitude of weight is variable; it depends on gravitational field...

## Motion With Non-uniform AccelerationMotion With Non-uniform Acceleration

Drag is the frictional force experienced by an object travelling through a fluid. Its magnitude depends on several factors, including the speed of the object, the shape (cross-sectional area) of the object, the roughness or texture of the object, and the density of...

## EquilibriumEquilibrium

The moment of a force is the turning effect of a force about some axis or point. It is defined by: Moment = force x perpendicular distance from the line of action of force from the pivot Moment = Fx The SI unit for the moment of a force is Nm. The principle of...

## KinematicsKinematics

Definitions: Displacement: a vector quantity that refers to how far an object is from its original position. Instantaneous speed: the speed of a car over a very short period of time, found by drawing the tangent to the distancetime graph and determining its gradient....

## ELECTRICAL CIRCUITSELECTRICAL CIRCUITS

## ENERGY, POWER AND RESISTANCEENERGY, POWER AND RESISTANCE

## CHARGE AND CURRENTCHARGE AND CURRENT

## STATIONARY WAVES: Part 3STATIONARY WAVES: Part 3

1. Stationary Wave: A stationary/standing wave is the superposition of two progressive waves with the same wavelength, moving in opposite directions. 2. As the waves, of the same wavelength and frequency meet at a point, the points where they interfere destructively...

## WAVE MOTION: Part 1WAVE MOTION: Part 1

...

## Wave–particle dualityWave–particle duality

## Module 3.5 – Newton’s laws of motion and momentumModule 3.5 – Newton’s laws of motion and momentum

17. The introduction of mandatory safety features in cars is a consequence of the scientific community analysing the forces involved in collisions and investigating potential solutions to reduce the likelihood of personal injury. Crash tests has allowed car...

## Module 3.4 – Forces in ActionModule 3.4 – Forces in Action

## Module 3.3 – Work, energy and powerModule 3.3 – Work, energy and power

## Module 3.2 – Forces in ActionModule 3.2 – Forces in Action

## Module 3.1 – MotionModule 3.1 – Motion

Distance travelled by an object is the length of path taken. a. SI unit is metre (m) b. Scalar quantity c. Can never be negative. 2. Displacement is the shortest distance from the initial to the final position of an object. a. SI unit is metre (m) b....

## The rules for determining percentage uncertaintiesThe rules for determining percentage uncertainties

A key assessment objective of the evaluative tasks is going to be determining the final uncertainty in a quantity. Here are some useful rules:

## Determining the uncertainty in the gradient using maximum and minimum gradientsDetermining the uncertainty in the gradient using maximum and minimum gradients

We can determine the uncertainty in the gradient by drawing lines of maximum and minimum gradients through their scattered data points. What happens when there is little scatter of the data points? This is when we draw error bars. Error bars show the range a point is...

## Determining the uncertainty in the y-intercept using maximum and minimum gradientsDetermining the uncertainty in the y-intercept using maximum and minimum gradients

We can also determine the uncertainty in the y-intercept by using lines of maximum and/or minimum gradients through their scattered data points. What happens when there is little scatter of the data points? This is again when we can draw error bars. a. Error bars may...

## Percentage differencePercentage difference

You may be asked to determine the percentage difference between experimental values and accepted values. ‘Experimental values’ are those that are derived from measurement or calculation, whereas ‘accepted’ or ‘theoretical’ values are values that are accepted by the...

## Scalars and VectorsScalars and Vectors

A Scalar quantity is a quantity which only has magnitude. Some examples of Scalar quantities are: o Mass o Time o Temperature o Length o Speed o Energy >A Vector quantity is a quantity that has both magnitude and direction. Some examples of Vector quantities are: o...

## Measurements and Uncertainties

Accuracy: An experiment is accurate if the quantity being measured has a value that’s very close to the commonly accepted or true value. For example an experimental value for the acceleration of free fall of 9.78 m s-2 is much more accurate than an experimental value...

## UncertaintiesUncertainties

Absolute Uncertainties: The absolute uncertainty (usually called absolute error - but "error" connotes "mistake", and these are NOT mistakes) is the size of the range of values in which the "true value" of the measurement probably lies >If single readings have been...

## Physical QuantitiesPhysical Quantities

Physical quantities have a numerical value and a unit. These are physical quantities that can be quantified: Examples are o Mass o Length o Temperature o Time Estimates of physical units can be made.

## S.I. Units: Systeme InternationaleS.I. Units: Systeme Internationale

S.I. Units: These are a set of base units and also a scientific method of expressing the magnitudes of quantities of important natural phenomena. S.I. Units are used to reduce confusion between different units that are used to measure the same natural phenomena. By...