Area cm², m² Volume cm³, m³, litre (l), millilitre (ml) Density Force Speed/ Velocity Acceleration Mass Time Length Temperature current kg/cm³, g/cm³ Newton (N) m/s, km/h m/s² kilogram (kg), gram (g) second (s) metre (m), kilometre (km), centimetre (cm) degrees Celsius (C ) ampere or amp (A) 1 km 1000m 100,000cm 1 tonne 1000kg 1000,000g 1 hour 60 minutes 3600 seconds 1 L 1000 ml 1000cm³ Page 1 of 30
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Speed o The rate of change in distance o Is a scalar quantity Velocity o The rate of change in displacement o Is a vector quantity Type d-t v-t a-t Gradient Velocity Acceleration Value Displacement Velocity Acceleration Area How to measure gradient: Displacement Gradient = Rise Run Average Speed = Total Distance Total Time Page 4 of 30
An object will have acceleration if: The magnitude of velocity changes The direction of motion changes When describing velocity, a direction must be given. Some objects only have two directions, e.g. backward, forward When this happens, you can name the two directions positive and negative so that calculations are simpler Example: Example: Change in Velocity = New velocity measurement Previous velocity measurement Change in Velocity = V - U Acceleration = Change in Velocity Time Acceleration = (V - U) T A person drives at a velocity of 40 m/s North He accelerates, increasing his velocity to 50 m/s North in 10 seconds o V = 5 m/s North o U = 4 m/s North o Change in Velocity = 5 m/s 4 m/s = 1 m/s North o T = 10 seconds o Acceleration = 1 m/s North 10 s = 0.1 m/s² A ball drops and hits the ground at 5 m/s and bounces back at 3 m/s in 1 seconds o Up = Positive o Down = Negative V = 3 m/s U = -5 m/s Change in Velocity = 3 m/s - (-5 m/s) = 3 m/s + 5 m/s o = 8 m/s Up T = 1 seconds Acceleration = 8 m/s Up 1 s 8 m/s² Up Page 5 of 30
Forces A force is a push or a pull A force is an action that can make another object change shape or change its velocity A force is an action that can make another object accelerate Are divided into two categories; Contact and Non-Contact E.g. gravitational, electrostatic, twisting etc. Friction is a contact force involving two bodies opposing each others motion o E.g. the friction of the tyres of a car on the road cause the car to move slower Gravitational force acts on falling objects. They reach a terminal velocity when the up thrust is equivalent to the gravitational force. o When objects fall, the force of gravity acts upon them o As gravity increases, air pressure increases o When air pressure is equal to gravity, the object travels in a straight line o This is called terminal velocity o This is the constant speed at which an object falls to earth When force acts on an object, it causes the object to change the value of velocity and the direction of movement. EXAMPLES OF FORCE: Weight: The gravitational force from the earth It acts vertically down Normal Force: Acts 90 to the surface Is equal to weight Friction Force: Has the direction opposite to the direction of movement Acts between two surfaces Tension Force: Acts against the deformation of a body It takes place in a string or a rope Drag Force: Acts in the case of air resistance It has the direction against motion Page 6 of 30
Mass: Is the amount of resistance an object has towards movement Is defined as the amount of substance in an object Force = mass acceleration F = m x a Weight = mass gravity W = m x g Gravity (10N/KG) When force acts on an object, it causes the object to change the value of velocity and the direction of movement. EXAMPLES OF FORCE: Weight: The gravitational force from the earth It acts vertically down Normal Force: Acts 90 to the surface Is equal to weight Friction Force: Has the direction opposite to the direction of movement Acts between two surfaces Tension Force: Acts against the deformation of a body It takes place in a string or a rope Drag Force: Acts in the case of air resistance It has the direction against motion Stopping Distance Stopping Distance = Thinking Distance + Breaking Distance Page 7 of 30
Factors affecting thinking distance: Thinking distance is the distance a car travels when the driver is reaction to a situation o Alcohol o Other drugs and some medicines o Distraction (e.g. mobile phones) o Speed o Tiredness Factors affecting braking distance Breaking distance is the distance a car travels after the breaks have been applied Moment o Weather o Condition of the road o Speed o Condition of tyres and breaks Momentum = Force Perpendicular Distance from the Pivot Force x Distance = Force x Distance 40 Newtons x 6 Metres = 80 Newtons x 3 Metres Is a turning force When a force causes rotation about a pivot When System is in Equilibrium Clockwise Moment = Anticlockwise Moment Page 8 of 30
Astronomy Definitions: Centre of Mass o Centre of mass is a single point in a body where all the mass appears to be Centre of Gravity o Centre of gravity is a single point in a body where all the force of gravity appears to act Initial linear region of force-extension graph is associated with Hooke s law Extension is proportional to the force providing the elastic limit is not exceeded Astronomy is the study of natural celestial bodies. Satellite o An object that orbits about a large mass Natural satellites are generally called moons Moons are found orbiting some planets o Moons do not produce light but reflects light Artificial satellites are man-made devices sent into orbit for: Page 9 of 30
Communication Military purposes Mapping Planet o A spherical body orbiting a star A planet does not produce light but reflects light Star o Is a celestial body that produces energy by nuclear reactions The sun is a star because it is a source of energy due to nuclear reactions between hydrogen atoms that form helium Solar System o Is a collection of planet and other celestial objects orbiting the sun Sun Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Asteroids Comets Comet o Is space debris made of rocks surrounded by ice o Spends a lot of time out of planetary system o Have highly eccentric elliptic orbits The Haley s Comet has an orbital time of 76 earth years Galaxy o Is a large collection of billions of stars orbiting around the centre made up of many stars Universe o All mass that exist in space including planets, stars and nebulae o A large collection of a billion galaxies Gravity o Is a force of attraction between any two or more objects with mass Larger objects have a stronger gravitational force than smaller objects Page 10 of 30
Astronauts on different planets: The force of gravity has a smaller effect when objects are further away Larger masses have a stronger gravitational field Causes the planets to orbit the sun Causes the moon and artificial satellites to orbit the earth Causes comets to orbit the sun Have the same mass o As their body does not physically change Have different weights o As weight is subject to the force of gravity Which is different on each planet Life Cycle of a Star Orbital Speed = (2 x π x Orbital Radius) Time Period V = (2 x π x r) t Large nebula rotates very quickly Nebula contracts by gravitational force of each particle forming a star Star burns for billions of years until all the nuclear reaction stops o A small star ends up as a white dwarf o A medium sized star (like the sun) will: Expand to form a red giant when nuclear reactions stop Red giant collapses, shrinking rapidly and then explodes Super Nova 1 o Everything in the star is blown away across the universe After the super nova, the medium sized star is left as a neutron star o A large star will: Expand to form a super red giant When it exhausts its fuel, it collapses, shrinking rapidly and explodes Super Nova 2 Finishes off as a very dense mass made of neutrons Its gravity is so strong that light cannot escape o It is called a black hole Spring Tides Page 11 of 30
Neap Tides When the moon is full or new, the gravitational pull of the moon and sun are combined At theses times, the high tides are very high and the low tides are very low During the moon s quarter phases, the sun and moon work at right angles, causing bulges to cancel each other The result is a smaller difference between high and low tides Mass Kilogram (kg) Energy Joule (J) Distance Metre (m) Speed Metre/second (m/s) Acceleration Metre/second 2 (m/s 2 ) Force Newton (N) Time Second (s) Power Watts (W) Energy transfers in many ways such as: Thermal (Heat) Light Electrical Sound Kinetic Chemical Nuclear Potential (Kinetic, Elastic and Gravitational) Page 12 of 30
Energy is conserved Energy cannot be created or destroyed, only transferred. Sankey Diagram Efficiency = Useful Energy Output Total Energy Input Efficiency = Work Total Energy Input Energy transfer can take place in many ways such as: Convection o Heat transfers in liquids and gases o Fluids (liquid or gas) become less dense when heated The lower density makes the warm fluid rise and cold fluid move down Conduction o Energy transfers through solids o Conduction occurs when there is contact o In metals, conduction is due to free electrons o Bad conductors are insulators Radiation (Infra-Red Radiation) o It is the way energy moves through space (vacuum) o It travels as electromagnetic waves with a speed of 300,000,000 ms -1. [3x10 8 ms -1 ] o It needs a medium to travel through Energy Loss at Home Insulation Windows o Needs double glazing Page 13 of 30
Roof o Fibre wool insulation Gaps o Draught excluders Walls o Cavity wall insulation Marble/Stone floors o Carpets Work Done = Force x Distance Moved W = F x d Work done is always equal to energy transferred measured in Joules (J) Work Done = Energy Transferred Energy Transferred = Force x Distance Moved Gravitational Potential Energy = Mass x Gravity x Height GPE = m x g x h Kinetic Energy = ½ x mass x speed 2 KE = ½ x m x v 2 Power is the rate of transfer of energy or the rate of doing work measured in Watts (W) Power = Work Done Time Taken P = W t Energy transfers involved in generating electricity are: Renewable sources of energy: o Wind o Water o Geothermal Resources o Solar Heating Systems o Solar Cells Non-Renewable sources of energy: o Fossil Fuels o Nuclear Power Page 14 of 30
Density Pressure Measure of mass per unit volume for any substance KG / M³ Measure of force per unit area N / M² Pa Pressure in liquids and gases Density of some substances: Pure Water o 1000 kg/m³ Air o 1.2 kg/m³ Atmospheric Pressure 100 000 N/m² Temperature Celsius ( 0 C) Kelvin (K) Force Newton (N) Pressure Pascal (Pa) Newton/ metre² (N/m²) Density Kilograms/metre³ (kg/m³) Grams/millilitre (g/ml) Grams/centimetre³ (g/cm³) Distance Metre (m) Area Metre² (m²) Energy Joule (J) Mass Kilogram (Kg) Speed Metre/second (m/s) Acceleration Metre/second² (m/s²) Density = Mass Volume D = m V Pressure = Force Area P = F a Pressure = Density x Height x Gravity P = D x h x g Page 15 of 30
Brownian Movement Brown observed pollen grains moving around randomly in water He concluded that water particles were colliding with pollen grains and causing random motion Brownian movement also supported the idea that gas particles are also moving in random motion in all directions with a range of speeds Assumptions of Kinetic Theory of Gases: Boyles Law Particles are points Particles are more in straight lines between collisions Collisions are elastic (bounce back with same speed) Many particles, lots of space Continuous random motion For a fixed mass of gas, the pressure is inversely proportional to the volume if the temperature remains constant Pressure is inversely proportional to volume Pressure is proportional to the inverse of volume Page 16 of 30
Charles Law Pressure Law For a fixed mass of gas, the volume is proportional to the absolute temperature if the pressure remains constant For a fixed amount of gas, the pressure is proportional to the absolute temperature if the volume remains constant Celsius Kelvin -273 0 0 273 100 373 As temperature increases, the speed of molecules increases Pressure 1 x Volume 1 = Pressure 2 x Volume 2 P1 x V1 = P2 x V2 Page 17 of 30
Transverse Waves A transverse wave is one that vibrates, or oscillates, at right angles to the direction in which the energy or wave is moving Longitudinal Wave Degree ( 0 ) Frequency Hertz (Hz) Force Metre (m) Speed Metre/second (m/s) Time Second (s) A longitudinal wave is one in which the vibrations, or oscillations, are along the direction in which the energy or wave is moving Transverse Waves Waves Inside Fluids Shock Waves Seismic Waves (Underground Waves) Sound Waves Longitudinal Waves Surface Waves Electromagnetic Waves Seismic Waves (Surface Waves) Light Waves Page 18 of 30
Amplitude Frequency Wavelength Period The maximum movement of particles from their resting position caused by a wave Unit: A The number of waves produced each second by a source, or the number passing a particular point each second Unit: Hz (Hertz, 1 s ) The distance between a particular point on a wave and the same point on the next wave (for example, from crest to crest) Unit: λ (in metres, m ) The time it takes for a source to produce one wave Unit: T (in seconds, s ) Waves are a means of transferring energy from place to place, without the transfer of matter Wave Speed = Frequency Wavelength v = f λ Wave speed is measured in metres per second ( m s ) Frequency = 1 Time Period f = 1 t Law of reflection states that the angle of incidence is equal to the angle of reflection when light strikes a plane mirror Page 19 of 30
Luminous Objects Objects that emit their own light E.g. o Sun o Stars o Fire o Light bulbs Non-Luminous Objects Objects that that do not emit light We can see them because of the light they reflect Virtual Images Real Images Images though which rats of light do not actually pass Images created with rays of light actually passing through them Properties of an image in a plane mirror: The image is as far behind the mirror as the object is in front Te image is the same size as the object The image is virtual that is, it cannot be produced on a screen The image is lateral invested that is, the left side and right side of the image appear to be interchanged Page 20 of 30
Medium A material through which light can travel Speed of light: In a vacuum and in air o 300 000 000 m/s In water: o 200 000 000 m/s Refraction Snell s Law: Is a property of waves changing speed (and direction) when passing a boundary States that the ratio of sine angle incidence and sine angle refraction is a constant for a boundary between two materials n = Sin i Sin r Refractive Index = Sin (Angle of Incidence) Sin (Angle of Refraction) Total Internal Reflection: Is an optical phenomenon where light (waves) refract and reflect back at a boundary Page 21 of 30
Critical Angle: Is the angle where light reflects back and refraction is along the boundary Reflectors Sin C = 1 n Sin (Critical Angle) = 1 Refractive Index Use tiny prisms in their construction The optical material is plastic lighter and less fragile then a mirror Page 22 of 30
Speed of sound depends on the air (gas) temperature (since particles may be closer when gas is cooler) Average speed of sound in air is approximately 340 m/s Average speed of sound in seawater is approximately 1500 m/s Average speed of sound in a solid is approximately 5000 m/s Audible Range for: Infrasounds Ultrasounds Loudness Echo Humans: o 20 Hz 20 000 Hz Dogs, dolphins and bats: o Over 20 000 Hz Sounds that cannot be heard by human beings as they are produced by objects that vibrate at frequencies lower than 20 Hz Sounds that cannot be heard by human beings as they are produced by objects that vibrate at frequencies higher than 20 000 Hz Is the measure of the power of a sound o A wave with a big amplitude is loud o A wave with a small amplitude is soft A reflected sound Echo Sounding Pitch When ships use echoes to discover the depth of the water beneath them The frequency of sound waves Measuring the Speed of Sound: Using echoes o (2 x distance between presentation of sound and large blank wall) time between presentation of sound and presentation of echo Using an oscilloscope Page 23 of 30
Live Wire Neutral Wire Current (I) Charge (Q or q) Energy (E) Resistance (R) Time (t) Voltage (V) Power (P) Ampere (A) Coulomb (C) Joule (J) OHM (Ω) Second (s) Volt (V) Watt (W) Provides the path along which the electrical energy from the power station travels Is alternately positive and negative causing alternating current (ac) to flow along it Brown in colour Completes the circuit Blue in colour Earth Wire Usually has not current flowing through it Is there for protection if an appliance develops a fault Green and yellow in colour Page 24 of 30
Hazards of Electricity: Frayed cables Long cables Damaged plugs Water around sockets Pushing metal objects into sockets Safety Devices: Fuses o Usually in the form of a cylinder or cartridge o Contains a thin piece of wire made from a metal that has a low melting point If too large a current flows in the circuit, the fuse wire becomes very hot and melts The fuse blows, shutting the circuit off Prevents shock and reduces possibility of an electric fire o The correct fuse to use is one that allows the correct current to flow but blows if the current is a little larger Trip Switches or Circuit Breakers o If too large a current flows in a circuit, a switch opens making the circuit incomplete o Once the fault in the circuit is corrected, the switch is reset, usually by pressing a reset button Does not need to be replaced Earth Wires o Provides a low-resistance path for the current if and when the live wire becomes frayed or breaks and comes into contact with the metal casing o Prevents severe electric shock as electricity passes through a person to the earth Double Insulation o Is when all electrical parts of an appliance are insulated with non-conductors so that they cannot be touched by the users o Appliances that have this do not require an earth wire Heating elements are designed to have a high resistance As the current passes through the element, energy is transferred and the element heats up E.g. o Toaster o Kettle o Dishwasher o Cooker Resistance prevents the flow of current, and causes an increase in temperature by doing so Page 25 of 30
Alternating Current (ac) Power = Current x Voltage P = I x V Energy = Power x Time E = P x t Energy = Current x Voltage x Time E = I x V x t The flow of electricity is constantly changing direction Direct Current (dc) The flow of electricity is always in the same direction Electric Current A flow of charge Good Conductor of Electricity Insulators A material through which electrons flow easily o Electrons carry charges A bad conductor of electricity Used to prevent the flow of charge Page 26 of 30
Ammeter Voltmeter Battery Current is the rate of flow of charge Charge = Current x Time Q = I x t Used to measure the size of the current flowing in a circuit Used to measure voltage Consists of several cells connected together Provides current flowing in one direction (dc) Light Emitting Diode (LED) Fitted to many appliances to show when the appliance is switched on or on standby Glows when current is flowing through it Page 27 of 30
Series Circuit No branches or junctions One switch can turn all the components on and off together If one bulb (or other component) breaks, it causes a gap in the circuit and all of the other bulbs will go off The voltage supplied by the cell or mains supply is shared between all the components o The more bulbs added, the dimmer they all become o The larger the resistance of the component, the bigger its share of the voltage Parallel Circuit Have branches or junctions Switches can be placed in different parts of the circuit to switch each bulb on and off individually, or all together If one bulb (or other component) breaks, only the bulbs on the same branch of the circuit will be affected Each branch of the circuit receives the same voltage o Even if more bulbs are added, they all stay bright Page 28 of 30
Resistance Is a measure of energy dissipated by charge when unit current flows All components offer some resistance to the flow of charge o Some circuits allow charges to pass through them very easily losing very little energy i.e. the components have a very low resistance o Some circuits do not allow charges to pass through them as easily and hence lose a significant amount of energy i.e. the components have a very high resistance The energy is converted into other forms, usually heat Voltage = Current x Resistance V = I x R Combine Series Resistance R = R1 + R2 +... Rn Combined Parallel Resistance 1 R = (1 R1) + (1 R2) +... (1 Rn) Series Parallel Voltage Divides Same Current Same Divides Combined Resistance High Low Fixed Resistors Included in circuits in order to control the sizes of currents and voltages Variable Resistors Thermistors Allows the resistance to be altered A resistor whose resistance changes quite dramatically with temperature Page 29 of 30
o Resistance decreases as temperature increases o E.g. Fire alarms Thermostats Light-Dependant Resistors (LDRs) Diodes Used in light sensitive circuits o Resistance increases as light exposed increases o E.g. Photographic equipment Automatic lighting controls Burglar alarms A resistor that behaves like a one-way valve or one-way streets Resistance is low to current flowing in a particular direction Resistance is high to current flowing in the opposing direction o Used in circuits where it is important that current flows only in one direction o E.g. Rectifier circuits that convert alternating current into direct current Light Emitting Diodes (LEDs) OHM s Law Diodes that glow when a current is flowing through them The current that flows through a conductor is directly proportional to the potential difference across its ends, provided its temperature remains constant Page 30 of 30