General physics
Length and time
Metre rule is used to determine length, measuring cylinder is used to
determine volume, Vernier callipers is used to determine the internal and
external diameter of objects and micrometre screw gauge is used to determine
thickness of thin objects like wire, paper etc.
For a distance of small value multiple readings (not less than 5) should be taken
and an average found.
Micrometre screw gauge
Vernier Callipers
For a time of small value a pendulum can be used where the periodic time T
can be obtained; if it takes 33s to have 20 oscillations of the pendulum then
time for one oscillation will be 33/20 (t/20) which is the period; time taken for
one complete oscillation.
Frequency is the number of cycles/oscillations in 1s.
Motion
Speed is the rate of change of distance; d/t, unit of speed is m/s
Velocity is speed in a specified direction, unit of velocity is m/s.
Speed is a scalar quantity while velocity is a vector quantity.
A scalar quantity has only magnitude while a vector quantity has both
magnitude and direction. Examples of scalar quantities are mass, distance,
speed etc.
A vector quantity has both magnitude and direction. Examples of vector
quantities are displacement, velocity, force, acceleration etc.
Distance time graph diagram
Velocity time graph diagram
 Area under graph gives the distance covered by the object (triangle
Equations of motion
V=U+at
V2=U2 + 2as
S=ut+1/2at2
s-distance
v- final velocity
u- initial velocity
t- time
a-acceleration
Motion along a circular track
When an object moves along a circle
The force that keeps it moving along the circle is always towards the centre of
the circle
As the car speeds up the frictional force between the tyres and the track
increases
When the driving force is too high the object skids off the track but in a
direction tangent to that point at which it leaves the track
The object can move at a constant speed along the track but its velocity will be
changing with time; if its velocity is changing the object is said to accelerate
because acceleration is change in velocity with time.
Force and motion
Force can do 3 things; change shape, speed and direction of an object
When an object jumps out of aircraft;
Its speed increases initially because its weight is far greater than air resistance
As it goes down air resistance increases so object slows down
At a certain stage air resistance is equal to weight and object moves with
constant velocity
Mass and weight
Mass is the quantity of matter in an object
It is always the same everywhere
Its unit is Kg
Weight is the force of gravity acting on an object
W=mg (was app my gee)
Weight is measure in Newton.
Weight changes from place to place because the value of g changes
accordingly.
On earth g is approximately 10m/s2 or 10N/Kg
Weight can be measured with a force meter or scale and mass is measured
with a balance.
Density
This is the ratio of an objects mass to its volume
D=m/v
Its unit is g/cm3
Density of a regularly shaped object
 Find the mass (m) of the object with a scale
 Find its volume (v) with a formula (lxbxh)
 Density=m/v
Density of an irregularly shaped object
Find the mass (m) of the object with a scale
Fill a measuring cylinder with water to a certain volume (V1)
Immerse the object completely in the water, the volume of the water rises to
volume (V2)
Density of object=m/V2-V1
Forces
Forces and their effects
Hooke’s law states that the force on an elastic body is directly proportional to
the applied force provided its elastic limit is not exceeded
F αe
F=Ke
F- force
e-extension
k-spring or force constant
Hooke’s law graph
Resultant of two forces acting along the same line and at different angles
Turning effect
Moment of a force about a point is the turning effect of that force about that
point
Moment= Force x perpendicular distance of force from the pivot
Unit is Nm
Systems that use moment include spanner, see saw etc.
For a system to be equilibrium; its anticlockwise moment must be equal to its
clockwise moment
ACW=CW
F1xd1=F2xd2
Conditions for equilibrium
Anticlockwise moment must be equal to its clockwise moment
Total upward force must be equal to total downward force
Centre of mass
This is the point where the total weight of the object acts
Determining the centre of mass of an object
Pin the object to the wall as shown in the diagram below at point A
When the pendulum comes to rest, draw a line AB following the thread
Pin the object to the wall at point C
When the pendulum comes to rest, draw a line CD following the thread
Where the 2 lines intersect is the centre of mass of the object
The experiment can be repeated for a third line (this acts as a check) and the
centre of mass is determined as shown below.
Momentum
It is the product of the mass of an object with its velocity
Momentum= mxv
Its unit is kgm/s
Law of conservation of momentum
Momentum before collision=momentum after collision
M1U1 +M2U2 = M1V1+M2V2 if objects do not stick together after collision
M1U1 +M2U2 = (M1+M2)V if they stick together after collision
Stability of objects
The wider the base of the object the more stable it is
The lower the centre of mass (closer the object to the ground) the more stable
it is.
Diagram
Energy, work and power
Kinetic energy (Ke) is energy due to motion=1/2mv2
Potential energy (pe) is energy due to position (height)=mgh
Energy can always be conserved as it is converted from one form to another
e.g when a stone falls from a height; pe is converted into ke and then heat and
sound
Example of starin energy is that of a wound up toy or catapault when it is
pulled.
Energy resources
Renewable energy does not run out (solar, wind etc)
Non-renewable energy can run out eg coal, oil etc
Note that the Sun is the source of energy for all our energy resources except
Geothermal,
Nuclear and Tidal (GNT)
Describe a renewable process by which electrical energy is obtained from the
energy stored in
water.
Hydroelectric
•
Hydroelectric named OR water from behind dam
•
K.E. of (falling) water used / P.E. of stored water
•
Turbine / waterwheel / paddle wheel operated
•
(Turbine) turns / drives a generator (that produces electricity)
Explain why the process described above can be regarded as renewable.
•
Rain (fills lakes in high places)
•
Cause of rain is the Sun, so renewable
Explain whether the Sun is the source of the energy stored in the water in
your explanation above
•
Sun evaporates water from sea etc. to fall (later) as rain
•
Sun is the source of energy.
Tidal flow
•
Tides / tidal flow named
•
K.E. of water used
•
Turbine / waterwheel / paddle wheel operated
•
(Turbine) turns / drives a generator (that produces electricity)
Explain why the process described above can be regarded as renewable.
•
Moon (and Sun) causes tides
•
Moon (and Sun) permanently in place, so renewable
Explain whether the Sun is the source of the energy stored in the water in
your explanation above
•
Attraction due to Moon’s (and Sun’s) gravity causes tides
•
Sun is a source of (part of) the energy OR Sun is not the primary source
of energy
Waves
•
Waves on surface of sea
•
K.E. of water used to oscillate a floating mechanism
•
Turbine / waterwheel / paddle wheel operated
•
(Turbine) turns / drives a generator (that produces electricity)
Explain why the process described above can be regarded as renewable.
•
Wind causes waves
•
Sun causes wind, so renewable
Explain whether the Sun is the source of the energy stored in the water in
your explanation above
•
Winds are air currents caused by thermal energy / heat from the Sun B1
•
Sun is the source of energy
Efficiency
Efficiency = Useful power output/Power input x100%
Efficiency = Useful energy output/Energy input x100%
Work
Workdone=energy transferred
W=Fxd=Change in energy
Unit of work is the Joule or Nm
Power
Power=W/t= change in energy/time
Unit of power is J/s or Nm/s or Watts
Pressure
P=F/A
Unit is N/m2
Pressure increases with depth
Barometer
It is used to measure atmospheric pressure
The space is a vacuum (no molecules)
Atmospheric pressure is about 760mmHg or 100000Pa
Diagram
Manometer
It is used to determine the pressure of a gas
P=760+h
P=760-h
Pressure in a liquid=hpg
Thermal physics
Simple kinetic molecular model of matter
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All matter is made of molecules
Molecules are always in motion
They possess kinetic energy
Kinetic energy of molecules is directly proportional to temperature of
object
States of matter/Molecular model
Solid particles do not move from one place to the other but they vibrate within
fixed positions because they have strong forces holding them together and this
explains why the particles have a fixed pattern.
Liquid molecules can move from one place to another because the force
between its molecules is not as strong as that of the solid, liquid molecules
have a regular pattern but can easily change which explains why liquid takes
the shape of its container.
Gas molecules are very free to move (further apart, lots of space) because
there is little or no force holding its molecules together and therefore gas
molecules have no pattern at all as they are always moving along straight lines
and in high speeds, this is called Brownian motion (random motion).
Note the faster the molecules of a gas the higher the temperature of the gas
because the molecules collide more often.
How air pressure is caused
Molecules of the gas collide
Collision causes change in momentum
Change in momentum with time produces force
Force per unit are produces pressure.
Evidence of random motion in liquid
Spread pollen grains on surface of water
Using a powerful microscope it is observed that the grains are in random
motion; the grains are hit by moving water molecules
Evidence of random motion in gas
Get a puff of smoke with a transparent container and cover it with a
transparent lid as shown below
Place a light source (producing light of high light intensity) close to the
container as shown in diagram
Using a powerful microscope, it is observed that the smoke specks are moving
randomly at high speeds; they are being hit by air molecules.
Evaporation
It is the escape of more-energetic molecules from the surface of a liquid
Factors affecting the rate of evaporation
The higher the temperature the higher the rate of evaporation; more
molecules will have enough energy to escape
The lower the humidity the higher the rate of evaporation; ----- molecules
move from a crowded area to a less crowded area.
The higher the wind speed the higher the rate of evaporation; more molecules
will be given energy to escape
The larger the surface area the higher the rate of evaporation; more molecules
will escape from the surface.
Evaporation causes cooling
 When more energetic molecules escape from a liquid, molecules left are
less energetic and cooler.
 If perfume is sprayed on the skin it feels cold because heat from the
body is used to cause the perfume molecules to escape.
Pressure changes
Pα1/V if Temperature is kept constant
If the volume of a fixed mass of gas is increased, its pressure decreases because
the space between its molecules has increased and then fewer collisions.
PV=Constant
P1V1=P2V2
Draw graph
PαT at constant volume
If the temperature of a fixed mass of gas is increased at constant volume, its
pressure increases because the rate of collision of molecules increases.
Draw graph
VαT at constant pressure
If the temperature of a fixed mass of gas is increased at constant pressure, its
volume increases because as the speed of the molecules is increased the
volume must be increased if the pressure has to be kept constant.
Graph
Thermal properties and temperature
Thermal expansion of solids, liquids and gases
Solids liquids and gases when heated expand because their molecules move to
occupy further space.
Everyday applications and consequences of thermal expansion
 Rollers are used and gaps are left on bridges to avoid buckling of the
road.
 Gaps and overlaps are used on rail lines to allow for expansion.
 Sagging of electric cables.
 Bimetallic strip is used to control or regulate temperature in electric iron
and other heating gadgets.
Measurement of temperature
Temperature is a number that is related to the average kinetic energy of the
molecules of a substance.
Physical property that varies with temperature may be used for the
measurement of temperature
 Change in length of liquid with temperature used in liquid in glass
thermometers
 Change in voltage with temperature used in thermocouple.
 Change in resistance with temperature used in thermistors.
 Change in volume of gas with temperature used in gas thermometers.
Sensitivity, linearity and range
Sensitivity
Change in length, distance moved (accept “how much it expands”) per unit /
given temp rise
Increasing sensitivity
Large bulb, thin or narrow bore or tube or use alcohol
Range
Difference between the highest and lowest temperatures
Increasing range
Long tube, wide bore, little liquid
Linearity
Linearity -distance between each degree on scale is the same, idea of equal
size divisions/expansion for equal temperature rises OR Δl / Δθ = constant OR
reference to l against θ graph straight line
Increasing linearity
Uniform bore, use alcohol/liquid expands uniformly
Thermocouple
Working of a thermocouple
 Place the cold junction on a surface of known temperature (pure melting
ice)
 Place the hot junction on the surface its temperature is to be measured
 The temperature difference between the two surfaces produces voltage
which drives current that can be measured and calibrated.
Uses of a thermocouple
 It can measure a wide range of temperatures (very high and low).
 It can measure rapidly changing temperatures.
 It can be connected to a computer to display results.
Thermal Capacity (Heat capacity)
Heat is a measure of the internal energy of a substance, it is measured in Joules
or heat is a measurement of the total energy of a substance; the total energy is
made of both ke and pe of the molecules.
Increase in internal energy of an object is due to increase in temperature;
increase in in temperature of an object is due to increase in the kinetic energy
of each molecule that makes up the substance.
Heat capacity of an object is the quantity of heat that is required to raise or
lower the temperature of a substance by 10C e.g the heat capacity of oil is
lower than that of water, this explains why oil boils at a lower temperature
compared to water because more heat is required to cause water to boil
compared to oil and this is why water is used as a coolant in car radiators; for
water temperature to rise a lot of heat is removed from the car engine thereby
cooling the engine.
Specific heat capacity of an object is the quantity of heat that is required to
raise or lower the temperature of 1kg of a substance by 10C.
Heat capacity=mc
m- mass of substance
c- specific heat capacity of substance; a constant for any given material e.g
specific heat capacity of water is 4200J/Kg 0C
Quantity of heat Q=mc(θ2-θ1) or Q=mcΔθ
C=Q/mΔθ
Determining the specific of a solid (Aluminium)
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Initial temperature (θ1) of block with a thermometer
Mass of block with a scale
Object is heated with a heater for a certain amount of time (t)
Final temperature (θ2) after time t.
Measure current I supplied by heater
Measure voltage V supplied by the heater
Heat (Q) supplied by heater using the formula Q=VIt
V-voltage
I-current
t-time
 Then c= VIt/m (θ2-θ1)
https://www.youtube.com/watch?v=BclB8UaSH4g
https://www.youtube.com/watch?v=8CgL6P6o81I
https://www.youtube.com/watch?v=hYJjojQXVqw
Determining the specific heat capacity of a liquid (water)
 Using a scale determine the mass (m1) of empty beaker
 Measure the mass (m2) of beaker with liquid
 Record the initial temperature (θ1) of water
 Water is heated with a heater for a certain amount of time (t)
 Final temperature (θ2) after time t.
 Measure current I supplied by heater
 Measure voltage V supplied by the heater
 Then c= VIt/ (m2-m1) (θ2-θ1)
Melting and boiling
Melting is a change of state from solid to liquid at a constant temperature as
heat is supplied.
Boiling is a change of state from liquid to gas at a constant temperature as heat
is supplied.
Melting point is the temperature that solid changes to liquid at a fixed
temperature or it is the temperature where solid and liquid co-exist.
Boiling point is the temperature that liquid changes to gas at a fixed
temperature or it is the temperature where liquid and gas co-exist.
Boiling point is the temperature at which the saturated vapour pressure (SVP)
is equal to atmospheric pressure.
Differences between evaporation and boiling
 Evaporation only happens on the surface of the liquid while boiling is
throughout the liquid.
 Boiling is at a fixed temperature while evaporation can happen at any
temperature e.g water on the surface of a table dries up without
reaching 1000C
During condensation and solidification molecules move close together and
heat is given off.
Latent heat
It is the heat given to a substance without any corresponding rise in
temperature
Heating Curve
Cooling curve
Latent heat is used to break the bonds (forces) holding molecules together so
that they can break away and escape as they have gained more energy.
Specific latent heat of a substance is the quantity of heat that is required to
change the state of 1Kg of the substance at a constant temperature. It is a
constant for any material.
Specific latent heat of fusion of ice is the quantity of heat required to change
1Kg of ice (solid) to water (liquid) at a constant temperature.
Specific latent heat of vaporisation of water or steam is the quantity of heat
required to change 1Kg of water (liquid) to steam or vapour (gas) at a constant
temperature.
Quantity of heat Q=ml
m-mass of substance
l-specific latent heat of substance
Determining specific latent heat of fusion of ice
Experiment is set up as shown below
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Measure the mass m of melted ice as water collected in beaker
Measure time t used in heating the ice
Measure current I supplied by heater
Measure voltage V supplied by the heater
 Then l =VIt/m
Possible precaution
Wait until the water drops at regular intervals before reading is taken
Granulated ice cube are used to provide larger surface area and reduce
amount of air molecules.
Determining specific latent heat of vaporisation of steam
Experiment is set up as shown below
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Measure the mass M1 of boiling water with beaker
Measure time t used in boiling the water
Measure the mass M2 of boiling water after time t
Measure current I supplied by heater
Measure voltage V supplied by the heater
Then l = VIt/ M1- M2
Improving on Heat experiments
The higher the temperature the more accurate the results
Take many readings and find average; smaller the readings the more the error.
Thermal processes
Conduction of heat is mainly through solids
Heated molecules at A end gain more kinetic energy, vibrate more and collide
more with nearby molecules (B region) transferring heat to molecules at B,
molecules at B gain the energy, vibrate more collide more with nearby
molecule (C region), the process repeats until the whole object is heated.
(https://slideplayer.com/slide/10656295/)
https://slideplayer.com/slide/16636972/
Air is a poor conductor of heat because its molecules are very far apart.
Experiment to show how different solids conduct heat
Effects of Conduction
To show that water is a poor conductor
The experiment is set up as shown below
 Ice cubes are forced down the test tube with the help of wire gauze (ice
floats in water)
 Water is heated at the top of the test tube (heating below will produce
convection current)
 It is observed that water at the top boils but ice at bottom does not melt
 Conclusion is that water is not able to conduct the heat down to melt the
ice
Conduction of heat and electricity is due to lattice vibrations and movement of
free electrons
Convection of heat is mainly through fluids (gas or liquid)
 Heated molecules at the bottom of the beaker gain heat, become less
dense and rise to the top of the liquid
 Cold heavier molecules fall or sink to take up the space
 This cycle of movement is called convection current
 This process continues until the whole liquid is heated up.
In convection molecules move from one place to the other but in conduction
they only vibrate about a fixed position.
Radiation
Radiation is heat transfer through a vacuum
Vacuum flask
Vacuum reduces heat loss by conduction and convection because there are no
molecules in a vacuum and both of them require molecules
Silvered surface reduces heat loss by radiation by reflecting heat away from
going through the vacuum; heat can travel through vacuum by radiation.
Lid prevents heat loss by evaporation.
Note that infra-red radiation is part of em spectrum
Absorbers and emitters
A good absorber of heat is a good emitter of heat therefore black objects are
good absorbers and emitters of heat; this explains why it is wrong to wear dark
coloured clothes on a hot day, dark coloured objects dry faster than shiny
objects of the same material, houses are painted white in hot climates to
reflect heat from buildings
Experiment to determine good absorbers of heat
Experiment is set up as shown below
The thermometer reading close to the dark object is higher than that close to
the shiny object
Dark coloured objects are good absorbers of heat
Experiment to determine good emitters of heat
Experiment is set up as shown below
The thermopile reading on the side of the dark surface is higher than that close
to the shiny surface.
Dark coloured objects are good emitters of heat.
Properties of waves, including light and sound
General wave properties
Waves transfer energy but not matter that explains why ripples of water does
not carry a cork to another place as it moves from one region of the water to
the other or why a building is not moved from one place to the other as
earthquake goes through parts of the earth.
Wave motion can either be transverse or longitudinal; in transverse wave,
direction of travel of wave is perpendicular to oscillation of molecules and
without transferring matter e.g all em waves, s wave, ripples in water etc
In longitudinal wave, direction of travel of wave is parallel to oscillation of
molecules without transferring matter e.g sound and p wave.
Mechanical wave is that which requires material medium to pass through eg
longitudinal wave (sound wave).
Electromagnetic waves do not require material medium eg gamma, x-ray, UV
etc.
Wavefront is the crest of a transverse wave or the compression of a
longitudinal wave.
It is the section through a wave that are in the same phase.
Distance between 2 wavefronts is one wavelength.
Amplitude is the maximum displacement of a wave from its rest position.
(https://www.youtube.com/watch?v=9VSHa1mKcTw)
Wavelength is the distance between successive crests, compression, troughs,
and rarefaction.
Graph of transverse wave
Diagram of longitudinal wave.
The higher the amplitude the more the pressure at compression region and the
lower the pressure in rarefaction region; lines at compression region is closer
while they are more spaced in rarefaction regions.
Frequency is the number of oscillations in one second and period (T) is the time
taken for one oscillation.
Relationship between Frequency and Period
F=1/T or T=1/f
Wave equation
V=fλ
V=velocity
F=frequency
λ = wavelength
Waves can undergo reflection, refraction and diffraction.
Reflection is the bouncing off of a wave from a surface
Angle of incidence =Angle of reflection
All angles are measured from the normal.
Diagrams of Reflection
Refraction is the bending of a ray as it moves from one medium to another; if
a ray moves from a less dense medium to a more dense medium, the refracted
ray bends towards the normal and vice versa.
If a ray is incident at 900 the ray goes straight through without bending (angle
of refraction is 00, there is no refraction).
Refraction is also the change in speed or direction of a ray as it moves from one
medium to another.
Refraction explains why the bottom of a pool appears shallower than it actually
is or the apparent bending of a spoon put in a glass of water
Diagrams of Refraction
https://www.youtube.com/watch?v=QKl1-G1UgE4
https://www.youtube.com/watch?v=kc2o73FyN3I
https://www.youtube.com/watch?v=sBb5WUw2_2I
https://www.youtube.com/watch?v=jNAEz3VS3_4
https://www.youtube.com/watch?v=mfytZxM8lho
https://www.youtube.com/watch?v=DR8ZRCHCXIhttps://www.youtube.com/watch?v=CiHN0ZWE5bk
1
https://www.google.com/search?safe=active&source=hp&ei=qsHiXLK3A8LYaP
6ntsAH&q=wavefront+diagram+from+shallow+to+deep&oq=wavefront+diagra
m+from+shallow+to+dee&gs_l=psyab.1.0.33i22i29i30.2492.21874..25180...0.0..0.1214.18954.324j2j6j4j2......0....1..gwswiz.....0..0i131j0j0i10j0i22i30j33i21j33i160.qBh6RS3JS2E#kpvalbx=1
Diffraction is the spreading of a wave as it passes through a hole or passes over
an edge (this explains why sound made on one side of a mountain spreads
down to the person at the bottom of the mountain on the other side of the
mountain).
The condition for diffraction is that the size of the hole must be equal to or
smaller than the wavelength of the wave; the smaller the hole the more the
diffraction or the angle of wavefront.
Reflection of light from a plane mirror
 The features of the image formed include;
 Same size as the object
 Same distance behind the mirror
 Laterally inverted
 Virtual (cannot be formed on a screen or formed by the apparent
intersection of rays).
Refraction of light
Refractive index n = Sin i /Sin r (the refractive index or index of refraction of a
material is a dimensionless number that describes how fast light propagates
through the material. For example, the refractive index of water is 1.333,
meaning that light travels 1.333 times as fast in vacuum as in water).
RI n = 1/Sin C
RI n = Speed of light in vacuum (air)/ speed of light in second medium
Critical angle and Total Internal Reflection TIR
Condition is that a ray must move from a denser medium to a less dense
medium; critical angle is the angle of incidence that makes the angle of
refraction to be 90o (for a ray moving from glass to air it is between 410-420)
but note that there is a weak reflected ray as shown in the diagram
When the angle is greater than the critical angle TIR occurs; this is used in
binoculars, rear lamp of cars, periscope, optical fibres and endoscope.
Diagrams of Critical angle and TIR
Diagrams of periscope, optical fibre
Explanation of the working of the endoscope
Light signals travel along the fibres and hit the required surface, reflected back
along the fibres and image is formed of the surface hit by the rays.
Converging lens
The principal axis is the horizontal line that runs through the centre of the lens
The principal focus is the point on the principal axis where rays converge on
passing through the lens
Focal length is the distance from the centre of the lens to the principal focus (f)
Image formed by a converging lens and ray diagrams
General rules
 A ray through the centre of the lens passes straight through it.
 A ray parallel to the principal axis passes through f after leaving the lens
 A ray through f’ leaves the lens parallel to the principal axis.
There are only two types of diagrams that can be drawn concerning the
converging lens
When the object is within the focal length then the diagram is shown below
(the nature of the image is always larger than the object (this is the case of a
magnifying glass), behind the object, upright (erect) and virtual)
When the object is outside the focal length then the diagram is shown below
(the image is always real and inverted, becomes smaller as you go away from
the lens)
Dispersion of white light
This is the splitting of white light into its component colours as the light passes
through a prism.
Red light is deviated least and violet most.
Monochromatic light is light with only one frequency
When light moves from one medium to another its frequency stays the same
but its velocity and wavelength changes (velocity and wavelength decreases as
it moves from less dense to denser medium).
Electromagnetic spectrum
Gamma x-Ray Uv V R IR Mw TV
-------------------------------------------------------Decreasing frequency Increasing wavelength→
Uses of Em waves
–– radio and television communications (radio
waves)
–– satellite television and telephones
(microwaves)
–– electrical appliances, remote controllers for
televisions and intruder alarms (infrared)
–– medicine and security (X-rays)
Disadvantages of em waves
Microwaves can cause damage to skin
X rays can cause mutation which can lead to cancer
Sound
Sound is made when an object vibrates and sets air molecules into motion
The harder the object the louder the sound produced (water=1500m/s,
steel=5000m/s, concrete= 3000m/s, glass 4540m/s, gold= 3240m/s air at 200=
340 m/s air at 400= 355 lead = 1210 m/s etc)
Diagram of sound wave
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The higher the amplitude the louder the sound
The higher the pitch the higher the frequency
Frequency is measured in Hertz (Hz)
Loudness of sound is measured in decibels (db)
Audible Frequency for Humans
Humans can only hear sound within 20-20000Hz, below 20Hz is infrasound and
above 20 KHz is ultra sound, ultra sound can be used to scan to determine the
sex of a baby
Experiment to determine speed of sound in air
Two men separated by a distance (d) one of them with a gun and the other
with a stop watch
When the gun is fired, the other man starts the stop watch when he sees the
smoke or spark from the gun and stops the watch when he hears the sound at
a time t.
Speed of sound is d/t
Or one man can stand from a reflecting surface separated by a distance d,
He shouts and starts the stop watch
He stops the stop watch when he hears the echo of his sound and records the
time t.
Speed of sound=2d/t
Experiment to determine distance between a surface or depth of an ocean
An echo sounder or source of sound is made to produce sound and the stop
watch is started
When the echo of the sound is heard from the bottom of the ocean or from a
surface the stop watch is stopped and time t is recorded
D=Sxt/2
Electricity and magnetism
Simple phenomena of magnetism
 There is a force between magnets caused by interference of magnetic
fields
 A magnet can be used to pick a pin A and pin A can pick another pin B
and so on (diagram)
 Magnetic materials can be attracted to a magnet and non-magnetic
materials cannot be attracted to a magnet (examples)
 Magnetic field is the region around a magnet where the magnetic force
is felt
 The direction of a magnetic field at a point is the direction of the force
on a North Pole at that point.
 Magnetic field is concentrated at the poles
Magnetic field
Attraction and repulsion
Methods of making a magnet
Stroking method (diagram)
 The end of the material to be magnetised acquires an opposite pole to
the pole of the magnet that is used in stroking.
Hammering the object in a magnetic field
Electrical method
 The components include a solenoid (coil), core and a cell to drive
current.
 The strength of the magnet depends on 3 Cs (current, coil, and number
of turns of coil)
https://www.google.com/url?q=https%3A%2F%2Fwww.miniphysics.com%2Fin
ducedmagnetism.html&sa=D&sntz=1&usg=AFQjCNFBuNKm2skR25z5_qs4XL1TxBGDw
Demagnetising a magnet
Hammering, heating and hitting a magnet in the east to west direction
Heating a magnet causes the electrons inside to spin and generally move to
higher energy states, which makes them end up in a position that’s opposed
to other electrons nearby. Because of this the electrons are no longer as well
lined up, so the magnetism of the whole object decreases. Eventually whole
regions of the magnet fail to be lined up properly and the magnet is
demagnetized.
Electrical method
You can also remove the magnetic property of a magnet by placing it in a
reversed magnetizing field. This will oppose the object’s magnetism. You can
do this by passing an alternating current through a component of the
magnet. This is how demagnetizing tools work.
One way to make a magnet is by applying an electrical field (electromagnet), so
it makes sense you can use alternating current to remove magnetism, too. To
do this, you pass AC current through a solenoid. Start with a higher current and
slowly reduce it until it's zero. Alternating current rapidly switches directions,
changing the orientation of the electromagnetic field.
Note you can't use DC current to achieve the same effect because this type of
current only flows in one direction.
 Pass alternating current through a solenoid
 Slowly withdraw the magnet from the east to west direction
 The stronger the current the faster the demagnetisation
Leave the Magnet Alone for a (Very) Long Time
Any amount of heat can cause a magnet to lose its magnetic properties. A
smaller amount of heat, such as at room temperature, will have this effect
over a much longer time period. For example, for a simple flat magnet to lose
its magnetic property, it would take an amount of time greater than a human
life time.
Pattern of magnetic field round a magnet
Diagram
Experiment to identify the pattern of magnetic field lines, including the
direction
Starting with the compass near one end of the magnet, the needle position is
marked using two dots. Then the compass is moved so that the needle lines
up with the previous dot.. and so on. When the dots are joined up, a
magnetic field line is formed.
Magnetic properties of iron and steel
When under the same magnetic force; iron attracts more iron fillings than
steel, when the magnetic force is removed, iron lets go almost all its iron
fillings but steel retains almost all its iron fillings- these observations show
that iron produces a stronger magnetic field and steel retains its magnetism
and that is why steel can be used in making permanent magnets.
Electrical quantities
Electric charge




There are two types of charge, positive and negative
Charge is measured in coulombs (C)
Like charges repel and unlike charges attract
The direction of an electric field at a point is the direction of the force
on a positive charge at that point.
 Electric field as a region in which an electric charge experiences a force
Field pattern diagrams
Charging by contact
When 2 objects are rubbed together, the one that becomes positively
charged has lost electrons and the one that becomes negatively charged
has gained electron (positive charge does not move)
Charging by induction
 When a negatively charged rod (object) is brought close to a neutral
object, the positive charges are attracted towards the rod and the
negative charges are repelled to the other end of the object as
shown in the diagram.
 The object is then earthed with an earthing wire as shown in the
diagram; electrons then flow out to the earth.
 The earthing wire is then removed
 The rod is also removed, the object becomes positively charged.
Diagram
 When a positively charged rod (object) is brought close to a neutral
object, the negative charges are attracted towards the rod and the
positive charges are repelled to the other end of the object as
shown in the diagram.
 The object is then earthed with an earthing wire as shown in the
diagram; electrons then flow from the earth to the object to
neutralise the positive charges.
 The earthing wire is then removed
 The rod is also removed, the object becomes negatively charged
because of excess electrons.
Current
 A good conductor has free electrons which are free to move while an
insulator does not have free electrons.
 Graphite is a form of carbon (non-metal) that is a conductor because oi
has a free electron.
 This free electron is also responsible for flow of heat and current.
 Current is the rate of flow of charge I=Q/t
 Current is as a result of flow of electrons
 Conventional current flows from + to – while electrons flow from – to
+.
Electromotive force
 Emf of an electrical source is measured in volts
 E.m.f. is energy supplied by a source in driving charge round a
complete circuit
 Potential difference (p.d.) across a circuit component is measured in
volts
 Potential difference is energy supplied by a source in driving charge
across a component
Energy = VIt
= VQ
V = Energy/Q or J/C (Joule per Coulomb)
1V= J/C
Resistance
 This is the opposition to the flow of current in a conductor
 It is measured in ohms (Ω)
R=V/I
Ohm’s Law Experiment
Ohm’s law states that voltage is directly proportional to current at
constant temperature
VαI
The circuit is connected as shown above.
 Switch is closed and the voltmeter an ammeter reading is taken
 The variable resistor is adjusted and new voltmeter an ammeter
reading is taken
 Step two is repeated until five or more readings are
 To ensure temperature is constant, the key is turned off and the
circuit is allowed to cool before the next reading is taken
 A graph of current against voltage is plotted as shown below
 An object obeys ohm’s law when a straight line graph is obtained
Graph 1
Graph 2
Graph 3
Graph 4
From graph 3 as temperature increases so does the resistance; this explains
why the graph is curved at some point.
Relationship between Resistance, area, length and diameter of a metal




Rαl – if length is doubled resistance is doubled
Rα1/A if area is doubled resistance is halved
Rα1/d2 if diameter is doubled resistance reduces by a factor of 4 (1/4)
If diameter of a wire is doubled and its volume remains constant its
resistance reduces by a factor of 16 (1/16); doubling the diameter
increases the cross sectional area, hence decrease the resistance by a
factor of 4. This increase in area will cause the length, to also decrease
by a factor of 4, giving an overall decrease in resistance of 4 ⋅ 4 =16.
Electrical working
Q=VIT
Q=I2Rt
Q=V2t/R
P=Q/t
P=VI
Electric circuits
Circuit diagrams
Circuit symbols
Series and parallel circuits
 Total R in series=R1+R2+R3-- Total R in parallel= R1xR2/R1+R2
 Combined resistance of two resistors in parallel is less than that of
either resistor by itself
 The sum of the p.d.s across the components in a series circuit is equal
to the total p.d. across the supply
 the current from the source is the sum of the currents in the separate
branches of a parallel circuit
Action and use of circuit components
 Variable potential divider- splits or divides p.d between components in
a circuit
 Diode- allows current to flow only in one direction, it also converts a.c
to d.c (rectifier)
 Light dependent resistor (LDR)- its resistance decreases with high light
intensity
 Thermistor – its resistance decreases with increase of heat
 Relay- uses electromagnetism concept,
 It has 2 circuits
 Small current in the first circuit produces large current in the
second circuit
 It can be used as a switch
Digital electronics
Analogue signals vary continuously while digital signals vary between only 2
variables (0 or 1, hot or cold, high or low)
AND gate
INPUT A INPUT B
0
0
0
1
1
0
1
1
OUTPUT
0
0
0
1
The output is
high only
when 2 inputs
are high
NAND gate
INPUT A INPUT B
0
0
0
1
1
0
1
1
OUTPUT
0
0
0
1
NAND OUTPUT
1
1
1
0
OR gate
INPUT A
0
0
1
1
INPUT B
0
1
0
1
OUTPUT
0
1
1
1
Output is
high once
tone input
is high
NOR gate
INPUT A INPUT B
0
0
0
1
1
0
1
1
OUTPUT
0
1
1
1
NOR OUTPUT
1
0
0
0
Output is
high
provided
one input
is low
Output is high only
when 2 inputs is low
or output is low
provided one input is
high
NOT gate (has only one input)
Dangers of electricity
 Damaged insulation can cause electric shock
 Overheating of cables can cause fire outbreak
 Damp conditions can cause electric shock
Fuse is used to protect electrical gadgets; it has wire of very low melting
point which melts when high current flows through a circuit.
Fuse value must be greater than the normal current through the appliance,
but as close to it as possible, so that the fuse will blow as soon as the current
gets too high. E.g a 10A kettle will require a 13A fuse.
Circuit breaker is larger than a fuse; it cuts power supply from parts of
buildings when high current develops in a part of the circuit, it uses
electromagnet principle and a relay
Note that a fuse and switch is always connected to the live wire.
Earthing of the (metal) case of electrical gadgets prevents shock.
Electromagnetic effects
Electromagnetic induction
 A conductor moving across a magnetic field or a changing magnetic
field linking with a conductor can induce an e.m.f. in the conductor
 The direction of an induced e.m.f. opposes the change causing it (Lenz’s
law)
Factors affecting the magnitude of an induced e.m.f.
 increasing the number of turns on the coil
 increasing the speed of moving the magnet
 increasing the strength of the magnetic field
ELECTRIC MOTOR
 It is a device that changes electrical
energy into kinetic energy
 It is used in drilling machines
 it has a coil of wire that rotates in a magnetic field when current
flows through it
 The rotation is because of the force produced when there is
interference between magnetic field and current
 It has a split ring or commutator through which the current gets to the
coil
 It also has brushes that make contact with the split rings
WORKING OF AN ELECTRIC MOTOR
 Current flows through the coil from the cell or power supply
 The coil experiences a force and rotates because of the force produced
when there is interference between magnetic field and current
 The magnetic field is at right angle to the current
 The direction of rotation of the coil is determined using fleming’s left
hand rule
 If the cell or polarity of the magnet is reversed the direction of rotation
of the coil also reverses
WORKING OF THE COMMUTATOR
• Brushes connect to each split ring every half turn
• This reverses direction of current every half turn
THE TURNING EFFECT ON THE COIL CAN BE INCREASED BY
 Increasing the current
 Using a stronger magnet
 Increasing the number of turns of the coil
 Increasing the area of the coil(a longer coil means higher forces
because there is a greater length of wire in the magnetic field)
AC GENERATOR
 It is a device that changes kinetic energy to electrical energy
 It is used in generators
 All the parts are the same except the ac generator uses slip rings
instead of split rings
WORKING OF AN AC GENERATOR




It produces alternating current that flows back and forth
When the coil rotates it cuts magnetic field lines so voltage is produced
This makes current flow
As the coil rotates each side travels upwards, downwards, upwards,
downwards… and so on
 So the current flows backwards, forwards…. And so on
 Therefore it is ac
GRAPH OF CURRENT/VOLTAGE AGAINST TIME
 It is a maximum when the coil is horizontal and cutting the magnetic
field at the fastest rate
 It is zero when the coil is vertical and cutting no magnetic field
THE CURRENT FROM AN AC GENERATOR CAN BE INCREASED BY
 Increasing the number of turns of the coil
 Increasing the area of the coil
 Using a stronger magnet
 Rotating the coil faster
TRANSFORMER
 A transformer is used to either step up or step down voltage
 A step up transformer has more turns of coil on the secondary or its
output voltage is higher than the input voltage
Transformer equation
Vp/Vs=Np/Ns or Vp/Vs=Is/Ip or VpIp=VsIs or Np/Ns=Is/Ip or NpIp=NsIs
Working of a transformer





AC is input at the primary
Alternating or changing magnetic field is formed
Magnetic field is channelled by the core to the secondary
Secondary coil cuts the field
Voltage is induced
Note that power is transmitted from power station at a high voltage to
minimise power loss
 This reduces the current
 This reduces heat produced because flow of current is what produces
heat
 P=I2R
DC CAN NOT WORK IN TRANSFORMERS BECAUSE IT CAN NOT PRODUCE A
CHANGING MAGNETIC FIELD
Question 1
Explain why the energy losses become greater when the length of the
transmission
cables is greater.
Ans.
1. resistance increases with/is proportional to length of cable
2. energy losses due to heating in cables or I2R
Question 2
Discuss the advantages and disadvantages of using transmission cables of
greater cross-sectional area.
Ans. Advantage -reduced resistance or less heat loss
Disadvantage -more metal or cables heavier or more pylons or more costly to
construct
Question 3
Explain why energy losses in the transmission cables are lower when the
voltage is high.
Ans.
any three of:
 (high voltage means) low(er) current for given supply power
 (low(er) current means) less heat/thermal energy (generated in cables)
OR P = I2R for given resistance (of cables)
 cables heated by current
Eddy current formed in a transformer develops heat, this heat can be reduced
by laminating the core; making core into thin sheets.
The magnetic effect of a current
 pattern of the magnetic field (including direction) due to currents in
straight wires and in solenoids
 The direction of a magnetic field line at a point is the direction of the
force on the N pole of a magnet at that point recall that direction of an
electric field at a point is the direction of the force on a positive charge
at that point
Force on a current carrying conductor
Dc motor
A current-carrying coil in a magnetic field experiences a turning effect and
that the effect is
increased by:
 increasing the number of turns on the coil
 increasing the current
 increasing the strength of the magnetic field
Atomic Physics
The nuclear atom
Atomic model
An atom is made up of particles:
 There is a central nucleus made up of protons and neutrons.
Around the nucleus, electrons orbit at high speed.
 Protons have a positive(+) charge and electrons have an equal
negative (-) charge
 Protons + Neutrons are called nucleons.
Nucleus
23
X
Atomic number=11
Number of protons=11
Number of electrons=11
Nucleon number=23 (Mass number, atomic mass)
Number of neutrons=12
Isotopes are atoms of the same element with same atomic number but
different number of neutrons; they have different number of neutrons.
1
H, 2H, 3H
Scattering of Alpha particles by Gold nucleus (Rutherford’s nuclear model)
 Most alpha particles are undeflected (the atom has a lot of space
around it)
 Some alpha particles are deflected slightly (repulsion of the alpha
particle from the gold nucleus because the particle and nucleus are
both positively charged)
 Very few particles bounce off the nucleus (the nucleus occupies very
small space of the atom and that is where most of the mass of the
atom concentrates)
Nuclear fusion is the process by which smaller nuclei fuse together to form a
larger nucleus and large amounts of energy is released e.g. energy at the
heart of the sun due to fusion of hydrogen, deuterium and tritium nuclei.
Nuclear fission is the process by which a large nucleus splits by itself or when
struck with a neutron to smaller atom(s) and large amounts of energy is
released.
Radioactivity (radioactive decay)
 This is the emission of ionizing radiation or particles caused by the
spontaneous disintegration of atomic nuclei.
 Spontaneous emission of radiation, either directly from unstable
atomic nuclei or as a consequence of a nuclear reaction.
Note that radioactivity is a random process.
Background radiation is the radiation that is in the environment which cannot
be eliminated.
It comes from cosmic rays, rocks (soil, buildings) and atmospheric gases
(noble gases (radon)). Also small amounts come from medical equipment,
nuclear power.
Detection of radiation
 Cloud chamber makes the tracks of alpha particles visible.
 Radiation darkens photographic plate
 Geiger Muller tube is used measure radiation
Characteristics of the three kinds of emission
Beta particle
(β)
Electron
Gamma ray (γ)
Charge
Relative
charge
Effects on
Yes
fields
(magnetic and
electric)
Penetrating
Weakeffect
stopped by
thin paper
Negative
-1
No charge
-
Yes
No (it is uncharged)
Moderatestopped by a
few mm of
aluminium
Ionising effect Strongest
Dangerous
Yes
Speed
0.1xspeed of
light
Mass
High
Medium
Yes
0.9x speed of
light
low
Strong- never completely
stopped, though lead and
thick
Concrete will reduce
intensity
Weakest
Yes
Speed of light
Nature
Alpha
particle (α)
2 protons
and 2
Neutrons
(Helium
nucleus) 4He
Positive
+2
Photon/Electromagnetic
radiation
-
Ionisation is the knocking out of electrons from atoms by radiation or the
losing or gaining of electrons by atoms.
Half life
It is the time it takes half of a substance to decay or disintegrate
Nuclear Safety in nuclear power stations
 Shield people from direct nuclear radiation
 Keep people’s time of exposure to radiation as short as possible
 Prevent radioactive materials from getting into the body
 Radioactive materials are kept in sealed containers made of lead, steel
or concrete to shield radiation
Nuclear safety measures in the Laboratory
For safety, a source should be;
 Stored in a lead container in a locked cabinet
 Picked up with tongs, not by hand
 Kept well away from the body, and not pointed at other people
 Left out of its container for as short a time as possible
Using radioactivity
 They can be used as tracers; detecting leaks in underground pipes and
checking the function of body organs like the thyroid gland.
 Chemotherapy or radiotherapy; gamma radiation from Cobalt 60 is
used to destroy cancer cells.
 Testing for cracks in metals; gamma radiation can be used to
photograph metals to reveal cracks
 Thickness monitoring;
 Carbon dating; this is used to determine the age of organic materials
like wood and cloth
 Dating of rocks; some rocks have radioactive isotopes trapped in them
and half-life calculations could be used to determine their age.
Space physics
6.1 Earth and the Solar System
The Earth is a planet that rotates on its axis, which is tilted, once in
approximately 24 hours. Once every 24 hours Earth turns — or rotates
on its axis — taking all of us with it. When we are on the side of Earth
that is facing the Sun, we have daylight. As Earth continues its spin, we
are moved to the side facing away from our Sun, and we have night
time.
6.1.1 The Earth
The Earth orbits the Sun once in approximately 365 days. It takes
approximately one month for the Moon to orbit the Earth.
The average orbital speed from the equation v = 2π r/T where r is the
average radius of the orbit and T is the orbital period.
https://www.youtube.com/watch?v=b25g4nZTHvM
https://kids.britannica.com/kids/article/season/399589
Seasons happen because Earth's axis is tilted at an angle of about 23.4
degrees and different parts of Earth receive more solar energy than
others. Because of Earth's axial tilt (obliquity), our planet orbits the Sun
on a slant which means different areas of Earth point toward or away
from the Sun at different times of the year.
As the earth spins on its axis, producing night and day, it also moves
about the sun in an elliptical (elongated circle) orbit that requires
about 365 1/4 days to complete. The earth's spin axis is tilted with
respect to its orbital plane. This is what causes the seasons.
The span of time between one new Moon and the next is called a lunar
cycle, lunation, lunar month, or synodic month and on average lasts for
29.53059 days. This translates to 29 days, 12 hours, 44 minutes, and 3
seconds; this explains the periodic nature of the Moon’s cycle of
Phases.
6.1.2 The Solar System
The Solar System contains one star, the Sun, the eight planets (Mars,
Venus, Earth, Mercury, Jupiter, Saturn, Uranus, Neptune and Pluto)
Minor planets that orbit the Sun (include dwarf planets such as Pluto
and asteroids in the asteroid belt), moons (that orbit the planets),
smaller Solar System bodies (including comets) and natural satellites.
The four planets nearest the Sun are rocky and small
and the four planets furthest from the Sun are
gaseous and large,
Accretion theory explains how planets formed from the gas, dust, and
ice revolving around an early sun forming an accretion disc. The dust
collected into clumps and would stick together due to gravitational
forces. An interstellar cloud is generally an accumulation of gas,
plasma, and dust in our and other galaxies.
The planets, minor planets and comets have elliptical orbits, and the
Sun is not at the centre of the elliptical orbit, except when the orbit is
approximately circular.
PLANETARY DATA
The strength of the gravitational field at the surface of a planet
depends on the mass of the planet and around a planet decreases as
the distance from the planet increases.
The Sun contains most of the mass of the Solar System and this
explains why the planets orbit the Sun.
The force that keeps an object in orbit around the Sun is the
gravitational attraction of the Sun.
The strength of the Sun’s gravitational field decreases and that the
orbital speeds of the planets decrease as the distance from the Sun
Increases.
An object in an elliptical orbit travels faster when closer to the Sun and
explain this using the conservation of energy.
6.2 Stars and the Universe
6.2.1 The Sun as a star
The Sun is a star of medium size, consisting mostly of hydrogen and
helium, and that it radiates most of its energy in the infrared, visible
and ultraviolet regions of the electromagnetic spectrum.
Stars are powered by nuclear reactions that release energy and that in
stable stars the nuclear reactions involve the fusion of hydrogen into
helium.
6.2.2 Stars
Galaxies are each made up of many billions of stars
The Sun is a star in the galaxy known as the Milky Way
Other stars that make up the Milky Way are much further away from
the Earth than the Sun is from the Earth.
Astronomical distances can be measured in light-years, where one
light-year is the distance travelled in (the vacuum of) space by light in
one year.
One light-year is equal to 9.5 × 1015m
The life cycle of a star
A star is formed from interstellar clouds of gas and dust that contain
hydrogen.
A protostar is an interstellar cloud collapsing and increasing in
temperature as a result of its internal gravitational attraction.
A protostar becomes a stable star when the inward force of
gravitational attraction is balanced by an outward force due to the high
temperature in the centre of the star.
All stars eventually run out of hydrogen as fuel for the nuclear reaction.
Most stars expand to form red giants and more massive stars expand
to form red supergiants when most of the hydrogen in the centre of
the star has been converted to helium.
A red giant from a less massive star forms a planetary nebula with a
white dwarf star at its centre.
A red supergiant explodes as a supernova, forming a nebula containing
hydrogen and new heavier elements, leaving behind a neutron star or a
black hole at its centre.
The nebula from a supernova may form new stars with orbiting
planets.
6.2.3 The Universe
The Milky Way is one of many billions of galaxies making up the
Universe and that the diameter of the Milky Way is approximately
100000 light-years.
Redshift is the increase in the observed wavelength of electromagnetic
radiation emitted from receding stars and galaxies.
The light emitted from distant galaxies appears redshifted in
comparison with light emitted on the Earth.
Redshift in the light from distant galaxies is evidence that the Universe
is expanding and supports the Big Bang Theory.
Microwave radiation of a specific frequency is observed at all points in
space around us and is known as cosmic microwave
background radiation (CMBR).
The CMBR was produced shortly after the Universe was formed and
that this radiation has been expanded into the microwave region of the
electromagnetic spectrum as the Universe expanded.
The speed v at which a galaxy is moving away from the Earth can be
found from the change in wavelength of the galaxy’s starlight due to
redshift.
The distance of a far galaxy d can be determined using the brightness
of a supernova in that galaxy.
The Hubble constant H0 as the ratio of the speed at which the galaxy is
moving away from the Earth to its distance from the Earth; recall and
use the equation H0 = v/d
The current estimate for H0 is 2.2 × 10–18 per second
The equation d/v = 1/H0 represents an estimate for the age of the
Universe and that this is evidence for the idea that all the matter in the
Universe was present at a single point.