CIE IGCSE/GCE Physics Formula Sheet
Chapter 1: General Physics
distance (m)
time (s)
displacement
(m)
Average velocity (ms−1 ) =
time (s)
final velocity (ms −1 ) − initial velocity(ms−1 )
Acceleration (ms−2 ) =
time (s)
Weight (N) = mass (kg) × gravitational field strength (ms-2)
Earth’s gravitational field strength = 9.8 ms-2 (as of 2023)
Force (N) = mass (kg) × acceleration (ms-2)
mass (kg)
Density (kgm−3 ) =
volume 3
Hooke’s law: Force (N) = constant (Nm-1) × extension (m)
Force (N)
Pressure(Pa) =
area (m2 )
Fluid Pressure (Pa) = density (kgm-3) × gravitational field strength (ms-2 or Nkg-1) ×
height (m)
Work (J) = force (N) × distance moved (m)
work (J)
Power (W) =
time (s)
Kinetic Energy (J) = ½ × mass (kg) × velocity2 (ms-1)
Gravitational potential energy (J) = mass (kg) × gravitational field strength (ms-2 or
Nkg-1) × height (m)
useful power output (W or J)
Efficiency (%) =
× 100%
total power input (W or J)
Moment (Nm) = Force (N) × perpendicular distance from pivot (m)
Sum of clockwise moments (Nm) = sum of anticlockwise moments (Nm)
Momentum (kgms-1) = mass (kg) × velocity (ms-1)
change in momentum (kgms −1 )
Impulsive Force (N) =
time (s)
Impulse (kgms-1 or Ns) = change in momentum (kgms-1)
Average speed (ms−1 ) =
Chapter 2: Thermal Physics
Boyle’s Law for changes in gas pressure at constant temperature :
pressure1 (Pa) × volume1 (m3) = pressure2 (Pa)× volume2 (m3)
Energy (J) = mass (kg) × specific heat capacity (Jkg-1°C-1) × temperature change (°C)
Celsius to Kelvin:
Temperature in Celsius (oC) = Temperature in Kelvin (K) - 273.15
Chapter 3: Waves
Wave speed (ms-1) = frequency (Hz) × wavelength (m)
1
Frequency (Hz) =
Period (s)
sine of the angle of incidence, i
Refractive index =
sine of the angle of refraction, r
speed of light in vacuum
Refractive index =
speed of light in material
1
Refractive index =
sine of critical angle
Page 1 of 99
Page | 1
Senpaicorner.com
𝑑
𝑡
𝑥
𝑣=
𝑡
𝑣−𝑢
𝑎=
𝑡
𝑠=
W = mg
F = ma
𝑚
𝑉
𝜌=
F = kx
𝐹
𝐴
𝑃 = 𝜌𝑔ℎ
𝑃=
W = Fd
𝑃=
𝑊
𝑡
KE = ½mv2
GPE = mgh
𝜂=
𝑃𝑜𝑢𝑡
× 100%
𝑃𝑖𝑛
M = Fd
F1d1 = F2d2
p = mv
𝐹=
𝛥𝑝
𝑡
𝛥𝑝 = 𝑚𝑣 − 𝑚𝑢
P1V1 = P2V2
Q = mcθ
C = K - 273.15
V = fλ
1
𝑇
𝑠𝑖𝑛 𝑖
𝑛=
𝑠𝑖𝑛 𝑟
𝑐
𝑛=
𝑣
1
𝑛=
𝑠𝑖𝑛 𝑐
𝐹=
Chapter 4: Electricity and Magnetism
charge (C)
Current (A) =
time (s)
energy transferred (J)
Voltage (V) =
charge (C)
Voltage (V) = current (A) × resistance (Ω)
Power (W) = current (A) × voltage (V)
Power (W) = current2 (A) × resistance (Ω)
Energy transferred (J) = current (A) × voltage (V) × time (s)
Energy transferred (J) = power (W) × time (s)
Resistors in series: Total Resistance (Ω) = sum of individual resistors (Ω)
Resistors in parallel:
1
1
=
total resistance (Ω) sum of individual resistors (Ω)
resistivity (Ωm) × length (m)
Resistance (Ω) =
𝑎𝑟𝑒𝑎(m2 )
Wires have a circular cross section, area = π × radius2
Transformers:
voltage in secondary coil (V) turns on secondary coil
=
voltage in primary coil (V)
turns on primary coil
Transformers:
voltage in secondary coil (V) current in secondary coil (A)
=
voltage in primary coil (V)
current in primary coil (A)
1
𝑅𝑡𝑜𝑡𝑎𝑙
=
1
𝑅1
+
𝑅 =
1
𝑅2
1
+…𝑅
𝜌𝑙
𝐴
𝑉𝑠 𝑁𝑠
=
𝑉𝑝 𝑁𝑝
𝑉𝑠 𝐼𝑠
=
𝑉𝑝 𝐼𝑝
𝐴
𝐴−4
4
𝑍𝑋 → 𝑍−2𝑌 + 2𝐻𝑒
Beta:
0
𝐴
𝐴
𝑍𝑋 → 𝑍+1𝑌 + −1𝑒
Gamma
𝐴
𝐴
𝑍𝑋 → 𝑍𝑌 + 𝛾
Page 2 of 99
Page | 2
V = IR
P = IV
P = I2R
W = IVt
W = Pt
Rtotal = R1+R2+R3+…Rn
Chapter 5: Nuclear Physics
Alpha:
Chapter 6: Space Physics
2
×
𝜋 × average radius of the orbit (m)
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑟𝑏𝑖𝑡𝑎𝑙 𝑠𝑝𝑒𝑒𝑑 (ms −1 ) =
orbital period (s)
distance of a far galaxy (m)
1
=
speed away from us (m𝑠 −1 ) Hubble Constant (𝑠 −1 )
Hubble Constant is 2.2 × 10–18 s-1
Senpaicorner.com
𝑄
𝑡
𝑊
𝑉=
𝑄
𝐼=
2𝜋𝑟
𝑇
𝑑
1
=
𝑣 𝐻0
𝑣=
𝑛
CIE IGCSE Physics Notes
Chapter 1 General Physics
Physical quantities and measurement techniques
S
SI
R
1.1
AN
• A ruler is used to measure length for distances between 1 mm and 1 meter.
• The SI unit for length is in meters.
• To measure the volume of a regular object you will need to know the formula and
several of its length. For e.g., to measure the volume of a solid box, you’ll need its
H
height x length x width.
• To measure the volume of an irregular object you put the object in a measuring
cylinder with water and measure the rise in water. The rise in water is the volume
of the object.
• Time is measured using clocks or watches.
• The SI unit for time is in seconds.
• You can increase the accuracy for measuring any object by taking an average value.
• For e.g., to measure the period of a pendulum, you can take the time it takes to
complete ten cycles instead of one and dividing the time by ten.
• A micrometre screw gauge is a tool used for measuring small widths, thickness, or
diameters
• It has a resolution of 0.01 mm
• A micrometre is made up of two scales:
1) main scale – this is on the sleeve (sometimes called the barrel)
2) the thimble scale – this is a rotating scale on the thimble
• The value measured from the micrometre is read where the thimble scale aligns
with the main scale.
Page | 1
Senpaicorner.com
Page 3 of 99
SI
R
CIE IGCSE Physics Notes
AN
S
• A scalar quantity has magnitude only.
• Example of scalar quantities include distance, time, speed and mass.
• A vector quantity has both magnitude and direction.
• Example of vector quantities include distance, velocity, acceleration and force.
• The easiest way to tell if a quantity is scalar or vector is to know whether you can
put ‘’negative’’ sign in front of it.
• Example mass and time are both scalars because there is no “-“ seconds or “-“
kilograms.
H
• Velocity is a vector because you can have “-“ in front of the unit as you will see
later.
• Vectors can be added using triangle or parallelogram method.
Page 4 of 99
Page | 2
Senpaicorner.com
CIE IGCSE Physics Notes
SI
R
Triangular method
H
AN
S
Parallelogram method
Page 5 of 99
Page | 3
Senpaicorner.com
CIE IGCSE Physics Notes
Motion
H
AN
S
SI
R
1.2
• Distance: The distance travelled by an object is the total length that is travelled
by that object.
• The SI unit for distance is also in meters.
• Speed: Rate of change in distance.
• SI unit: meter per second (m/s)
• Speed is a scalar quantity
v=
d
t
v is the speed, d is the distance travelled and t is the time taken
• Velocity: Is speed with a given direction!
• SI unit: meter per second (m/s)
• Velocity however is a vector quantity
Page 6 of 99
Page | 4
Senpaicorner.com
CIE IGCSE Physics Notes
v=
s
t
v is the speed; s is the displacement and t are the time taken
• Note: In velocity the positive/ negative sign indicates direction.
Example problem
SI
5 m/s
S
Speed of top arrow:
Velocity of top arrow:
Speed of bottom arrow:
Velocity of bottom arrow:
R
5 m/s
H
AN
• Acceleration: Rate of change of velocity.
• The SI unit for acceleration is m/s2
• Acceleration is a vector quantity
a=
v−u
t
• In IGCSE you need to be able to read as well as plot displacement-time graphs
and velocity-time graphs!
• For a displacement-time graph, the gradient represents the velocity.
• For a velocity-time graph, the gradient represents the acceleration while the
area under the graph represent the displacement.
Page 7 of 99
Page | 5
Senpaicorner.com
CIE IGCSE Physics Notes
Displacement-Time graph
Velocity is
constant
and ‘’-‘’
Velocity is
constant
and “+’’
Velocity is
not
constant
but
increasing
Velocity is
not
constant
but
decreasing
S
SI
R
Velocity is
zero!
AN
Flex your brain!
A car starts from rest and accelerates at a constant acceleration of 3m/s2 for 10
seconds. The car then travels at a constant velocity for 5 seconds. The brakes are
H
then applied and the car stops in 5 seconds. What is the total distance travelled by
the car?
Page 8 of 99
Page | 6
Senpaicorner.com
CIE IGCSE Physics Notes
Velocity-Time graph
Acceleration
is not
constant but
increasing
Constant
and positive
acceleration
Constant
but negative
acceleration
SI
S
Acceleration
is not
constant but
decreasing
R
Zero
acceleration!
AN
• Free falling: Free falling is a motion under gravitational force as the only force
acting on the moving object.
• The acceleration of a free-falling object is always constant.
H
• On the surface of the earth, the acceleration due to gravity, g is equal to 9.8ms-2.
• In reality objects are slowed by air resistance. Once air resistance is equal to the
force of gravity, the object stops accelerating. The object is said to have reached
terminal velocity.
Page 9 of 99
Page | 7
Senpaicorner.com
CIE IGCSE Physics Notes
Launching Object Upward
Motion
Velocity-Time Graph
Acceleration-Time
Graph
Velocity-Time
Graph
Acceleration-Time
Graph
AN
S
SI
Motion
R
Dropping Object from a High Place
Object Falling and Bounce Back
H
Motion
Velocity-Time Graph
Page 10 of 99
Page | 8
Senpaicorner.com
Acceleration-Time
Graph
CIE IGCSE Physics Notes
• Two forces act on a parachutist upon jumping out of a plane
1) Weight
S
SI
R
2) Air resistance
H
AN
• Plotting the motion on a speed-time graph
Page 11 of 99
Page | 9
Senpaicorner.com
CIE IGCSE Physics Notes
Mass and weight
R
1.3
• Mass: Mass is defined as the amount of matter in an object.
S
SI
• The SI unit is in kg
• Mass is a scalar quantity.
• Weight: Is the force of gravity acting on an object.
• The SI unit is in Newtons
Density
H
1.4
AN
Weight = mass x gravitational acceleration
W = mg
• Density is defined as mass per unit volume.
• The SI unit for density is kgm-3
𝜌=
𝑚
𝑣3
Page 12 of 99
Page | 10
Senpaicorner.com
CIE IGCSE Physics Notes
• You can determine the mass of an object by using a weighing scale.
• The volume for the object can be calculated out for regular shapes (cylinder, box
etc.) or using a measuring cylinder for irregular shapes.
• An object will float if it is less dense then medium it is in and sink if more dense.
Forces
H
AN
S
SI
R
1.5
• Force: Push or pull exerted on an object.
• Forces can change the shape and size of an object and can even change the
direction and cause deceleration or acceleration of an object.
• SI unit: Newton (or kgms-1)
• Force is a vector quantity.
• Inertia is a property of a body that tends to maintain its state of motion.
• Newton’s 1st Law: In the absence of external forces, an object at rest remains at
rest and an object in motion continues in motion with a constant velocity.
• Newton’s 2nd law: States that the acceleration of an object is directly proportional
to the resultant force acting on the object and inversely proportional to mass.
• So basically
Fnet = ma
• When the forces acting on an object
are
not balanced, there must be a net force
Page 13
of 99
acting on it. This net force is known as the unbalanced force.
Page | 11
Senpaicorner.com
CIE IGCSE Physics Notes
• Where F is the force, m is the mass and a is the acceleration. Hence, the resultant
force will cause an object to accelerate.
Find the resultant force and acceleration
A box of mass 150kg is placed on a horizontal floor with a smooth surface (which
means no friction). Find the acceleration of the box when 300N force is pulling it to
SI
R
the left and 600N is pulling it to the right. Hint: Whenever there’s more than 1 force
acting on an object you’ll need to find the resultant force. Draw out the problem!
proportional.
AN
S
• Hooke’s Law: Springs extend in proportion to loads, as long as they are under their
proportional limit.
• Limit of proportionality: Point and which load and extension are no longer
H
• Elastic limit: Point at which spring will not return to its original shape even after
the load is removed.
Page 14 of 99
Page | 12
Senpaicorner.com
CIE IGCSE Physics Notes
• Circular motions: An object at steady speed in a circular orbit is always
accelerating as its direction is changing, but it gets no closer to the centre
• Centripetal force: is the force acting towards the centre of a circle. It is a force
that is needed (not caused by) a circular motion, for example when you swing a ball
on a string round in a circle, the tension of the string is the centripetal force. If
the string is cut then the ball will travel in a straight line at a tangent to the circle
at the point where the string was cut (Newton’s first law)
• Newtons 3rd law: if object A exerts a force on object B, then object B will
exert an equal but opposite force on object A or, more simply: to every action
there is an equal but opposite reaction
R
• Centrifugal force also known as the non-existent force is the force acting away
from the centre of a circle. This is what makes a slingshot go outwards as you spin
it. The centrifugal force is the reaction to the centripetal force (Newton’s third
law). It has the same magnitude but opposite direction to the centripetal force
H
AN
S
SI
(“equal but opposite”).
Page 15 of 99
Page | 13
Senpaicorner.com
H
AN
S
SI
R
CIE IGCSE Physics Notes
• Friction is a force that acts in a direction that is opposite to the direction of
motion.
• It can occur between two surfaces that are in contact with one another or even
when an object moves through fluids (e.g., air resistance)
• Friction can cause an object to slow down and produce heat.
Page 16 of 99
Page | 14
Senpaicorner.com
CIE IGCSE Physics Notes
• Turning effect: Moments of a force are measured in Newton meters, can either
be clockwise or anticlockwise.
R
• Equilibrium is achieved when the clockwise moment = anticlockwise moments and
when the sum of all forces are equal to zero.
H
AN
S
SI
• Centre of mass is an imaginary point in a body (object) where the total mass of
the body can be thought to be concentrated.
• For stability the centre of mass must be over the centre of pressure.
• For a symmetrical object of uniform density (such as a square) the centre of mass
is located at the point of symmetry.
• When an object is suspended from a point, the object will always settle so that its
centre of mass comes to reset below the pivoting point.
• This can be used to find the centre of mass of an irregular shape:
Page 17 of 99
Page | 15
Senpaicorner.com
CIE IGCSE Physics Notes
• Momentum is defined by the equation:
R
Momentum
SI
1.6
Momentum = mass x velocity
p=mxv
S
• The units of momentum are kg/ ms-1
• Momentum is a vector quantity
AN
• The conservation of momentum states that in the absence of external forces
(such as friction), the total momentum of a system remains the same.
H
• I.e., mom before = mom after
• Impulse is the change in momentum
Impulse = mv – mu
OR
Page
99 – mu
F x18t of
= mv
Page | 16
Senpaicorner.com
CIE IGCSE Physics Notes
Energy, work and power
AN
Potential energy
S
SI
R
1.7
• Gravitational potential energy: The energy stored in an object as the result
H
of its height.
• SI units: Nm or Joule
• Quantity: Scalar
𝑊 = 𝑚𝑔 × ℎ
where h is the relative height of the object.
• Elastic potential energy: The energy stored in elastic materials when you
stretch or compress the spring.
• SI units: Nm or Joule
• Quantity: Scalar
1
𝑊 = 𝐹𝑥
2
• Where x is the length of the compressed or elongated spring.
Kinetic energy
Page 19 of 99
• Kinetic energy: The energy of a moving object.
Page | 17
Senpaicorner.com
CIE IGCSE Physics Notes
• SI units: Nm or Joule
• Quantity: Scalar
1
𝑊 = 𝑚𝑣 2
2
Where v is the speed of the object
• The law of conservation of energy states that energy cannot be created or
destroyed, it can only change from one form to another.
• Sankey diagrams summarize all energy transfers taking place in a process.
• For example, in a 100 Joules electric incandescent lamp, only 10 Joules of its
electricity gets converted into useful light while the remaining 90 Joules is wasted
as heat.
AN
S
SI
R
• The Sankey diagram can hence be drawn as:
H
• Try the following questions:
Ah Kau climbs 35 steps of a staircase. Each step is 10cm in height. If Ah Kau
weighs 45kg, find the work done by him to reach the top of the 35 steps.
Page 20 of 99
Page | 18
Senpaicorner.com
CIE IGCSE Physics Notes
H
AN
S
Find the energy stored in the spring.
SI
R
Determine the kinetic energy of a 2000kg bus that is moving at a speed of
35m/s.
The Sankey diagram above shows the efficiency of a solar panel
What is the input power to the panel?
Page 21 of 99
Page | 19
Senpaicorner.com
H
AN
S
SI
R
CIE IGCSE Physics Notes
• Work is done by a constant force to move an object a certain distance
• SI unit: Joule
• Quantity: Scalar
Page 22 of 99
Page | 20
Senpaicorner.com
CIE IGCSE Physics Notes
𝑊 =𝐹×𝑠
Where F is the force and s is the distance travelled.
Diagram above shows a 10 N force is pulling a metal. The friction between the block
and the floor is 5N. If the distance travelled by the metal block is 2m, find
a) the work done by the pulling force
S
SI
R
b) the work done by the frictional force
H
AN
• Energy: Is the capacity to do work.
• SI units: Joules
• Quantity: Scalar
• Energy sources can come from renewable or non-renewable sources.
• Renewable source of energy is inexhaustible, for e.g. solar, hydroelectric, wind,
etc. e.g. hydro dams, tidal power scheme, wave energy, geothermal resources,
nuclear fission, solar cells, solar panels.
• Non-renewable source of energy: is exhaustible for example fossil fuels. Eg, fossil
fuel.
• The conservation of energy principle states that energy cannot be created or
destroyed by can change from one form to another.
• Efficiency: The percentage of usable energy.
• SI units: dimensionless or %
• Quantity: dimensionless
𝜂=
𝑂𝑢𝑡𝑝𝑢𝑡
× 100%
𝐼𝑛𝑝𝑢𝑡
Page 23 of 99
Page | 21
Senpaicorner.com
CIE IGCSE Physics Notes
• Where W is the energy or work done.
S
Pressure
H
AN
1.8
𝑊
𝑡
SI
𝑃=
R
• Power: Is the rate at which work is done.
• SI units: Watt or J/s
• Quantity: Scalar
•
Pressure, P is the force, F exerted per unit area, A
𝑃=
𝐹
𝐴
•
The SI unit for force is Newtons.
•
•
The SI unit for area is m2.
The SI unit for pressure is then Newton/m2 or Pascal.
Page 24 of 99
Page | 22
Senpaicorner.com
CIE IGCSE Physics Notes
Which of the following orientation do you think exerts the biggest force on the
surface? Hint: think about the area
•
SI
R
Imagine they are filled with water
The pressure exerted by liquids (or gas) can be found by using
H
AN
S
𝑃 = ℎ𝜌𝑔
•
Fluids exert pressure on the fluids below due the weight of the fluid. The
pressure acts in all directions.
•
The three factors affecting fluid pressure
-depth of the fluid
-density of the fluid
-gravitational acceleration (9.8 m/s2 if you are from earth)
•
•
The deeper the fluid, the higher its pressure.
For instance the pressure at the bottom of the sea is much higher than at the
surface making necessary special equipment in order to explore its depths like a
submarine.
Page 25 of 99
Page | 23
Senpaicorner.com
CIE IGCSE Physics Notes
Which of the following do you think will “shoot” the farthest? Hint: Density of
D < Density of W. Think logically…….
D
W
W
D
R
h
SI
What is the pressure exerted by the water on the bubble assuming h is
S
a) 1m?
AN
b) 5m?
H
c) 10m?
Hint: Density of water is 1000 kgm-3
h
Calculate the depth of the water if the maximum pressure at the base of the
dam is 750 kPa.
Page 26 of 99
Page | 24
Senpaicorner.com
CIE IGCSE Physics Notes
Chapter 2 Thermal Physics
2.1 Kinetic particle model of matter
▪ Matter exist in one of four different states.
State
Solid
Characteristics
• Fixed shape and volume.
• Strong forces of attraction
between particles.
• Have a fixed pattern (lattice)
• Atoms vibrate but cannot change position.
Liquid
Gases
• Fixed volume but changes shape depending on
container
• Weaker attractive forces that solids
• No fixed pattern
• Particles slide past each other
• No fixed shape volume, gases fill up their
containers
• Almost no intermolecular forces
• Particles are far apart, and move quickly,
gases spread out to fill up the container and
exert equal pressure on all surfaces.
• They collide with each other and bounce in all
directions.
Page 27 of 99
Page | 1
Senpaicorneer.com
CIE IGCSE Physics Notes
▪ Matter can change from solid to liquid via melting and liquid to solid via freezing.
▪ These changes occur at the melting point.
▪ Liquid can also change to gas via boiling and gas to liquid via condensing.
▪ These occur at the boiling point.
• Molecules in a gas move around randomly and very quickly.
• The temperature of a gas is related to the average kinetic energy of the
molecules.
Page 28 of 99
• The higher the KE of the molecules,
the higher its temperature.
Page | 2
Senpaicorneer.com
CIE IGCSE Physics Notes
• For example, the average KE of a glass of water at 80 oC is higher than the
average KE of a glass of water at 30 oC.
• Hence, the lowest possible temperature that can be achieved in this universe is 273 oC (not infinity!)
• At this temperature all molecules cease moving hence, the average KE = 0
• The motion of the molecules often cause them to collide with the surface of
nearby walls.
• This collision causes a change in momentum when the molecule bounces off the
wall (recall from previous chapter change in momentum over time gives you force).
• Each collision applies a force across a surface area of the walls.
• Recall from previous chapter force per unit area is pressure.
• Recall Brownian motion is the erratic motion of small particles when observed
through a microscope which is caused by collision between said particles and the
molecules of the gas (liquid).
• The SI unit of temperature is in Kelvin. However, Celsius is more frequently used.
• You can convert Celsius to Kelvin by using
K = TOC + 273
Convert the following to Kelvin
a) -273 OC
b) 0 OC
c) 100 OC
Page 29 of 99
Page | 3
Senpaicorneer.com
CIE IGCSE Physics Notes
• When the temperature of a gas in a fixed container is increased, the KE (speed)
of molecules increase.
• This causes the molecules to collide more frequently against the container thus
increasing pressure.
• However, if you decrease the volume while keeping the temperature of the gas
constant (as in the case of the piston below) the pressure will increase.
• This is due to more collisions of the molecules with the container.
• This phenomenon can be described using Boyle’s Law
P1V1 = P2V2
• The graph above shows the inverse relationship between pressure and volume of
Page 30 of 99
an ideal gas at constant temperature.
Page | 4
Senpaicorneer.com
CIE IGCSE Physics Notes
2.2 Thermal properties and temperature
• When most substance is heated, they expand due to higher average KE.
• The molecules start knocking into each other and push each other apart.
• Solids expand a little due to the stronger bonds holding each molecule.
• Liquids expand more than solid but less that gas since the molecular bond
strength holding them is between solid and gas.
• Gas expands the most due to it have the weakest molecular bonds.
• Best example of this phenomenon is a thermometer.
Page 31 of 99
Page | 5
Senpaicorneer.com
CIE IGCSE Physics Notes
• As the temperature of thermometer increases, the liquid inside of the
thermometer expands.
• To do well in this chapter you must first understand the difference between
temperature and heat.
• Temperature is related to the average speed (or KE) of individual molecules.
• The SI unit for temperature is in Kelvin.
• Heat is a form of energy (not a force).
• As such its SI unit is Joules.
• Specific heat capacity is the amount of heat required to change the temperature
by 1oC or 1K for a mass of 1kg of the substance.
• A lower heat capacity means the object heats up easier, while a higher heat
capacity means an object heats slower.
• The specific heat capacity (c) can be calculated by using
𝑐=
𝑄
𝜃𝑚
Here Q is the thermal energy (heat), θ is the change in temperature and m is the
mass of the substance.
• The SI unit of c is Joules OC-1kg-1 (definitely the longest unit in physics so far!)
Temperature
Time
• The above is a familiar plot of temperature vs time
• When a substance is heated its temperate would normally increase due to the
average KE increasing (sloped part of the graph)
• However, when the substance is changing phase either solid to liquid or liquid to
gas, the temperature stays the same (flat part of the graph)
• This happens because the energy is being used to break the bonds between the
molecules instead of increasing the KE (hence temperature)
Page 32 of 99
Page | 6
Senpaicorneer.com
CIE IGCSE Physics Notes
• Liquid can change to gas through either boiling or evaporation.
• The difference between both is as follows:
Boiling
Evaporation
Occurs at fixed temperature
Occurs at any temperature
Quick process
Slow process
Takes place throughout the liquid
Takes place only at the surface of the
liquid
Bubbles are formed in the liquid
No bubbles are formed
Temperature remains constant
Temperature may change
Thermal energy supplied by an energy
Heat supplied by surroundings
source
• Evaporation constantly occurs on the surface of liquids.
• It is the escape of the more energetic particles.
• If the more energetic particles escape, the liquid contains fewer high energy
particles and lower energy particles so the average temperature decreases.
• Evaporation can be accelerated by:
-increasing temperature: more particles have enough energy to escape
-increasing surface area: more molecules are close to the surface
-reduce the humidity level in the air: if the air is less humid, fewer particles are
condensing.
-blow air across the surface: removes molecules before they can return to the
liquid
• Evaporation can cool objects down if the surface of the object is in contact with
the liquid.
• Best example is sweating.
Page 33 of 99
Page | 7
Senpaicorneer.com
CIE IGCSE Physics Notes
2.3 Transfer of thermal energy
Page 34 of 99
Page | 8
Senpaicorneer.com
CIE IGCSE Physics Notes
• Thermal energy is transferred via 3 mechanisms:
Mechanism
Conduction
•
•
Convection
•
•
•
Radiation
•
•
Page 35 of 99
Page | 9
Senpaicorneer.com
Method
In non-metals - when heat is
supplied to something, its atoms
vibrate faster and pass on their
vibrations to the adjacent atoms.
In metals – conduction happens in
the previous way and in a quicker
way – some electrons are free to
move, they travel randomly in the
metal and collide with atoms and
pass on the vibrations
As a fluid (liquid or gas) warms up,
the particles which are warmer
become less dense and rise.
They then cool and fall back to the
heat source, creating a cycle called
convection current.
As particles circulate they
transfer energy to other particles.
Thermal radiation is mainly infrared waves (chapter 3) but very hot
objects also give out light waves.
Infra-red radiation is part of the
electromagnetic spectrum.
CIE IGCSE Physics Notes
• Thermal radiation is mainly infra-red waves, but very hot objects also give out light
waves.
• Infra-red radiation is part of the electromagnetic spectrum.
• Unlike the other two mechanism, thermal radiation can travel through a vacuum and
does not need a medium.
• An emitter sends out thermal radiation.
• A reflector reflects thermal radiation, therefore is a bad absorber.
• An emitter will cool down quickly, an absorber will heat up more quickly and a
reflector will not heat up quickly
• The color of an object affects how good it is at emitting and absorbing thermal
radiation as shown below:
Matt Black White Silver
Emitter
Best
Worst
Reflector Worst
Best
Absorber best
worst
• Factors affecting thermal radiation is
-temperature of the object (hotter = more radiation)
-color of the object (black = more radiation)
-surface area of the object (greater surface area = more area for radiation to
emit from)
Page 36 of 99
Page | 10
Senpaicorneer.com
CIE IGCSE PHYSICS NOTES
Chapter 3 Waves
3.1 General properties of waves
Page 37 of 99
Page | 1
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• Which of the picture above shows a wave in action?
• Waves transfer energy between points without transferring matter
• Best way to visualize this would be to use a slinky and shake it up and down.
• You will see a wave but the rings on the slink does not actually travel with the
wave.
• Amplitude (A) is the maximum displacement from the original position.
• The SI unit for amplitude is in meters.
• Wavelength (λ) is the horizontal distance between two points that are in phase.
• The SI unit for amplitude is in meters as well.
• The period (T) is the time taken for the wave to complete a cycle or return to its
original displacement.
• The SI unit for periods is seconds.
• Frequency (f) is the number of complete cycles in a second (i.e., how many times
did the wave go up, down and up again or down, up, and down again in 1 second).
• The SI unit for frequency is hertz (Hz) OR seconds-1.
• Hence the relationship between frequency (f) and period (T) is
𝑓=
1
𝑇
Page 38 of 99
Page | 2
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• The speed of a wave can be calculated using the following equation
Speed (m/s) = Frequency (Hz) x Wavelength (m)
v=fxλ
• There are two types of waves.
• In a transverse wave, particles vibrate perpendicular the lines of motion and
consists of a series of “peaks” and “valleys”.
• In a longitudinal wave, particles vibrate along the lines of motion and consists of a
series of compression and expansion.
• Examples of transverse waves include; electromagnetism, water waves and Sseismic waves.
• Examples of longitudinal waves include: sound waves and P-seismic waves.
• A wave must be able to demonstrate these three phenomena in order to be
considered as a wave.
• Reflection is the change of direction when a wave collides with a reflective barrier.
• Refraction is the change of direction when the wave goes through a change of
medium.
• Refraction occurs when the direction of motion is not perpendicular to the border
between the deep and shallow regions.
• The speed of the water changes when there is a change in the depth of the water.
Page 39 of 99
Page | 3
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• From deep to shallow waters, the wave’s speed decreases as the wavelength
becomes shorter.
• From shallow to deep waters the wave’s speed increases as the wavelength becomes
longer (Hint: recall v = fλ).
• One way to imagine this is to picture deep waters as a broad road allowing many
cars to travel and shallow water as a narrow road causing a jam.
Deeper
Hint: 1) Draw a line representing the direction of the wave
propagation first (blue arrow)
2) Then only draw the normal line (green arrow)
• Diffraction is shown when a wave spreads when the wave passes through an opening
or an edge.
• Diffraction increases when the size of the gap decreases or the wavelength of the
waves increases.
• A ripple tank can be used to demonstrate the above three phenomenon.
Page 40 of 99
Page | 4
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
3.2
Light
• Light is a wave because it undergoes reflection, refraction and diffraction.
• Reflection
i=r
• Types of mirrors
• Reflection in plane mirror
• The image form is upright, virtual, laterally inverted and same size as object.
Page 41 of 99
Page | 5
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• Refraction
• Refraction is the bending of light ray at the boundary of two medium as the light
ray propagates from a medium to another with different density.
• When light passes through a medium which is denser
i>r
• When light passes through a medium which is less dense
i<r
• Snell’s law states that the value of (sin i) / (sin r) is constant for light passing
from one given medium into another
sin i
= constant, n
sin r
Here n is the refractive index. Remember that n>1
• Another equation for refractive index is
Refractive index, n =
speed of light in vacuum c
=
speed of light in medium v
Page 42 of 99
Page | 6
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Note: The greater the refractive index, the denser is the medium. Hence, the
speed of light in the medium will be slower.
• Total internal reflection and the critical angle
Where
𝑛=
1
sin 𝑐
Note: The light ray must propagate from an optically denser medium to an optically
less dense medium. The angle of incident must exceed the critical angle.
• Some phenomenon related to internal reflection and the critical angle
1) Mirage
2) Rainbow
Page 43 of 99
Page | 7
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• For a converging lens (convex lens), when parallel rays of light pass through a lens,
they are brought to focus at a point known as the principal focus (f).
• The distance of the principal focus from the lens is called the focal length which
depend on the curvature of the lens.
• There are three rules for drawing ray diagram for convex lens
• The characteristics of the image form using a convex lens is always either virtual
or real; upright or inverted; magnify or diminish.
• DO NOT memorize the characteristics for different object positions.
Page 44 of 99
• Try to use the three rules and draw them out!!!!
Page | 8
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• When light is refracted by a prism, the incidence ray is not parallel to the emergent
ray, since the prism’s sides are not parallel.
• If a beam of white light is passed through a prism it is dispersed into a spectrum.
• White light is a mixture of colours, and the prism refracts each colour by a
different amount – red is deviated the least and violet the most.
• The seven colours of the spectrum are red, orange, yellow, green, blue, indigo
and violet.
• Light is an electromagnetic wave; hence it is a transverse wave.
• Red has the largest wavelength.
• Violet has the shortest wavelength.
• Light of a single wavelength is known as monochromatic.
Page 45 of 99
Page | 9
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
3.3 Electromagnetic spectrum
• Electromagnetic waves are transverse waves.
• It consists of electric field and magnetic field components.
• It can propagate without the need of a medium to carry them unlike mechanical
waves.
• The speed that electromagnetic waves travel at is 3x108 ms-1.
• If this number seems familiar it’s because that’s the speed of light.
• Light is a wave or more specifically an electromagnetic wave.
• There are seven types of waves in the electromagnetic spectrum as shown below.
• Based on the diagram below, frequency (f) increases from left to right.
• While wavelength (λ) decreases from left to right.
• This is due to v = f x λ
• The speed of the wave is constant
(v),46hence
Page
of 99 if the frequency (f) decreases the
wavelength (λ) must increase to compensate.
Page | 10
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• Electromagnetic radiation is used for communication and transmission of
information.
• The waves that are used in this way are radio waves (radio), microwaves (mobile
phone, Bluetooth and WIFI), infrared radiation (aircon remove control) and visible
light (optical fiber).
• The method of communication requires the use of a code or signals.
• There are two types of signal
1) Analogue
Page 47 of 99
2) Digital
Page | 11
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• An analogue signal changes in frequency and amplitude with time.
• A digital signal has only 0s and 1s
• Digital signals have advantages over analogue signals.
• Digital signals have increased capacity, better quality and can be stored and
processed by computers.
• Increased capacity allow digital signals to carry more information compared to
analogue.
• Both digital and analogue can pick up unwanted signals that distort the original
sound (remember hearing static over radio?)
• However, the advantage of digital is that noise in digital signals can be clean up in
process known as regeneration because each pulse is 0 or 1 other values can be
removed.
Page 48 of 99
Page | 12
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
3.4 Sound
• Recall that sound waves are longitudinal waves.
• Sound waves are mechanical waves as they require a medium to propagate
through.
• Sound waves travel through solid, liquid and gas by “passing along” the vibration
from one particle to the next.
• Hence the speed of sound is highest in solids (concrete: 5000m/s) then in liquids
(pure water: 1400m/s) and slowest in gases (air: 330m/s)
Page 49 of 99
Page | 13
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• The speed of sound can be calculated by using
𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑠𝑜𝑢𝑛𝑑 =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑏𝑦 𝑠𝑜𝑢𝑛𝑑
𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
• An echo is produced when sound is reflected of a surface
• Pitch is related to the frequency of the sound.
• The greater the frequency, the higher the pitch.
• Humans can hear between 20 Hz and 20 kHz.
• Human vocal range is between 80 Hz to 1100 Hz.
• Soprano singers would be in the higher range of frequency while bass singer would
be on the lower!
• Sound waves less than 20 Hz are known as infrasound while those above 20 kHz are
known as ultrasound.
• Loudness is related to the amplitude of the sound. The bigger the amplitude the
louder the sound.
Page 50 of 99
Page | 14
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Chapter 4 Electricity and Magnetism
4.1 Simple phenomena of magnetism
•
Magnets have a magnetic field around them and two opposite poles (north and
south). Like poles repel and unlike poles attract.
•
Magnets can attract magnetic materials and induce magnetism in them. Nonmagnetic materials are not affected.
•
Induced magnetism is weak and can be strengthened by stroking with a magnet.
•
The most effective method is using a solenoid with a DC current.
Ferromagnetic materials (e.g., iron, nickel, cobalt) can be magnetized, but not all
magnetic materials are ferromagnetic (e.g. aluminum, copper, gold).
•
•
Soft ferromagnetic materials are used for temporary magnets, while hard
ferromagnetic materials are used for permanent magnets.
Permanent magnets are used in a variety of applications, such as refrigerator
magnets, motors, generators, and speakers. Electromagnets are temporary
magnets that are created by running an electric current through a coil of wire.
They are used in applications where the magnetism is needed only temporarily,
•
such as cranes and doorbells.
Magnetic forces are due to the interactions between magnetic fields. The
Page 51 of 99
strength of a magnetic field depends on the strength of the magnet and the
Page | 1
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
distance from the magnet. The spacing between magnetic field lines indicates
the strength of the field - the closer the lines, the stronger the field.
•
•
Magnetic field lines go from north to south. The south pole of a magnet is
attracted to the north end of a compass needle.
Materials can be demagnetized by a demagnetizing field (using a solenoid with
AC), high temperature, or physical impact.
Page 52 of 99
Page | 2
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
4.2
Electrical quantities
•
Electrical charge can be either positive or negative. The unit of charge is the
•
coulomb (C). Like charges repel and opposite charges attract. Electrons are the
cause of charge and are negatively charged (1.6x10-19 C).
When electrons flow into a neutral object, it becomes negatively charged. When
electrons are removed, it becomes positively charged.
•
Electric current is the rate of charge flow in a circuit. It is measured in
Page 53 of 99
amperes (A) and can be calculated using the formula
Page | 3
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
𝐼=
•
•
𝑄
𝑡
where Q is the charge in coulombs and t is the time in seconds.
The current flows in the opposite direction of the electrons.
An electric field is a region where charges experience electric force. It is
represented by arrow lines and is stronger at the source and weaker further
away. A stronger field is indicated by more lines. Positive charges have arrow
lines pointing outwards, while negative charges have arrow lines pointing inwards.
You can combine ‘+’ and ‘-’ fields to get more exotic shapes (see below).
Page 54 of 99
Page | 4
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Page 55 of 99
Page | 5
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
Electromotive force (e.m.f.) and potential difference (voltage) are often confused
because they are similar concepts.
•
•
Electromotive force is the work done by a cell to drive a unit of charge around a
complete circuit. It is measured in volts.
Potential difference (voltage) is the work done to transfer a unit of charge across
two points of different potential. It is calculated using the formula
𝑉=
𝑊
𝑄
where V is the potential difference in volts, W is the work done in joules, and Q
is the charge in coulombs.
•
Resistance is the opposition to electrical current. It is measured in ohms (Ω) and
is determined by the material and shape of a conductor. The higher the
resistance, the more work is required to push the same amount of current through
the conductor.
•
Ohm's Law states that the potential difference (voltage) across a conductor is
directly proportional to the current flowing through it, provided that the
conductor is ohmic and the temperature and other physical properties remain
constant. The equation for Ohm's Law is:
Page 56 of 99
Page | 6
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
V = IR
•
where V is the potential difference (voltage) in volts, I is the current in amperes,
and R is the resistance in ohms. This equation can also be rearranged to solve for
any of the three variables: I = V/R, R = V/I.
The resistance of a conductor is affected by several factors:
1) Length: The longer the length of the conductor, the greater its resistance.
2) Diameter or area: The larger the area of the conductor, the lower its
resistance.
3) Temperature: The higher the temperature of the conductor, the greater
its resistance.
4) Material: The type of material of a conductor can affect its resistance,
with some materials being more conductive and others being more
insulative.
•
•
Resistance is the opposition to electrical current. It is measured in ohms (Ω) and
is determined by the material and shape of a conductor. The higher the
resistance, the more work is required to push the same amount of current through
the conductor.
Power is the rate of work done or energy transferred. Recall the equation for
power is
𝑃=
•
𝑊
𝑡
where P is power, w is work, and t is time. Depending on the information given,
the equation for power can be written in different forms.
Electrical power is the rate at which electrical energy is transferred. It is
measured in watts (W) and can be calculated using the following equation:
P = V*I
where P is power, V is voltage (potential difference), and I is current.
Page 57 of 99
Page | 7
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
4.3 Electric circuits
Page 58 of 99
Page | 8
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
Thermistors are resistors whose resistance decreases with increasing
temperature. They are used in temperature sensing and control applications.
Light-dependent resistors (LDRs) are resistors whose resistance decreases with
•
increasing light intensity. They are used in light sensing applications.
Fuses and relays are electrical components that are used to protect circuits and
•
•
•
devices from excessive current. Fuses are one-time use components that break
the circuit when the current exceeds a certain level, while relays are switch-like
components that can open or close a circuit under certain conditions.
Diodes are two-terminal electronic components that allow current to flow in only
one direction. They are used to protect circuits and devices from reverse
current and voltage.
Light-emitting diodes (LEDs) are diodes that emit light when current flows
through them. They are used as indicators and in lighting applications.
Page 59 of 99
Page | 9
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
A parallel circuit is a type of electrical circuit in which the components are
connected in parallel, meaning that they are connected to the same voltage
•
•
source and have their own individual current paths.
In a parallel circuit, the total current is equal to the sum of the individual
branch currents.
The total resistance in a parallel circuit is calculated using the formula:
1/Rt = 1/R1 + 1/R2 + 1/R3 + ...
•
•
where Rt is the total resistance, and R1, R2, R3, etc. are the resistances of the
individual branches.
The voltage across each component in a parallel circuit is the same.
A series circuit is a type of electrical circuit in which the components are
connected in series, meaning that they are connected in a chain and only have
•
•
one current path.
In a series circuit, the total current is equal to the current through any one of
the components.
The total resistance in a series circuit is calculated by adding the resistances of
the individual components using the formula:
Rt = R1 + R2 + R3 + ...
•
where Rt is the total resistance, and R1, R2, R3, etc. are the resistances of the
individual components.
The voltage across each component in a series circuit is different. The voltage
drop (difference in potential) across a component is proportional to the
resistance of the component.
Page 60 of 99
Page | 10
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Characteristic
Total current
Series Circuit
Equal to any one branch
current
Parallel Circuit
Sum of branch currents
Calculated using 1/Rt = 1/R1 + 1/R2 +
Total resistance
Voltage across
components
Rt = R1 + R2 + R3 + ...
Different, proportional to
resistance
Page 61 of 99
Page | 11
Senpaicorner.com
1/R3 + ...
Same
CIE IGCSE PHYSICS NOTES
4.4 Electrical safety
•
Damaged insulation on electrical wires can cause electric shock, which can result
in serious injury. For example, if a frayed wire is touched, the person may
•
receive an electric shock.
Overheating of electrical cables can be caused by coiling them up tightly, which
can lead to a fire hazard. For example, if an extension lead is coiled up tightly
and then plugged in, it may overheat and potentially cause a fire.
Wet conditions can increase the risk of electrocution due to water's ability to
•
conduct electricity. For example, if an electrical appliance is used near a wet
floor, there is an increased risk of electrocution.
Excess current can be caused by overloading of plugs, extension leads, and
•
sockets when using a mains supply. This can result in overheating and potentially
cause a fire. For example, if a single socket is used to power multiple appliances
•
that exceed the socket's current rating, it can cause excess current and
potentially start a fire.
Fuses are used to protect electrical circuits from excessive current by melting
(blowing) if the current becomes too high. They should be chosen based on the
current rating of the appliance they are protecting. For example, if a 15-amp
fuse is used to protect a 20-amp appliance, it may not trip in the event of an
excess current and could potentially cause a fire.
Page 62 of 99
Page | 12
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
Circuit breakers are automatic switches that open the circuit when the current
exceeds a certain value. They can be reset after tripping and offer better
protection than fuses because they can be used multiple times. For example, if a
circuit breaker trips due to excess current, it can be reset once the cause of
the excess current has been addressed, whereas a fuse must be replaced after
it has blown.
Page 63 of 99
Page | 13
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
4.5 Electromagnetic effects
•
•
•
Electromagnetic induction occurs when a magnet is moved in and out of a
solenoid, causing the magnetic field flux of the magnet to be cut by the coil,
which in turn induces an electromotive force (e.m.f.) in the wire.
If the solenoid is connected to a closed circuit, an induced current will flow
through the circuit.
The production of electric current through electromagnetic induction only
occurs when the magnet or solenoid is moving relative to one another.
Page 64 of 99
Page | 14
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
Faraday's Law states that the magnitude of the induced e.m.f. is directly
proportional to the rate of change of magnetic flux through a solenoid or the
rate of the magnetic flux being cut. Increasing the speed of the magnet, using
a stronger magnet, or increasing the number of coils in the solenoid will all
increase the induced e.m.f.
•
•
Lenz's Law states that the induced current always flows in the direction that
opposes the change in magnetic flux. This law obeys the conservation of energy
principle, as work is done to move the magnet against the repulsive force, which
is then converted to electric energy (current).
Electromagnetic induction occurs when a straight conductor (e.g. wire) moves
and cuts through a magnetic field, causing an e.m.f. to be induced across the
conductor. If the conductor is a complete circuit, current will flow in the
conductor. The direction of the current can be determined using Flemming's
RHR.
Example problems
Find the direction of the induced current.
Page 65 of 99
Page | 15
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
When a bar magnet is moved into a solenoid, the solenoid will cut the magnetic
flux of the bar magnet, inducing a current and e.m.f. in the solenoid. The induced
•
•
current will produce another magnetic field around it, the pole and direction of
which can be determined using Lenz's Law.
Applications of electromagnetic induction include DC generators and AC
generators.
An AC generator is a device that converts mechanical energy (e.g. from a turbine
or engine) into electrical energy. It is based on the principle of electromagnetic
induction, which states that a changing magnetic field can induce an e.m.f. in a
•
conductor.
AC generators consist of a rotating magnet (the rotor) or a rotating coil of wire
(the armature) and a stationary coil of wire (the stator). As the magnet or
armature rotates, it cuts through the magnetic field of the stator, inducing an
e.m.f. in the wire. This e.m.f. causes a current to flow in the wire, producing an
•
•
•
AC voltage.
The frequency of the AC voltage produced by an AC generator is directly
proportional to the speed of the rotor or armature.
In some AC generators, the rotor or armature is connected to the external
circuit via slip rings and brushes. These components allow the current to flow
from the rotating part of the generator to the stationary part, while minimizing
electrical loss due to friction.
AC generators are used in many applications, including power plants and portable
generators. Understanding how they work is important for studying electricity
and electrical devices.
•
•
•
•
An AC generator produces voltage that periodically changes direction
Plotting the e.m.f. of an AC generator against time produces a sine wave
The peaks of the sine wave represent the maximum positive and negative values
of the voltage
The troughs of the sine wave represent
the minimum positive and negative values
Page 66 of 99
of the voltage
Page | 16
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
The zero points of the sine wave represent points where the voltage is zero
•
The position of the generator coil determines the position of the peaks, troughs,
•
and zeros on the sine wave
As the magnet or armature of the AC generator rotates, the position of the
generator coil changes, causing the e.m.f. to follow a sine wave pattern
•
An electromagnet is a temporary magnet made by winding an insulated wire around
a soft iron core, forming a solenoid
•
When current passes through the solenoid, it produces a magnetic field
The solenoid becomes magnetized and functions as an electromagnet
The strength of the electromagnet depends on the number of turns in the
solenoid, the type of material used for the core, and the amount of current
flowing through the solenoid
Electromagnets are used in a wide range of applications, including motors,
generators, relays, and speakers
•
•
•
•
The right-hand thumb rule is a way to find the direction of the magnetic field
•
around a conductor carrying current.
The right-hand thumb rule can be used for straight wires, single coils, and
solenoids.
•
Straight wire
Page 67 of 99
Page | 17
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
Coil
•
Solenoid
Page 68 of 99
Page | 18
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
When a current-carrying conductor is placed in a magnetic field, the interaction
between the two magnetic fields produces a force on the conductor.
•
To determine the direction of this force, use Fleming's left-hand rule.
Page 69 of 99
Page | 19
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
1) Place your thumb, forefinger, and middle finger perpendicular to each
other.
2) Point your forefinger in the direction of the magnetic field, your middle
finger in the direction of the current, and your thumb in the direction of
the force.
•
The strength of the force can be increased by:
1) Increasing the current
2) Using a stronger magnet
3) Using a longer wire
4) Arranging the wire perpendicular to the direction of the magnetic field
•
•
•
•
A current-carrying conductor placed in a magnetic field generates a force
The direction of this force can be determined using Fleming's left-hand rule
A current-carrying coil placed in a magnetic field generates a pair of opposing
forces
These forces constitute a couple, causing the coil to rotate
Page 70 of 99
Page | 20
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
Examples of equipment that use this effect include DC motors and moving coil
meters.
•
Two current-carrying conductors placed close to each other will generate a
force between them
If the currents in both conductors flow in the same direction, the conductors
will repel each other
•
•
If the currents flow in opposite directions, the conductors will attract each
other
Page 71 of 99
Page | 21
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
A transformer is a device that changes the potential difference of an AC
current
•
•
•
•
•
•
It consists of a primary and secondary coil wound on a soft iron core
When AC current flows in the primary coil, a changing magnetic flux is
generated and transferred to the secondary coil through the iron core
Induces an EMF in the secondary coil, magnitude determined by the ratio of
primary to secondary turns
Input current flows through primary winding, output exits through secondary
winding
Current in primary must be AC to generate changing flux
In an ideal transformer, input power = output power and induced current in
secondary is AC and has the same frequency as input
𝑉𝑃 𝐼𝑝 = 𝑉𝑆 𝐼𝑆
•
Relationship between input and output voltage, current, and power:
𝑉𝑃 𝑁𝑃
=
𝑉𝑠
𝑁𝑠
•
A step-up transformer increases voltage on secondary coil relative to primary
•
coil and reduces current
A step-down transformer decreases voltage on secondary coil relative to
•
primary coil and increases current.
The turns in primary and secondary coils are inversely proportional to voltage in
primary and secondary coils. Page 72 of 99
Page | 22
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Page 73 of 99
Page | 23
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Chapter 5 Nuclear Physics
H
AN
S
SI
R
5.1 The nuclear model of the atom
•
Almost all the mass of an atom is concentrated in the nucleus
The nucleus consists of protons and neutrons
•
Total number of protons and neutrons is called the nucleon number
•
Page 74 of 99
Page | 1
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Isotopes are atoms of certain elements with the same proton numbers but
•
different nucleon numbers (difference in number of neutrons)
Isotopes have the same chemical properties but different physical quantities
•
H
AN
S
•
(e.g., molecular mass, density)
Protons can be thought of as atomic DNA
Ions are formed when an atom gains or loses electrons
Examples of isotopes: Protium, Deuterium, Tritium (isotopes of the hydrogen
element)
SI
•
R
•
•
Alpha particles are positively charged particles
Scattering of alpha particles by gold foil refers to the deflection of alpha
particles when they collide with the atoms of a gold foil
The experiment was performed by Ernest Rutherford in 1909 to determine the
•
structure of the atom
The results of the experiment showed that most of the mass of an atom is
•
•
concentrated in a small, dense nucleus
•
•
A few alpha particles were deflected at large angles, indicating that they had
encountered something massive in the gold foil
This led Rutherford to propose that the atom consists of a positively charged
nucleus surrounded by electronsPage 75 of 99
Page | 2
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
The experiment helped to confirm the atomic model with a central nucleus and
•
H
AN
S
SI
R
electrons in orbit around it.
The 3 findings from the scattering of alpha particles by gold foil experiment:
1) The majority of alpha particles passed through the foil without being
deflected.
2) Some alpha particles were slightly deflected, suggesting the existence of
empty spaces within the foil.
3) A small number of alpha particles were greatly deflected or completely
bounced back, suggesting the presence of dense, positively charged
•
objects within the foil.
Nuclear fission involves the splitting of a heavy nucleus into two or more smaller
•
nuclei
The nucleus is typically bombarded by a neutron, causing the nucleus to become
•
•
unstable
This instability leads to the nucleus splitting into two or more smaller nuclei
When the nucleus splits, it also Page
releases
a large amount of energy and additional
76 of 99
free neutrons
Page | 3
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
The free neutrons can then go on to collide with other nuclei, leading to a chain
reaction
•
•
This chain reaction can be harnessed to produce nuclear energy or used in
nuclear weapons
Nuclide equation: An example of a nuclear fission reaction is the fission of
uranium-235 (U-235): U-235 + neutron -> Ba-141 + Kr- 92 + 3 neutrons
•
Nuclear fusion involves the joining of two or more lighter nuclei to form a
heavier nucleus
•
This requires high temperatures and pressures to overcome the repulsive forces
•
between the positively charged nuclei
When the nuclei are joined, they form a single, heavier nucleus
The process releases a large amount of energy, which can also be harnessed to
•
produce energy or used in weapons
During the process of fusion, a small amount of mass is transformed into a large
R
•
H
AN
S
SI
amount of energy, according to the famous equation E=mc^2. This equation
states that energy (E) is equal to mass (m) times the speed of light (c) squared.
In the process of fusion, the total mass of the system decreases, but the total
energy released is much greater.
Page 77 of 99
Page | 4
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Radioactivity
H
AN
S
SI
R
5.2
•
Radioactivity refers to the spontaneous emission of radioactive particles from
an unstable nucleus
The emission is a way for the nucleus to become more stable by reducing its
energy
There are three types of radioactive emission: alpha, beta and gamma
•
Alpha emission involves the release of alpha particles, which are helium nuclei
•
Beta emission involves the release of beta particles, which are high-energy
electrons
Gamma emission involves the release of gamma rays, which are high-energy
•
•
•
•
photons
The instability of the nucleus can be due to an imbalance of protons and
Page 78 of 99
neutrons, known as isotopes
Page | 5
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
The process of radioactivity can result in the nucleus changing into another
element through a decay process.
A thick
sheet of
paper
Deflection
in electric
field
Deflection
in magnetic
field
Can be
deflected
Can be
deflected
H
AN
S
Can be
deflected
R
Protection
β
γ
Negative
No charge
Less than
Less than β
α
More than
Most
α
penetrating
A few
Several
millimetres centimetres
of Perspex
of lead
or
aluminium
Can be
Not
deflected
deflected
SI
α
Charge
Positive
Ionization Strongest
ionization
Penetration
Least
Page 79 of 99
Page | 6
Senpaicorner.com
Not
deflected
CIE IGCSE PHYSICS NOTES
Example problem
Determine which of the following emissions are alpha, beta and
H
AN
S
SI
R
gamma emissions
Page 80 of 99
Page | 7
Senpaicorner.com
H
AN
S
SI
R
CIE IGCSE PHYSICS NOTES
•
The nucleus of an unstable isotope emits nuclear radiation, including α, β, and γ
rays, to become stable
•
•
•
•
The process of emitting nuclear radiation is called radioactive decay
Radioactive decay occurs spontaneously and randomly
The unstable nucleus before decay is called the parent nuclide
The stable nucleus produced after decay is called the daughter nuclide
Page 81 of 99
Page | 8
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
Alpha decay
𝐴
𝐴−4
4
𝑍𝑋 → 𝑍−2𝑌 + 2𝐻𝑒
1)
During an alpha decay, a radioactive atom X decay and emits an alpha
particle ( 42𝐻𝑒).
2)
Atom X losses 2 neutron and 2 proton and become atom Y.
e.g.
238
234
4
92𝑈 → 90𝑇ℎ + 2𝐻𝑒
•
Beta decay
R
𝐴
𝐴
0
𝑍𝑋 → 𝑍+1𝑌 + −1𝑒
A beta particle is an electron emitted from a nucleus.
2)
The beta particles are very small and move with very high speed.
3)
During a beta decay, a radioactive atom X decay and emits a beta particle
SI
1)
( −10𝑒).
4)
One of the neutron is disintegrated to become proton and electron. The
nucleus
Hence, the proton number goes up by 1 while the nucleon number remains
AN
5)
S
electron is emitted out from the nucleus whereas the proton stay in the
unchanged.
e.g.
•
H
234
234
0
90𝑇ℎ → 91𝑃𝑎 + −1𝑒
Gamma Emission
Gamma emission causes no change in nucleon or proton number. This is because
gamma ray is an electromagnetic radiation and not a particle.
𝐴
𝐴
𝑍𝑋 → 𝑍𝑌 + 𝛾
•
Unstable nucleus undergoes radioactive decay
Daughter nucleus may still be unstable
•
Daughter nuclide undergoes another radioactive decay
•
Process continues until stable nuclide is reached
This is called series decay
•
•
Page 82 of 99
Page | 9
Senpaicorner.com
SI
R
CIE IGCSE PHYSICS NOTES
Example problem
H
AN
S
State the radioactive decays that the element has gone through.
Page 83 of 99
Page | 10
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
Radioactive decay occurs randomly and spontaneously, transforming an unstable
nucleus into a more stable one.
•
•
SI
R
•
The number of unstable nuclei in a sample decreases with time.
Half-life is defined as the time taken for the number of unstable nuclei in a
sample to reduce to half of its original number.
Example: Antimony-133 has a half-life of 2.5 minutes.
S
Example problem
H
AN
The diagram shows the graph of the activity of a radioisotope, X, against time.
What is the half-life of the radioisotope substance?
Page 84 of 99
Page | 11
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Radioisotopes have a wide range of applications in various fields. One of the most wellknown uses of radioisotopes is in archaeology, where Carbon-14 is used for carbon
dating. In industry, radioisotopes are used for monitoring the content of food, which
helps ensure that the food is safe for consumption. In agriculture, radioisotopes can be
used for a variety of purposes, including pest control. By introducing a small amount of
radioactive material into the soil, farmers can effectively control the population of
pests, reducing damage to crops and increasing yields. Overall, radioisotopes play a
significant role in many areas of science and technology, providing valuable tools for
•
•
•
AN
•
Ionizing nuclear radiation has effects on living things.
Cell Death: Ionizing radiation has enough energy to damage or kill living cells.
Mutations: Ionizing radiation can cause changes in the genetic material of living
cells, leading to mutations.
Cancer: Prolonged exposure to ionizing radiation can increase the risk of
developing cancer.
Safe movement, use, and storage of radioactive materials is essential to
H
•
S
SI
R
research, development, and practical applications.
mitigated the risk of nuclear radiation.
•
•
Proper handling and transportation to minimize exposure to radiation
Storage in secure, designated areas to prevent contamination
•
Use of protective equipment, such as gloves and masks, when handling
radioactive materials
Several safety precautions for handling ionizing radiation are needed.
•
Reduce Exposure Time: Minimize the amount of time spent near a source of
•
•
•
ionizing radiation.
Increase Distance: Increase the distance between the source of radiation and
living tissue to reduce exposure.
Use Shielding: Place materials, such as lead or concrete, between the source of
radiation and living tissue to absorb radiation and reduce exposure.
Page 85 of 99
Page | 12
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Chapter 6 Space Physics
6.1 Earth and the Solar System
• The Earth is a planet that rotates on its axis, which is an imaginary line that
passes through the North and South poles. The axis is tilted at an angle of 23.5
degrees from the vertical. The Earth rotates from west to east, which means
that the Sun and the Moon appear to rise in the east and set in the west. The
Earth takes about 24 hours to complete one rotation, which is why we have day
and night.
• The Earth also orbits around the Sun, which is a star that provides light and heat
to our planet. The Earth's orbit is not a perfect circle, but an ellipse, which means
that sometimes the Earth is closer to the Sun and sometimes farther away. The
Earth takes about 365 days to complete one orbit, which is why we have a year.
The tilt of the Earth's axis and its orbit around the Sun cause the seasons,
because different parts of the Earth receive different amounts of sunlight
throughout the year.
Page 86 of 99
Page | 1
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• The Moon is a natural satellite that orbits around the Earth. The Moon reflects
the light from the Sun, which makes it visible in the night sky. The Moon takes
about 28 days to complete one orbit, which is why we have a month. The shape of
the Moon changes as it orbits around the Earth, because we see different parts
of its illuminated side. These changes are called phases of the Moon.
• The average orbital speed of an object is how fast it moves along its orbit. It
depends on how far away it is from what it orbits and how long it takes to
complete one orbit. We can calculate the average orbital speed using this formula:
𝑣=
2𝜋𝑟
𝑇
where v is the average orbital speed, r is the average radius of the orbit, and T is
the orbital period (the time for one orbit).
• For example, if we want to find out how fast the Earth moves around the Sun, we
can use this formula:
v = 2π (150 million km)/(365 days) = 29.8 km/s.
This means that the Earth travels about 30 km every second along its orbit
around the Sun.
Page 87 of 99
Page | 2
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Page 88 of 99
Page | 3
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• The Solar System is a collection of objects that orbit the Sun, which is the only
star in our system and contains most of its mass.
• The eight planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and
Neptune. They are divided into two groups: the inner rocky planets and the outer
gas giants.
• There are also minor planets such as dwarf planets (e.g. Pluto) and asteroids, as
well as moons that orbit the planets and smaller bodies such as comets and
natural satellites.
• The Solar System was formed about 4.6 billion years ago from a cloud of gas and
dust that collapsed and rotated to
form
Page
89 ofan
99accretion disc. The Sun formed at the
center and the planets formed from the remaining material.
Page | 4
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• The planets have elliptical orbits around the Sun, which means they are not always
at the same distance from it. The time it takes for a planet to complete one orbit
is called its orbital period.
• The Sun emits electromagnetic radiation that travels through space at a constant
speed of 3.0 x 108 m/s. This radiation can be divided into different regions based
on its wavelength and frequency, such as visible light, infrared, ultraviolet, Xrays, and gamma rays.
• The distance between objects in the Solar System is so large that it takes time
for light to travel from one place to another. For example, it takes about 8
minutes for light to reach Earth from the Sun, and about 5 hours to reach Pluto.
• The gravitational force between two objects depends on their masses and their
distance apart. This force keeps the planets in orbit around the Sun and also
affects their shapes and motions.
• Some planets have rings made of dust and ice particles that orbit them. Saturn
has the most spectacular rings in our Solar System.
• Some planets have natural satellites or moons that orbit them. Earth has one
moon, while Jupiter has more than 70. Some moons have interesting features such
as volcanoes, geysers, or oceans.
• The Sun has a very strong gravitational field that pulls the planets towards it.
The closer a planet is to the Sun, the stronger the pull and the faster the planet
orbits around it. The farther a planet is from the Sun, the weaker the pull and
the slower the planet orbits around it.
• For example, Mercury is the closest planet to the Sun and it orbits at an average
speed of 47 km/s. Neptune is the farthest planet from the Sun and it orbits at an
average speed of 5 km/s.
Page 90 of 99
Page | 5
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
Surface
Gravitational
field
Density
(kg/m^3)
temperature
(°C)
strength
(m/s^2)
88.0
5429
167
3.7
108.2
224.7
5243
464
8.9
Earth
149.6
365.2
5514
15
9.8
Mars
228.0
687.0
3934
-65
3.7
Jupiter
778.5
4331
1326
-110
23.1
Saturn
1432.0
10747
687
-140
9.0
Uranus
2867.0
30589
1270
-195
8.7
Neptune 4515.0
59800
1638
-200
11.0
Orbital
Orbital
distance
(10^6 km)
duration
(days)
Mercury 57.9
Venus
Planet
• The planets do not orbit in perfect circles, but in ellipses, which are like
stretched circles.
• When a planet is closer to the Sun, it is at a point called perihelion. When a planet
is farther from the Sun, it is at a point called aphelion. The distance between
perihelion and aphelion is called eccentricity. The more eccentric an orbit is, the
more oval-shaped it is.
• For example, Mars has a more eccentric orbit than Earth, so its distance from
the Sun varies more. At perihelion, Mars is 207 million km from the Sun. At
Page 91
of 99
aphelion, Mars is 249 million km from
the
Sun.
Page | 6
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• When a planet is closer to the Sun, it has more kinetic energy (energy of motion)
and less potential energy (energy of position). When a planet is farther from the
Sun, it has less kinetic energy and more potential energy. The total energy of a
planet in its orbit is always constant. This means that when a planet moves faster,
it also moves closer to the Sun, and when it moves slower, it also moves farther
from the Sun.
• This is an example of conservation of energy, which means that energy cannot be
created or destroyed, but only changed from one form to another.
Page 92 of 99
Page | 7
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
6.2
Stars and the Universe
• The Sun is a star of medium size that consists mostly of hydrogen and helium.
• The Sun releases most of its energy in the infrared, visible and ultraviolet regions
of the electromagnetic spectrum. This energy comes from nuclear fusion of
hydrogen nuclei into helium in the core of the Sun.
• Nuclear fusion is a reaction in which two or more atomic nuclei are combined to
form one or more different atomic nuclei and subatomic particles. This releases
or absorbs energy depending on the mass difference between the reactants and
products.
• Nuclear fusion is the main source of energy for all stars, and it also produces
most of the elements in the universe. The Sun fuses about 500 million metric tons
of hydrogen each second.
• Nuclear fusion requires very high temperatures and pressures to overcome the
repulsion between positively charged nuclei. The Sun's core has a temperature of
about 15 million kelvin and a density of about 150 times that of water.
Page 93 of 99
Page | 8
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• Galaxies are huge collections of stars, gas and dust that are held together by
gravity. There are billions of galaxies in the universe, each with billions of stars.
Our Sun is one of the stars in the Milky Way galaxy, which is shaped like a spiral.
Page 94 of 99
Page | 9
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• The Sun is very far away from Earth, about 150 million kilometres. But other
stars in the Milky Way are much further away, some as far as 100,000 lightyears. A light-year is the distance that light travels in one year, which is about
9.5 trillion kilometres. That's a very long way!
• Stars are born from clouds of gas and dust in space, called nebulae.
• Gravity makes these clouds collapse and heat up, forming protostars. When
protostars get hot enough, they start to fuse hydrogen atoms into helium atoms,
releasing energy. This is called nuclear fusion and it makes stars shine.
• A protostar becomes a stable star when the inward force of gravity is balanced
by an outward force due to the high temperature in the centre of the star. This
is called hydrostatic equilibrium and it lasts for most of the star's life. The Sun
is a stable star right now.
• Stars have different life cycles depending on their mass. Low-mass stars like our
Sun live longer than high-mass stars because they use up their fuel more slowly.
Page 95 of 99
Page | 10
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
• When a star runs out of hydrogen in its core, it starts to fuse helium and other
heavier elements. This makes the star expand and cool down, becoming a red giant
or a red supergiant depending on its mass.
• A red giant from a low-mass star eventually sheds its outer layers, forming a
planetary nebula with a white dwarf star at its centre. A white dwarf is very hot
and dense, but it gradually cools down and fades away, becoming a black dwarf.
• A red supergiant from a high-mass star explodes as a supernova, forming a nebula
containing hydrogen and new heavier elements. The supernova also leaves behind a
very dense core that can become a neutron star or a black hole depending on its
mass.
• The nebula from a supernova may form new stars with orbiting planets. This is
how new generations of stars are born.
Page 96 of 99
Page | 11
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
The Milky Way is a huge collection of stars, gas and dust that forms a spiral
shape. It is one of many billions of galaxies in the Universe. A galaxy is a group
97 of 99 The diameter of the Milky Way is
of stars that are held togetherPage
by gravity.
Page | 12
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
about 100000 light-years, which means it would take light 100000 years to
travel from one end to the other.
•
Redshift is an effect that happens when light from a star or a galaxy is
stretched as it moves away from us. This makes the light appear more red than
it really is. The faster the star or galaxy is moving away, the more redshifted
its light is. We can measure the amount of redshift by comparing the
wavelengths of the light we receive with the wavelengths of the light we expect
from the star or galaxy.
•
Redshift in the light from distant galaxies is evidence that the Universe is
expanding. This means that all the galaxies are moving away from each other and
from us. The further away a galaxy is, the more redshifted its light is, and the
faster it is moving away. This suggests that all the galaxies were closer
together in the past, and that they started moving apart from a single point in
space.
Page 98 of 99
Page | 13
Senpaicorner.com
CIE IGCSE PHYSICS NOTES
•
The Big Bang Theory is a scientific model that explains how the Universe began
and evolved. It says that about 13.8 billion years ago, all the matter and energy
in the Universe was concentrated in a very small, hot and dense region. Then, a
huge explosion happened, which started the expansion of the Universe. As the
Universe expanded, it cooled down and formed stars, galaxies and other
structures.
•
Cosmic Microwave Background Radiation (CMBR) is a type of electromagnetic
radiation that fills all of space. It has a very low temperature of about -270°C.
It was produced shortly after the Big Bang, when the Universe was very hot and
filled with radiation. As the Universe expanded, this radiation stretched and
cooled down into microwaves. CMBR is evidence for the Big Bang Theory because
it shows that the Universe was once much hotter and denser than it is now.
•
The Hubble Constant (H0) is a number that tells us how fast the Universe is
expanding. It is equal to the ratio of the speed at which a galaxy is moving away
•
from us to its distance from us. The current estimate for H0 is 2.2 × 10–18 per
second, which means that for every megaparsec (a unit of distance equal to 3.26
million light-years) a galaxy is away from us, it moves away at a speed of 2.2
km/s.
The Hubble Constant can also be used to estimate the age of the Universe. If
we assume that the Universe has been expanding at a constant rate since the
Big Bang, then we can use this equation:
𝑑 1
=
𝑣 𝐻
where d is the distance of a far galaxy, v is its speed away from us, and H0 is
the Hubble Constant. This equation gives us an estimate for how long it took for
that galaxy to reach its current distance from us, which is also an estimate for
how long ago the Big Bang happened. This estimate is about 14 billion years,
which agrees with other evidence for the age of the Universe.
Page 99 of 99
Page | 14
Senpaicorner.com