Unit 12
12: Motion in a circle
A radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.
𝜋 rad = 180°
angular displacement Δ𝜃: the change in angle, in radians, of a body as it rotates around a circle.
distance travelled around the circle Δ𝑠
radius of the circle 𝑟
angular speed 𝜔: the rate of change in angular displacement with respect to time. This is a scalar quantity.
angular displacement Δ𝜃 =
𝜔=
Δ𝜃 2𝜋 (the angular displacement of a complete cycle)
=
= 2𝜋𝑓
Δ𝑡
𝑇 (the time period to complete a cycle)
𝑣 (constant linear speed of the uniform circular motion)
⇔ 𝑣 = 𝑟𝜔
𝑟
centripetal force: the resultant force towards the centre of the circle required to keep a body in uniform
circular motion. It is always directed towards the centre of the body’s rotation and perpendicular to the
linear velocity.
𝜔=
𝑣 𝑣 2 𝑟 2 𝜔2
=
=
= 𝑟𝜔2
𝑡
𝑟
𝑟
𝑚𝑣 2
𝐹 = 𝑚𝑎 =
= 𝑚𝑟𝜔2
𝑟
𝑎=
Ngô Phương Ngân
Unit 13
13: Gravitational fields
The force of gravity is an attractive force between any two objects due to their masses. The direction of the
gravitational field is always towards the centre of the mass. Gravitational forces cannot be repulsive.
gravitational field: a region of space where a mass experiences a force due to the gravitational attraction of
another mass
gravitational field strength at a point is the gravitational force exerted per unit mass on a small object
placed at that point
𝐹𝑔
𝑚
Newton’s law of gravitation states that any two point masses attract each other with a force that is directly
proportional to the product of their masses and inversely proportional to the square of their separation.
𝑔=
𝐺𝑚1 𝑚2
𝑟2
Circular orbits: The gravitational force of the planet on the satellite is the centripetal force that keeps the
satellite in its uniform circular orbit.
𝐹𝑔 =
𝑚𝑣 2 𝐺𝑀𝑚
𝐺𝑀
2𝜋𝑟 2 4𝜋 2 𝑟 2
4𝜋 2 𝑟 3
= 2 ⇔ 𝑣2 =
=(
) =
⇔
𝑟
𝑟
𝑟
𝑇
𝑇2
𝐺𝑀
All satellites, whatever their mass, will travel at the same speed 𝑣 and the same orbital period 𝑇 in a
particular orbit radius 𝑟.
𝐹𝑐 = 𝐹𝑔 ⇔
geostationary orbit: an orbit of a satellite such that the satellite remains directly above the same point of
the Earth at any time
The satellite remains directly above the equator and is in the plane of the equator.
The satellite always orbits at the same point above the Earth’s surface.
The satellite moves from west to east, which is the same direction as the Earth spins.
The satellite has an angular speed equal to that of the Earth.
The satellite has an orbital period of 24 hours, which is equal to the Earth’s rotational period.
𝐺𝑀𝑚
𝐹𝑔
𝐺𝑀
2
𝑔= = 𝑟
= 2
𝑚
𝑚
𝑟
gravitational potential at a point is the work done per unit mass in bringing a test mass from infinity to the
point
−𝐺𝑀
𝐺𝑀
×𝑟 =−
2
𝑟
𝑟
−𝐺𝑀 −𝐺𝑀
1 1
Δ𝜙 =
−
= 𝐺𝑀 ( − )
𝑟2
𝑟1
𝑟1 𝑟2
𝜙 = −𝐹𝑔 × 𝑟 =
gravitational potential energy of a mass at a point in a gravitational field is the work done in bringing the
mass from infinity to that point
𝐺𝑀𝑚
𝑟
−𝐺𝑀𝑚 −𝐺𝑀𝑚
1 1
Δ𝐸𝑃 =
−
= 𝐺𝑀𝑚 ( − )
𝑟2
𝑟1
𝑟1 𝑟2
𝐸𝑃 = 𝜙𝑚 = −
Ngô Phương Ngân
Unit 14
14: Temperature
thermal energy: the energy possessed by an object due to its temperature
thermal equilibrium: a condition when two or more objects have the same temperature so that there is no
net flow of energy between them
A thermometer is any device that is used to measure temperature
A thermodynamic scale of temperature (Kelvin) is a scale that does not depend on the property of any
particular substance. 2 fixed points
absolute zero (0 K): the lowest possible temperature on the thermodynamic temperature scale,
when it is impossible to remove any more energy from a matter
the triple point of water: where ice, liquid water, and water vapour can coexist: 273.16 K = 0.01℃
specific heat capacity: the heat required to raise the temperature per unit mass of a given substance per
unit change in temperature
specific heat capacity 𝑐 =
energy supplied 𝑄
⇔ 𝑄 = 𝑚𝑐Δ𝑇
mass 𝑚 × temperature change Δ𝑇
specific latent heat 𝐿: the energy required per unit mass of a substance to change its state without any
change in temperature
For melting and freezing: specific latent heat of fusion
For boiling and condensation: specific latent heat of vaporisation
𝑄 = 𝑚𝐿
Ngô Phương Ngân
Unit 15
15: Ideal gases
mass
amount of substance
The amount of matter, the resistance that a body
The number of constituent particles contained in a
offers to a change in its speed or position upon the
body, atoms, ions, or molecules
application of a force
Unit: mole
Unit: kilogram
1 mol of a substance has a mass of A g, where A is the atomic mass of that substance
The Avogadro constant 𝑁𝐴 is the number of particles in 1 mol of a substance
Boyle’s law: the pressure exerted by a fixed mass of gas is inversely proportional to its volume, provided the
temperature of the gas remains constant
𝑝∝
1
1
⇔ 𝑉 ∝ ⇔ 𝑝1 𝑉1 = 𝑝2 𝑉2
𝑉
𝑝
Charles’s law: the volume occupied by a gas at constant pressure is directly proportional to its
thermodynamic temperature
𝑉∝𝑇
Combining the two laws:
𝑉∝
𝑇
⇔ 𝑝𝑉 ∝ 𝑇
𝑝
𝑝𝑉 = 𝑛𝑅𝑇 = 𝑁𝑘𝑇
Boltzmann constant 𝑘 =
molar gas constant 𝑅
Avogadro constant 𝑁𝐴
The kinetic theory of gases models the thermodynamic behaviour of gases by linking the microscopic
properties of particles (mass and speed) to macroscopic properties of particles (pressure and volume). The
number of molecules of gas in a container is very large, therefore the average behaviour (e.g. speed) is
usually considered. Basic assumptions:
Molecules of gas behave as identical, hard, perfectly elastic spheres.
The volume of the molecules is negligible compared to the volume of the container.
The time of a collision is negligible compared to the time between collisions.
There are no intermolecular forces.
The molecules are in continuous random motion.
1
𝑝𝑉 = 𝑁𝑚⟨𝑐 2 ⟩
3
𝑐r.m.s. = √⟨𝑐 2 ⟩
The exact relationship between the mean speed and the root-mean-square speed depends on the
distribution of the speeds of the molecules. If all the molecules have the same speed then ⟨𝑐⟩ = 𝑐r.m.s.
The average velocity of all the molecules is zero since they are moving in all directions. We usually deal with
the kinetic energy of the molecules, which is proportional to the square of the velocity, which is why we use
the mean-square speed instead of squared mean speed.
1
1
3
𝑝𝑉 = 𝑁𝑚⟨𝑐 2 ⟩ = 𝑁𝑘𝑇 ⇔ 3𝑘𝑇 = 𝑚⟨𝑐 2 ⟩ ⇔ 𝐸𝐾 = 𝑚⟨𝑐 2 ⟩ = 𝑘𝑇
3
2
2
Ngô Phương Ngân
Unit 16
16: Thermodynamics
internal energy 𝑈: the sum of the random distribution of kinetic and potential energies associated with the
molecules of a system
kinetic energy: the energy which a body possesses by virtue of being in motion
potential energy: the energy possessed by a body by virtue of its position relative to others,
stressed within itself, electric charge, and other factors
Ideal gas molecules are assumed to have no intermolecular forces, which means that there is no potential
energy, only kinetic energy. Therefore the change in internal energy of an ideal gas is equal to the total
kinetic energy of the molecules of the gas.
3
Δ𝑈 = Δ𝐸𝐾 = 𝑘Δ𝑇 ⇒ Δ𝑈 ∝ Δ𝑇
2
Work done when the volume of a gas changes at constant pressure: 𝑊 = 𝑝Δ𝑉
Work done by the gas: 𝑊 = 𝑝(𝑉2 − 𝑉1 )
Work done on the gas: 𝑊 = 𝑝(𝑉1 − 𝑉2 )
First law of thermodynamics: increase in internal energy Δ𝑈 =
thermal energy transferred to the body 𝑄 + mechanical work done on the system 𝑊
Ngô Phương Ngân
Unit 17
17: Oscillations
simple harmonic motion: a body executes simple harmonic motion if its acceleration is directly proportional
to its displacement from its equilibrium position, and in the opposite direction to its displacement. 𝑎 ∝ −𝑥
𝑎 = −𝜔2 𝑥
If the object begins oscillating from its amplitude position then 𝑥 = 𝑥0 cos(𝜔𝑡) and 𝑣 = −𝑣0 sin(𝜔𝑡)
If the object begins oscillating from the equilibrium position then 𝑥 = 𝑥0 sin(𝜔𝑡) and 𝑣 = 𝑣0 cos(𝜔𝑡)
𝑣 = ±𝜔√𝑥02 − 𝑥 2 ⇒ 𝑣0 = ±𝜔𝑥0
Both the kinetic and potential energies of a system in SHM are represented by sinusoidal functions which
are varying in opposite directions to one another.
Ngô Phương Ngân
Unit 17
The total energy of a system undergoing SHM:
1
1
1
𝐸 = 𝐸𝐾 max = 𝑚𝑣02 = 𝑚(𝜔𝑥0 )2 = 𝑚𝜔2 𝑥02
2
2
2
damping: a damped oscillation is one in which resistive forces cause the energy of the system to be
transferred to the surroundings as internal energy
light damping: system oscillates about equilibrium position with decreasing amplitude over a
period of time
Ngô Phương Ngân
Unit 17
critical damping: the minimum damping that causes the oscillating system to return to its
equilibrium position in the minimum time and without oscillating. Any lighter damping will allow
the system to oscillate one or more times; any heavier damping will cause the system to take a
longer time to return to its equilibrium position.
heavy damping: damping is so great that the displaced object never oscillates but returns to its
equilibrium position very slowly
resonance: when a system oscillates with maximum amplitude by absorbing energy from a vibrating source.
It occurs when the frequency of the driving force is equal to the natural frequency of the oscillating system.
natural frequency 𝑓0: the frequency at which a body vibrates when there is no (resultant external) resistive
force acting on it
Ngô Phương Ngân
Unit 18
18: Electric fields
electric field: a force field or region in which an electric charged particle or object experiences a force
electric field strength at a point is the force per unit charge exerted on a stationary positive charge at that
point
𝐹𝐸 = 𝑞𝐸 ⇔ 𝐸 =
𝐹𝐸
𝑞
The electric field strength is a vector quantity, always directed away from a positive charge and towards a
negative charge. Opposite charges attract, negative charges repel.
Electric field strength of the uniform field between charged parallel plates:
electric field strength 𝐸 =
potential difference between the plates Δ𝑉
separation between the plates Δ𝑑
Coulomb’s law of electrostatics: any two point charges attract each other with a force that is directly
proportional to the product of their charges and inversely proportional to the square of their separation
𝐹𝐸 =
𝑄1 𝑄2
4𝜋ε0 𝑟 2
A positive force is a repulsive force, a negative force is an attractive force.
Electric field strength due to a point charge in free space:
𝐸=
𝑄
4𝜋𝜀0 𝑟 2
electric potential at a point is equal to the work done per unit positive charge in bringing a test charge from
infinity to that point
potential gradient: rate of change of electric potential with respect to displacement in the direction of the
field
Ngô Phương Ngân
Unit 18
Electric potential in the field due to a point charge
𝑉=
𝑄
4𝜋𝜀0 𝑟
For a positive charge: As the distance from the charge decreases, the potential increases as more
work has to be done on a positive test charge to overcome the repulsive force.
For a negative charge: As the distance from the charge decreases, the potential decreases as less
work has to be done on a positive test charge since the attractive force will make it easier.
Δ𝑉 =
𝑄 1 1
( − )
4𝜋𝜀0 𝑟1 𝑟2
electric potential energy at a point is the work done in bringing a charge from infinity to that point
𝑄𝑞
4𝜋𝜀0 𝑟
𝑄𝑞 1 1
Δ𝐸𝑃 =
( − )
4𝜋𝜀0 𝑟1 𝑟2
𝐸𝑃 = 𝑊 = 𝑉𝑞 =
Ngô Phương Ngân
Unit 19
19: Capacitance
capacitor: an electrical device used to store energy in electrical and electronic circuits, commonly for a
backup release of energy if the power fails
capacitance of a parallel-plate capacitor is the charge on the plates (one plate as the charges on both plates
are equal) of the capacitor per unit potential difference across the plates. Unit: Farad
𝑄
𝑉
In series:
𝐶=
Kirchhoff’s first law: 𝐼 = 𝐼1 = 𝐼2 ⇔ 𝑄 = 𝑄1 = 𝑄2
Kirchhoff’s second law: 𝑉 = 𝑉1 + 𝑉2
𝐶=
𝑄
𝑄
𝑄1 𝑄2 𝑄 𝑄
1
1
1
⇔ 𝑉 = = 𝑉1 + 𝑉2 =
+
= + ⇔ = +
𝑉
𝐶
𝐶1 𝐶2 𝐶1 𝐶2
𝐶 𝐶2 𝐶2
In parallel:
Kirchhoff’s first law: 𝐼 = 𝐼1 + 𝐼2 ⇔ 𝑄 = 𝑄1 + 𝑄2
Kirchhoff’s second law: 𝑉 = 𝑉1 = 𝑉2
𝑄
⇔ 𝑄 = 𝐶𝑉 = 𝑄1 + 𝑄2 = 𝐶1 𝑉1 + 𝐶2 𝑉2 = 𝐶1 𝑉 + 𝐶2 𝑉 ⇔ 𝐶 = 𝐶1 + 𝐶2
𝑉
The electric potential energy stored in a capacitor is the area under the potential-charge graph.
𝐶=
1
1
𝑊 = 𝑄𝑉 = 𝐶𝑉 2
2
2
1
time constant 𝜏 = 𝑅𝐶 is the time it takes for the current in the circuit to fall to 𝑒 of the initial current
1
𝑥 = 𝑥0 𝑒 −𝜏 , 𝑥 could represent current, charge, or potential difference for a capacitor discharging through a
resistor
Ngô Phương Ngân
Unit 20
20: Magnetic fields
magnetic field: a force field in which a magnet, a current-carrying conductor, or a moving charge
experiences a force.
Fleming’s left-hand rule
𝐹𝐵 = 𝐵𝐼𝐿 sin 𝜃 = 𝐵𝑄𝑣 sin 𝜃
magnetic flux density 𝐵: the force experienced by a current-carrying conductor in a magnetic field per unit
length, per unit current, when the current is perpendicular to the direction of the field. Unit: Tesla
Hall effect: the production of a potential difference across an electrical conductor when an external
magnetic field is applied in a direction perpendicular to the direction of the current
Hall voltage 𝑉𝐻 : the potential difference produced across the sides of a conductor when an external
magnetic field is applied perpendicular to the direction of the current
Ngô Phương Ngân
Unit 20
How a stable Hall voltage is developed in short: The magnetic force due to the magnetic field causes the
charge carriers to build up on one side of the Hall probe. As the charge carriers build up, they set up an
electric field that cause an electric force on the charge carriers in the opposite direction to the magnetic
force, so the two forces cancel out and no more charge carrier is attracted to that side. The Hall voltage is
between that side and the opposite side.
𝑉𝐻 =
𝐵𝐼
𝑛𝑡𝑞
Maxwell’s right-hand grip rule
magnetic flux Φ: the product of magnetic flux density normal to a circuit and the cross-sectional area of the
circuit. Unit: weber
Φ = 𝐵𝐴 sin 𝜃 with 𝜃 being the angle between the direction of the magnetic field and the frame of
the coil
Φ = 𝐵𝐴 cos 𝜙 with 𝜙 being the angle between the direction of the magnetic field and the direction
that the area is facing
magnetic flux linkage 𝑁Φ: the product of magnetic flux for a circuit and the number of turns. Unit: weber
Faraday’s law of electromagnetic induction: The magnitude of the induced e.m.f. is directly proportional to
the rate of change of magnetic flux linkage.
Lenz’s law: An induced e.m.f. is in a direction so as to produce effects that oppose the change producing it.
𝜀=−
Δ𝑁Φ
Δ𝑡
Ngô Phương Ngân
Unit 21
21: Alternating currents
𝑥 = 𝑥0 sin(𝜔𝑡) where 𝑥 can represents alternating current or voltage
𝑥0
𝑥r.m.s. =
√2
rectification: the process of converting alternating voltage into direct voltage
half-wave rectification
full-wave rectification
Ngô Phương Ngân
Unit 22
22: Quantum physics
photon: a quantum of electromagnetic radiation energy
Einstein relation: photon energy 𝐸 = Planck's constant ℎ × 𝑓 =
ℎ𝑐
𝜆
electronvolt eV: the energy gained by an electron travelling through a potential difference of 1 volt
𝐸
𝑐
photoelectric effect: an interaction between a photon and an electron in a metal, in which the electron is
removed from the surface of a metal
photon momentum 𝑝 =
threshold frequency 𝑓0: the minimum frequency of the incident electromagnetic radiation that would eject
electrons from the surface of a metal
threshold wavelength 𝜆0 : the longest wavelength of the incident electromagnetic radiation that would
eject electrons from the surface of a metal
work function energy 𝜙: the minimum photon energy needed by an electron to free itself from the surface
of a metal
1
2
Einstein’s photoelectric equation: photon energy ℎ𝑓 = work function 𝜙 + 𝐸𝐾 max 2 𝑚𝑣max
ℎ𝑓0 = 𝜙 ⇔ 𝑓0 =
𝜆0 =
𝜙
ℎ
ℎ𝑐
𝜙
The maximum kinetic energy of photoelectrons is independent of intensity, whereas the photoelectric
current is proportional to intensity.
photoelectric current: current due to photoelectrons
ℎ
de Broglie wavelength: the wavelength associated with a moving particle. 𝜆 = 𝑝
energy levels/states: a quantized energy state of an electron in an atom
emission line spectrum: a spectrum with bright-coloured lines of a unique wavelengths
absorption line spectrum: a spectrum with dark lines of a unique wavelengths seen against the background
of a continuous spectrum
ℎ𝑓 = 𝐸1 − 𝐸2
Ngô Phương Ngân
Unit 23
23: Nuclear physics
𝐸 = 𝑚𝑐 2
mass defect: the difference between the total mass of the individual separate nucleons and the mass of the
nucleus
Δ𝑚 = 𝑍𝑚𝑝 + (𝐴 − 𝑍)𝑚𝑛 − 𝑚nucleus
binding energy: the minimum external energy required to completely separate all the nucleons (neutrons
and protons) of a nucleus to infinity. 𝐸 = 𝑐 2 Δ𝑚
nuclear fusion: the process in which two light nuclei join together to form a heavier nucleus
nuclear fission: the process in which a massive nucleus splits into two smaller nuclei
In both of these processes, the products will be more stable than the starting nuclei, which means the
binding energy per nucleon is higher.
count rate: the number of particles (alpha or beta) or gamma-ray photons detected per unit time by a
Geiger-Muller tube. Count rate is always a fraction of the activity of a sample.
activity 𝐴: the rate of decay of nuclei of a radioactive source. Unit: Becquerel
Δ𝑁
= −𝜆𝑁
Δ𝑡
decay constant 𝜆: the probability that an individual nucleus will decay per unit time interval
𝐴=
Δ𝑁
𝐴
=
𝑁Δ𝑡 𝑁
half-life 𝑡1 of an isotope is the mean time taken for half of the active nuclei in the sample to decay
𝜆=
2
ln 2
𝜆=
𝑡1
2
𝑥 = 𝑥0 𝑒 −𝜆𝑡 , 𝑥 could represent activity, number of undecayed nuclei, or received count rate
Ngô Phương Ngân
Unit 24
24: Medical physics
Ultrasound
piezo-electric crystal: a material that produces an e.m.f. when it is stressed, causing its chape to change.
Also, when a voltage is applied across it in one direction, it changes its dimensions slightly.
piezo-electric effect: the production of an e.m.f. across a crystal by putting the crytal under stress. The
opposite effect is applying a p.d. across the crystal causing it to change shape.
An ultrasound transducer converts electrical energy into mechanical (sound) energy and back again, based
on the piezo-electric effect. Therefore, it can act as both a receiver or transmitter of ultrasound.
generation of ultrasound
detection of ultrasound
An alternating p.d. is applied across a piezo-electric
crystal, causing it to change shape.
When the ultrasound wave returns, the crystal
The alternating p.d. causes the crystal to vibrate and vibrates which produces an alternating p.d. across
produce ultrasound waves.
itself.
The crystal vibrates at the frequency of the
This received signal can then be processed and used
alternating p.d., so the crystal must be cut to a
for medical diagnosis.
specific size in order to produce resonance.
specific acoustic impedance: the resistance to the propagation of ultrasound waves through tissues; how
difficult it is for an acoustic wave to travel through the medium
specific acoustic impedance 𝑍 = density of material 𝜌 × speed of sound in the medium 𝑐
Two materials with the same acoustic impedance would give no reflection. Two materials with a large
difference in values would give large reflections.
impedance matching: the use of a gel to reduce the intensity of unwanted, reflected ultrasound between
skin and air. The gel has a similar acoustic impedance to the skin.
intensity reflection coefficient of a boundary between two media
𝐼𝑅 (𝑍1 − 𝑍2 )2
=
𝐼0 (𝑍1 + 𝑍2 )2
X-rays
attenuation: the gradual decrease of intensity of radiation as it passes through a medium
𝐼 = 𝐼0 𝑒 −𝜇𝑥 , applies for both ultrasound and X-ray
In practice, absorption is not a serious problem in an ultrasound scan as scanning relies on the reflection of
ultrasound at the boundaries between different tissues.
attenuation/absorption coefficient 𝜇: a constant that depends on the material and the frequency of the Xrays
computerised axial tomography (CAT or CT): a technique in which X-rays are used to image the body in
order to produce a 3D image
How CT works in short: X-rays are ejected at different angles around the body to produce 2D images of
layers of the body, then the 2D images are combined to produce a 3D image
PET (Positron Emission Tomography)
radioactive tracer: a substance containing radioactive nuclei that is introduced to the body and can be
absorbed by tissue in order to study the structure and functions of organs in the body. These usually are
able to bind to organic molecules (e.g. glucose, water) and have short half-life. They will undergo 𝛽 + decay.
The radioactive tracer is injected or swallowed into the body. Once the tissues and organs have absorbed
the tracer, they appear on the screen as a bright area for a diagnosis.
Ngô Phương Ngân
Unit 24
When a positron is emitted from the tracer, it travels until colliding with an electron. The positron and the
electron will annihilate and their mass becomes pure energy in the form of two gamma rays moving in
opposite directions. Their mass-energy and momentum are conserved in the process.
annihilation: When a particle meets its equivalent anti-particle, they are both destroyed and their mass is
converted into energy.
The pairs of gamma rays emitted will hit the detectors in straight lines called lines of response. Information
about different lines of response can be combined to determine the position where annihilation occurs and
an image of the tracer concentration in the tissue can be created by processing the arrival times of the
gamma-ray photons.
Ngô Phương Ngân
Unit 25
25: Astronomy and Cosmology
luminosity: the total radiant power emitted from a star. Unit: Watts
radiant flux density: the radiant power passing normally through a surface per unit area
𝐿
4𝜋𝑑2
standard candle: an astronomical object of known luminosity
𝐹=
Wien’s displacement law: the black body radiation curve for different temperatures peaks at a wavelength
which is inversely proportional to the temperature
black body: an idealised object that absorbs all incident electromagnetic radiation falling on it. It has a
characteristic emission spectrum and intensity that depends only on its thermodynamic temperature
𝜆max ∝
1
𝑇
Stefan–Boltzmann law: The total energy emitted by a black body per unit area per unit time is proportional
to the fourth power of the thermodynamic temperature of the body. 𝐿 = 4𝜋𝜎𝑟 2 𝑇 4
redshift: a term used to describe the increase in the observed wavelength of the electromagnetic waves
due to recession of the source. For non-relativist galaxies, Doppler redshift can be calculated using:
Δ𝜆 Δ𝑓 𝑣
≈
≈
𝜆
𝑓
𝑐
As an astronomical object appears redder, it means that the observed wavelength has increased, therefore
the object has undergone redshift, which means that the objects in the Universe are receding. This leads to
the idea that the space between the Earth and the galaxies must be expanding. If the galaxies are moving
away from each other, then they must’ve started from the same point at some time in the past. If this is
true, the universe likely began in an extremely hot, dense singular point which subsequently began to
expand very quickly. This idea is known as the Big Bang theory.
Hubble’s law: the recession speed of a galaxy is directly proportional to its distance from us
Big Bang theory: a model of the creation of the Universe from an extremely hot and dense state and its
subsequent evolution
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