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Physics A Level

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PHYSICS A-LEVEL
AUTHOR: KG/ ARCTIC KITTEN
For Edexcel Physics
2018
CONTENTS
Topic 2: Mechanics .............................................................................................................................................................................. 2
Topic 3: Electric Circuit ........................................................................................................................................................................ 4
Topic 4: Materials ................................................................................................................................................................................ 7
Topic 5: Waves and Particle nature of light ....................................................................................................................................... 10
Topic 6: Further Mechanics ............................................................................................................................................................... 16
Topic 7: Electric and Magnetic Field .................................................................................................................................................. 17
Topic 8: Nuclear and particles Physics .............................................................................................................................................. 22
Topic 9: Thermodynamics ................................................................................................................................................................. 27
Topic 10: Space ................................................................................................................................................................................. 29
Topic 11: Nuclear Radiation .............................................................................................................................................................. 33
Topic 12: Gravitation ......................................................................................................................................................................... 35
Topic 13: Oscillation .......................................................................................................................................................................... 37
TOPIC 2: MECHANICS
Name
Definition
Formulae
STATIC
Centre of mass
Centre of gravity
The point from which all the mass of the object appears to act
The point from which all the weight of the object appears to act
KINEMATICS
1
𝑠 = 𝑒𝑑 + π‘Žπ‘‘ 2
2
𝑣 = 𝑒 + π‘Žπ‘‘
Suvat equations
𝑣 2 = 𝑒2 + 2π‘Žπ‘ 
(𝑒 + 𝑣)𝑑
2
NEWTON’S LAWS
𝑠=
Newton’s First Law
Newton’s Second
Law
An object will remain at rest, or in a state of uniform motion in a straight line,
unless acted upon by a resultant force
The resultant force is directly proportional to the rate of change of
momentum and in the same direction of the momentum
To every action, there’s an equal and opposite reaction
Newton’s Third Law
ο‚©
ο‚©
ο‚©
ο‚©
Act on different bodies
Opposite direction
Same magnitude
Same kind
MOMENT
Moments
The force multiplied by the perpendicular distance from the pivot to the line
of action of the force
Law of moments
For any object in equilibrium the sum of the clockwise moments about any
point is equal to the sum of the anticlockwise moment about the same point
𝑀 = 𝐹𝑑
Unit: Nm
WORK DONE, ENERGY & POWER
The product of:
Work Done
F (magnitude of the force)
π‘Š = 𝐹𝑠 π‘π‘œπ‘  πœƒ
s (magnitude of displacement s of point of application of force)
Unit: 𝐽 = π‘π‘š
cos  ( is the angle between the force and displacement vector)
Energy
Kinetic energy
The property of object that gives it the ability to do work
The work done to accelerate an object of mass m, from rest to a speed v
βˆ†πΈπ‘˜ = πΈπ‘˜′ − πΈπ‘˜ = π‘Šπ·
Potential energy
The ability of an object to do work by virtue of its position or state
Gravitational
potential energy
The energy an object has due to its position in a gravitational field
1
πΈπ‘˜ = π‘šπ‘£ 2
2
𝑝2
=
2π‘š
𝐸𝑝 = π‘šπ‘”β„Ž
The rate of doing work with respect to time
Power
Unit: π‘Š =
𝐽
𝑠
𝑃=
βˆ†π‘Š
βˆ†π‘‘
1 watt is 1 J of E transferred in 1 sec
Efficiency
𝑒𝑓𝑓 =
π‘ˆπ‘ π‘’π‘“π‘’π‘™ 𝐸 π‘œπ‘’π‘‘π‘π‘’π‘‘
π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐸 𝑖𝑛𝑝𝑒𝑑
END
𝑃 = 𝐹𝑣 π‘π‘œπ‘  πœƒ
TOPIC 3: ELECTRIC CIRCUIT
Name
Definition
Formulae
ELECTRICITY
Electron-volt
Energy transferred when an electron moves through a potential
difference of one volt
Drift velocities
Motion of electron in
a wire
Current
𝑛: π‘β„Žπ‘Žπ‘Ÿπ‘”π‘’ π‘π‘Žπ‘Ÿπ‘Ÿπ‘–π‘’π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦
Different metals have different conductivity because different n
emf
π‘£π‘Ÿπ‘Žπ‘›π‘‘π‘œπ‘š
= 106 π‘š⁄𝑠
π‘£π‘‘π‘Ÿπ‘–π‘“π‘‘
= 10−4 π‘šπ‘š⁄𝑠
The rate of flow of charged particle
Potential difference
1𝑒𝑉
= 1.6 × 10−19 𝐽
The energy/charge transferred between two point
WD per unit charge to move a charge around the circuit
Emf = pd when 𝐼 = 0 because no energy/ pd lost on resistors
𝐼=
βˆ†π‘„
βˆ†π‘‘
𝐼 = π‘›π‘’π‘£π‘‘π‘Ÿπ‘–π‘“π‘‘ 𝐴
𝑉=
π‘Š
𝑄
πœ€ = 𝑉 + πΌπ‘Ÿ
Plot V (across battery) against I
Gradient = -r
Y intercept is emf
Resistance
The opposition to the flow of electrical current
Ohm’s Law
A special case where 𝐼 ∝ 𝑉 for constant temperature
𝑅=
𝑉
𝐼
Total resistance
Resistivity
Power
Critical temperature
Numerically equal to the resistant of a unit length and a unit area of wire
𝑉2
𝑅
The temperature below which its resistivity instantly drop to zero
𝑃 = 𝐼𝑉 = 𝐼 2 𝑅 =
πœŒπ‘™
𝐴
Unit: π›Ίπ‘š
𝑅=
CURRENT-POTENTIAL GRAPH
Ohmic conductors
Filament bulb
Diodes
Thermistor
LDR
Require a minimum driving V in
the forward direction
Temperature , more energy
transfer to lattice ions
Electrons gain energy from light
Forward direction: low R
 current flow, Temperature 
Obeying Ohm’s Law
Ions vibrates more, probability
of collision , electron lose
more energy
Threshold voltage 0.6V
Electrons to conduction band
Backward direction: high R
𝐼 = π‘›π‘žπ‘£π΄  so resistance 
Few charge carriers ο‚Ž leakage
charge carriers density ,
current 
Reverse pd high enough
overcome E barrier
𝑉 = 𝐼𝑅 resistance 
Light intensity , electrons to
conduction band
Charge carriers density , current 
𝑉 = 𝐼𝑅 resistance 
END
TOPIC 4: MATERIALS
Name
Definition
Formulae
LIQUIDS
𝑑𝑖𝑠𝑝
Upthrust
Terminal
velocity
The upthrust on an object in a fluid =the weight of the fluid displaced by the
object
Upthrust + drag = weight
No resultant force so velocity is constant
π‘ˆ = π‘šπ‘“
𝑔
𝑑𝑖𝑠𝑝
π‘ˆ = πœŒπ‘“ 𝑉𝑓
𝑔
π‘ˆ+𝐷 =π‘Š
Falling object:
At first, 𝐷 = 0
𝐷 ∝ 𝑣 so drag force increases
π‘Š − π‘ˆ − 𝐷 = 𝐹 so resultant force decreases
When 𝐷 + π‘ˆ = π‘Š no resultant forces so N1L terminal velocity
Fluid
Streamline
Path line
Steady flow
Substance that can flow
A curve whose tangent at any point is along the direction of the velocity of the
fluid particle at that point
The path taken by a fluid particle as it moves
Occurs when no aspect of the fluid motion change with time
Fluid move with uniform lines in which velocity is constant over time
Laminar flow
•
•
•
No mixing of layers
Flows in layers/flowlines/streamlines
No abrupt change in direction or speed of flow
Mixing of layers
Turbulent flow
Contains eddies/vortices
Abrupt/random changes in speed or direction
For a spherical object of rad r
Stokes’ Law
Moving slowly through a fluid with speed v
𝐹𝑑 = 6πœ‹ο¨ π‘Ÿπ‘£
The flow of fluid is laminar
The thickness of a fluid. Viscosity increase, rate of flow decrease (spread
quicker)
Viscosity
Liquids,   with temperature

Gasses,  
Drag for
turbulent flow
Hysteresis
𝐢𝑑 :drag coef, no unit
A: area of object facing fluid flow
1
𝐹𝑑 = 𝐢𝑑 π΄πœŒπ‘£ 2
2
The extension under a certain load will be different depending on its history of
past load and extension
HOOKE’S LAW
Hooke’s Law
The extension, e, is directly proportional to the applied force, if the limit of
proportionality is not exceeded
k: the stiffness of the spring/ the spring constant
𝐹 = π‘˜π‘’
Outside the region that obeys Hooke’s law:
Extension not proportional to force (greater extension for same force)
Deform plastically, not return to original shape
Elastic’s
Potential Energy
The ability of a deformed material to do work as it regains its original length
Area under a force-extension graph
1
π‘Š = 𝐹𝑒
2
1
π‘Š = π‘˜π‘’ 2
2
YOUNG MODULUS
Stress
The force per unit cross-sectional area perpendicular to the surface
Strain
Fractional change in length of the material
The stress per unit strain
Using thin long wire to measure Young modulus:
Young’s
Modulus
Small extension is hard to measure and has high uncertainty
𝐹
𝐴
Thin wire has smaller A hence larger P for a given F
𝑃=
Long wire: greater extension for a given stress
𝐹
𝐴
𝑒
πœ–=
𝐿
𝜎
𝐸=
πœ–
𝜎=
Name
Definition
Note
GRAPH
P/ Limit of
The maximum extension that an object can
proportionality exhibit, which still obeys Hooke’s Law
The maximum extension or compression
that a material can undergo and still return
E/ Elastic limits
to its original dimension when the force is
removed
Y/ Yield point
The point after which a small increase in
stress produces an appreciably greater
increase in strain.
UTS/ Ultimate
Tensile Stress
The maximum tensile stress the material can
withstand before breaking
PEYU
If the mass exceeds maximum mass
State
maximum load
The elastic limit is exceeded
Spring deform permanently
Spring constant change
PROPERTIES OF MATERIALS
Strength
The maximum compressive stress applied before breaking
Strong/ Weak
Strong: High breaking stress (steel)
Weak: Low breaking stress
Stiff/ Flexible
Stiff: High Young’s Modulus, large stress for
small deformation
Flexible: Low Young’s Modulus
Tough/ Brittle
Tough: large plastic deformation region on
graphabsorb lots of energy
Brittle: little plastic deformation before breaking
οƒ°absorb little energy
Elastic/ Plastic
Elastic: Regain their original shape when
deforming force/stress is removed
Plastic: Extend extensively and irreversibility for a
small increase in stress beyond the yield point
(copper, clay)
Hardness
Resistance to scratch on surface
Hard/ Soft
Hard: Not easy to scratch or indent
Soft: Easy to scratch or indent
Ductile/
Malleable
Ductile: Undergo large plastic deformation
under tension and hence can be made/
drawn into wires
Malleable: Undergo large plastic deformation under
compression and hence can be hammered into thin
sheets
END
TOPIC 5: WAVES AND PARTICLE NATURE OF LIGHT
Name
Definition
Note
BASICS OF WAVE
Mechanical wave
Wave require medium to travel through
Electromagnetic
wave
Require no medium to travel through
Longitudinal
Waves
Compression
Rarefaction
Has oscillations that are parallel to the
direction of movement of the wave energy
(Vibrations of the particles parallel to the
direction of propagation of the wave)
Area in which particle oscillation put them
closer than their equilibrium state
Area in which the particle oscillation put
them further apart than their eq state
Transverse wave
The oscillations are perpendicular to the
direction of movement of the wave energy
Displacement
Distance and direction from the equilibrium
position
Amplitude
The magnitude of maximum displacement
from the equilibrium position
Frequency
The number of complete oscillations per unit
time
Period
The time taken for one complete oscillation
𝑣=
Speed
Wavelength

= 𝑓
𝑇
𝑇
𝑣 = √ (π‘‘π‘Ÿπ‘Žπ‘›π‘ π‘£π‘’π‘Ÿπ‘ π‘’)
πœ‡
Minimum distance between two point on a
wave with the same displacement
STANDING/ STATIONARY WAVES
No net transfer of energy
Standing wave
Nodes
Antinodes
2𝑙
𝑛
Points where the amplitude of oscillation is 0
=
Points where amplitude of oscillation is
maximum
Two waves with same amplitude and
wavelength travelling at opposite direction/
Producing standing reflected off
wave
Principle of superposition give resultant
displacement
Nodes and antinodes produced
Snapshot of the wave
Constructive interference occurs when phase
difference = 0
Destructive interference occur when phase
difference = πœ‹
𝑇
2𝑙
𝑣 = √ ; 𝑣 = 𝑓;  =
πœ‡
𝑛
Harmonics
∴𝑓=
Name
𝑛
𝑇
×√
2𝑙
πœ‡
Definition
Note
PHASE
Phase of
oscillation
The stage of a given point on a wave is
through a complete cycle
Phase
difference
The difference in phase angle between two
parts of the same oscillation or between two
oscillation
In phase
Antiphase
Phase difference = π‘›πœ‹, n even
Path difference = 𝑛
Phase difference = π‘›πœ‹, n odd
Path difference= 𝑛/2
Wave front
The line of a crest or trough of a transverse
wave/ compression of rarefaction of
longitudinal wave
Coherence
Waves with same frequency and constant
phase difference
πœ‹
OP: 2πœ‹ − 2 =
OO’:
3πœ‹
2
OQ: πœ‹
3πœ‹
2
πœ‹
2
πœ‹
πœ‹
− =
2
2
− = πœ‹
Monochromatic Same frequencies
Interference
The superposition outcomes of a combination
of waves
Constructive
Interference
Take place when the path difference is a
whole number of wavelength
Destructive
Interference
Path difference is 1/2, 3/2, 5/2… wavelength
Produce interference:
Superposition takes place
Path difference = π‘›πœ† in phase
In phase: constructive interference
Antiphase: destructive interference
Antiphase amplitude = minimum = 0
Fringes
Principle of
superposition
Pattern of light and dark band
When two or more waves meet, the total displacement at any point is the sum of the
displacements that each individual wave cause at that point
Polarisation
Orientation of the plane of oscillation of a transverse wave
Polarised waves
Oscillations occurs in only one plane or directions perpendicular to the direction of propagation of
the wave
Reflected light/ incident light is polarised
Polarised light vibrates in one direction
Polaroid only allow oscillation in one plane
Polaroid
When planes are parallel it allows plane through, the intensity is high
Perpendicular block the light, intensity = 0
Each rotation by πœ‹ will alternatively block and allow the light through
Name
Definition
LENS
Focal length
Focus
The distance from the centre of the length to the focal point
The point where parallel incident rays be made to meet by the refraction of the lens
1 1 1
= +
𝑓 𝑒 𝑣
Thin lens equation
π‘š=
Magnification
𝑃=
Power
Combination
Convex lens
β„Ž1 𝑣
=
β„Ž0 𝑒
1
𝑓
𝑃 = 𝑃1 + 𝑃2
Cause light to converge, f is positive
Converge parallel rays to a focus at the focal length from the lens
Cause light to diverge, f is negative
Concave lens
Images
Name
Diverge parallel rays to appear to have come from a virtual focus at the focal length
back from the lens
𝑣 > 0: real, inverted
𝑣 < 0: virtual, upright
Definition
Formulae
Note
REFRACTION – TOTAL INTERNAL REFLECTION
Refraction
The change in direction of a
wave occurs when its speed
change due to a change of
medium
Refractive
index
Relative
refractive
index
𝑐
𝑣
𝑣1
πœ‡12 =
𝑣2
1
πœ‡12 =
πœ‡21
πœ‡=
Wave travelling from medium
1 to medium 2
If πœ‡2 > πœ‡1 Then material 2 is optically denser
than material 1.
Absolute
refractive
index
𝑐
≥1
𝑣1
πœ‡2
πœ‡12 =
πœ‡1
πœ‡1 =
Light travelling in medium 1
𝑣2 < πœ‡1
πœƒ2 < πœƒ1
πœ‡1 sin πœƒ1
= πœ‡2 sin πœƒ2
Snell’s law
Reflection
The change in direction of a
wave at an interface between
two different media so that
the wave returns into the
medium from which it
originated
Critical angle
The angle of incidence for
which the angle of refraction
is 900
Total
Internal
Reflection
(TIR)
When the angle of incidence
is bigger than critical angle →
light does not refract but
bounces back at the interface
1
= sin 𝐢
πœ‡1
1
𝐢 = sin−1
πœ‡1
DIFFRACTION
Diffraction
The spread out of the wave
when it meets a solid
obstacle
For most of the light waves
there is destructive
interference
Diffraction
gratings
Path difference = 𝑑 sin πœƒ
Constructive interference →
𝑛
𝑑 sin πœƒ = 𝑛
𝑑
=
1
π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ 𝑙𝑖𝑛𝑒
𝑛: π‘œπ‘Ÿπ‘‘π‘’π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ
π‘›π‘šπ‘Žπ‘₯ ≤
Name
𝑑

Definition
Notes
WAVE THEORY
Young’s double slit
experiment
Monochromatic coherent light passes through two parallel slits
Light behaves light a wave
The waves through the slits diffract, two diffracted waves overlaps
Principle of superposition determines the resultant wave displacement at any point
Constructive interference where in phase ο‚Ž bright fringe
Destructive interference where out of phase ο‚Ž dark fringe
The size of wavelength of photon is similar to the size of the slit
PHOTOELECTRIC EFFECT
Photon
Photoelectron
Experiment
Results
Packet of electromagnetic radiation
Electron released from a metal surface as a result of
its exposure to electromagnetic radiation
Shine light on a metal surface, electron might be
emitted
Increase frequency
Increase amplitude
𝑓 < 𝑓0
No electron emitted
Nothing happen
𝑓 > 𝑓0
Max KE of electron increase as
frequency 
Number of electron emitted/ s ,
max KE does not change
Photon cause emission of electron from surface of
metal
Photon has energy 𝐸 = β„Žπ‘“
1
β„Žπ‘“ = πœ™ + π‘šπ‘£π‘šπ‘Žπ‘₯ 2
2
One photon hit one electron
Explanation
If 𝐸 > πœ™ emission occurs
1
π‘šπ‘£ 2
2
is KE of electron emitted
Max because some energy lost to get to the metal
surfaces
Threshold frequencies
Work function
Minimum frequency that can cause electron
emission
If 𝑓 < 𝑓0 no e- are emitted
If 𝑓 ≥ 𝑓0 e- are emitted
Minimum energy needed to remove an electron
from the metal surface
The energy in waves theory depend only on amplitude not frequency
Wave theory not explain
photoelectric effect
Increasing light intensity should increase maximum KE, max KE not depend of frequency
Predict a delay between shining the light and emission of electron
Cannot account for a threshold frequency of the metal/ emission occurs at all
frequencies
Increase the light intensity increase number of electron emitted/s
Particle theory explain
One photon release one electron
Energy of photon depend on frequency not intensity 𝐸 = β„Žπ‘“
Intensity determines number of electrons
Wave-particle duality
Quantum object sometimes have wave like properties & sometime have particle like
properties depend on the experiment done on them
ENERGY LEVELS/ QUANTISATION OF ENERGY
Electron gains energy (become excite) and move to
higher levels
Line spectrum/ Photon
emission
Electron has fixed energy level
Electrons fall to lower level, reduce energy by
emitting photons
Energy lost:
𝑬 = 𝒉𝒇
Photon has specific energy hence form line
spectrum
Ground state
The lowest energy level for a system
Excitation
The energy state that is higher energy than the
ground state
Energy level
A specific quantity of energy an electron can/ is
allowed to have inside an atom
De Broglie wavelength
The wavelength associated with a particle with a
given momentum
END
=
β„Ž
β„Ž
=
𝑝 π‘šπ‘£
TOPIC 6: FURTHER MECHANICS
Name
Definition
Formulae
MOMENTUM
𝑝 = π‘šπ‘£
Momentum
Impulse
Change in momentum
𝐼 = πΉβˆ†π‘‘ = βˆ†π‘
𝑑
(𝑝
)
𝑑𝑑 π‘‘π‘œπ‘‘π‘Žπ‘™
𝑑
πΉπ‘Ÿπ‘’π‘ π‘’π‘™π‘‘π‘Žπ‘›π‘‘ =
(π‘šπ‘£)
𝑑𝑑
𝑑𝑣
πΉπ‘Ÿπ‘’π‘ π‘’π‘™π‘‘π‘Žπ‘›π‘‘ = π‘š
= π‘šπ‘Ž
𝑑𝑑
π‘‘π‘š
πΉπ‘Ÿπ‘’π‘ π‘’π‘™π‘‘π‘Žπ‘›π‘‘ = 𝑣
𝑑𝑑
𝑑𝑣
π‘‘π‘š
πΉπ‘Ÿπ‘’π‘ π‘’π‘™π‘‘π‘Žπ‘›π‘‘ = π‘š
+𝑣
𝑑𝑑
𝑑𝑑
π‘π‘Ÿπ‘’π‘ π‘’π‘™π‘‘π‘Žπ‘›π‘‘ = 0
πΉπ‘Ÿπ‘’π‘ π‘’π‘™π‘‘π‘Žπ‘›π‘‘ =
If π‘š = π‘π‘œπ‘›π‘ π‘‘
Newton’s second Law
If π‘š ≠ π‘π‘œπ‘›π‘ π‘‘, 𝑣 = π‘π‘œπ‘›π‘ π‘‘
If π‘š ≠ π‘π‘œπ‘›π‘ π‘‘, 𝑣 ≠ π‘π‘œπ‘›π‘ π‘‘
If πΈπ‘Ÿ = 0
Conservation of
momentum
The total momentum before a collision is the same as total
momentum after collision
(provided that there is no external force acting on the
system)
Elastic collision
KE is conserved (e.g. Identical masses move apart at 90O)
Inelastic collision
KE is not conserved (e.g. explosions, stick after collision)
π‘π‘–π‘›π‘–π‘‘π‘–π‘Žπ‘™ = π‘π‘“π‘–π‘›π‘Žπ‘™
CIRCULAR MOTION
Angular velocity
Centripetal
acceleration
Centripetal force
A resultant force is required to produce and maintain
circular motion
No reaction forces
Weightlessness
For astronauts on ISS, gravitational force = centripetal force,
hence no reaction force
END
𝑣 = πœ”π‘Ÿ
2πœ‹
πœ”=
𝑇
2
𝑣
π‘Ž=
= πœ”2 π‘Ÿ
π‘Ÿ
π‘šπ‘£ 2
𝐹 = π‘šπ‘Ž =
= π‘šπœ”2 π‘Ÿ
π‘Ÿ
TOPIC 7: ELECTRIC AND MAGNETIC FIELD
Name
Definition
Formulae
Notes
ELECTROSTATICS
Radial field
π‘˜π‘„π‘ž
π‘Ÿ2
1
π‘˜=
4πœ‹πœ€0
= 8.9 × 109
𝐹=
Coulomb’s Law
Forces between two charges obey an
inverse
Electric field
A region where a charged particle
experience a force
Electric field
strength
The force per unit charge acting on a
small positive charge
𝐸=
The work done against the electric
field in moving the charge from infinity
to that point in the field
𝐸𝑃𝐸 =
Electrical
Potential
Energy
Electrical
Potential
𝑃 𝐸
=
𝐼 𝑄
𝑄
𝐸𝐴 =
πœ€0
𝑉=
𝐹 π‘˜π‘„
= 2
π‘ž
π‘Ÿ
𝑉=
π‘˜π‘„π‘ž
π‘Ÿ
π‘˜π‘„
π‘Ÿ
CAPACITOR
Field strength are equal at all point
Uniform field
Arrows show the direction of a small (+) charges will
move when placed in the electric field
Equipotential
surface
The plates, always perpendicular to the electric field line
Electric field
strength
d: distance from positive plate
Capacitance
Charge stored per unit p.d.
Capacitor
A device for storing charges
𝑉
𝑑
𝑄
𝐢=
𝑉
π΄πœ€0 πœ€π‘Ÿ
=
𝑑
𝐸=
πœ€π‘Ÿ : relative permittivity
For air, πœ€π‘Ÿ = 1
Energy stored
by a capacitor
Time constant
Charging
1
π‘Š = 𝑄𝑉
2
1 2
= 𝐢𝑉
2
𝑄2
=
2𝐢
The area under the graph (triangle)
1
π‘Š = 𝑄𝑉 = π‘„π‘‰π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’
2
Time taken for the charge to fall to
0.37 of its initial value
RC
Shape of graph (current) exponential decay, current decrease by
equal fraction in equal time interval
The cell pushes charges through the circuit
A current flows, charges are added to the || until 𝐼 = 0
𝐼 = 𝐼0 𝑒
𝑉𝑐 increases, 𝑉𝑅 decreases, 𝐼 decrease
𝑄
πœ€ = 𝐼𝑅 +
𝐢
−𝑑⁄
𝑅𝐢
𝑙𝑛𝐼 = 𝑙𝑛𝐼0 −
𝑑
𝑅𝐢
Discharging
Capacitor pushes charges (opposite direction) through the resistor
from negative plate to positive plate
A current flow, charges are removed exponentially till 0
Changing AC
to DC
Smoothed DC, Exponential decay
Rectified circuit
Capacitor store charges
Current change direction
If RC > T of AC, the capacitor
(Charge battery: without
Normal circuit
doesn’t fully discharge before
being charged
diode charges and discharge)
π΄πœ€0
𝑑
So as d , C, Q, I
𝐢=
Microphone
condenser
1
𝑓
If 𝑅𝐢 < , I vary with frequency f
Root mean
square
Irms is equal to the direct current
that give the same average power
output
π‘½π’“π’Žπ’” =
π‘°π’“π’Žπ’” =
Μ… = π‘°πŸπ’“π’Žπ’” 𝑹
𝑷
Name
Definition
π‘½πŸŽ
√𝟐
π‘°πŸŽ
√𝟐
Formulae
Note
FLUX
𝐹
𝐼𝐿
The force per unit length per unit
current on a long straight wire
perpendicular to the magnetic field
lines
√πœ€0 𝐼0
Flux
The B*(the area perpendicular to the
field lines)
πœ™
= 𝐡𝐴 cos πœƒ
Unit: Wb
Flux linkage
For a coil of N turn
Φ = π‘πœ™
Unit: Wb or Wb turn
Magnetic
flux density
𝐡=
1
=𝑐
MAGNETIC FIELD
Magnetic
field
The direction of magnetic field is the
direction North pole of compass will
point if placed in the field
A moving charge create a magnetic
field
Field line are concentric circles
The magnetic field gets weaker as the
distance from the wire increase
Magnetic
field around
a wire
Right-hand grip rule tells the direction
of the field
All magnetic field are closed loops
All magnetic field are created by a
moving electrical charge
Fleming’s left-hand rule give direction
Two parallel wires carry current in the
same direction attracts
CURRENT CARRYING CONDUCTOR
𝐹
= 𝐡𝐼𝑙 sin πœƒ
Equation
The coil will rotate
Speed of the motor depend on B, I, N,
Area of the coil
The dynamo
effect
The commutator ensures that the
current always flow in the same
direction around the loop so the loop
rotate in the same direction.
Magnetic flux goes from 0 to a
maximum
An alternating emf is produced
CHARGED PARTICLE BEAMS
Equation
F perpendicular to v, v is constant
hence centripetal force
𝐹
= π΅π‘žπ‘£ sin πœƒ
ELECTROMAGNETIC INDUCTION
Faraday’s
Law
Magnitude of the induced emf is
directly proportional to the rate of
change of flux linkage
Lenz’s Law
The induced emf cause a current to
flow as to oppose the change in flux
linkage that creates it
ℇ=
𝑑(π‘πœ™ )
𝑑𝑑
ℇ
=
−𝑑(π‘πœ™ )
𝑑𝑑
As magnet move, there’s a change in flux
Faraday’s law: induced emf proportional to the rate
of change in flux
Initial increase in emf as magnet get closer to the coil
Magnet &
coil
When magnet is fully inside the coil there is no
change in flux so no emf
Changing direction of magnet, direction of emf
change
Magnitude of emf depends on the speed of magnet
Same total flux so the areas of two graphs are equal
Work done by magnet:
Lenz’s law, induced current creates a B field to
oppose motion
Hence force in opposite direction to its motion
Flux changeο‚Žinduced emf
To create a current in the coil work must be
done so there is a force
ο‚Ž induce B field in the coil oppose the change
in B field
π‘Š = 𝐹𝑠 hence work is done
Ways to create induced emf:
Moving the magnet
Changing the current (turn on off)
Change into alternating current
TRANSFORMER
An electrical machine for converting an input AC PD into a different output AC PD
𝑁𝑠 > 𝑁𝑃 : Step up transformer
𝑁𝑠 < 𝑁𝑃 : Step down transformer
𝑉𝑆 𝑁𝑆 𝐼𝑃
=
=
𝑉𝑃 𝑁𝑃 𝐼𝑆
Transformer effect
The changing I in the primary coil create an changing B field in the iron core
There is a changing in flux linked to the second coil
Faraday’s law (ℇ =
𝑑(π‘πœ™ )
𝑑𝑑
) there’s an induced emf
Ideal transformer: No flux loss
𝑁
Since 𝑁𝑆 < 1 Step down transformer so low emf across secondary coil
Energy loss
𝑃
Ohmic
losses
The primary and secondary coils get hot
Flux
losses
Not all the flux stays in the iron core
Hysteresis Magnetising and demagnetising the core
losses
produce heat
Eddy
current
The changing flux in the iron core creates
current in the core, which also generate
heat, dissipate energy
Make wire resistances small so heating losses are
small
Use soft iron core so the flux linkage is as large as
possible & hysteresis losses are as small as
possible
Use laminated core, so the eddy current are as
small as possible
Power plant
END
TOPIC 8: NUCLEAR AND PARTICLES PHYSICS
Name
Definition
Nucleon/ mass
number
Number of nucleons in the nucleus
Proton/ atomic
number
Number of protons in the nucleus
Notes
A metal is heated
Free electron gain KE
Thermionic
Emission
KE > Φ the electron escape from the metal surface
(how charged particles produced for use in particles accelerator)
RUTHERFORD SCATTERING
Rutherford’s
Scattering
Fire a beam of alpha particles at a very thin sheet of gold
Count the number of α particles scattered at different angles
Most go straight through θ ~ 0o
Results
Some α particles will be deflected by large angles (θ ~ 90o)
A few α particles reflected/ go straight back (θ ~ 180o)
Conclusion
The atom is mostly empty
All the positive charges and most of the mass is contained in a very small region
Most does not get near enough to any matter to be affected
Reasons
Some came close enough to the charge to be affected
A few deflected so nucleus must have mass much greater than the alpha particle mass to cause
this deflection
PARTICLE PHYSICS
Particle Physics
For every particle that is an identical particle with opposite electric charge called its antiparticles
Antiparticles
When a particle meets its own antiparticle, they annihilate, the energy released makes new
particles
De Broglie:
𝝀=
Investigate
Nucleons
Structure
𝒉
𝒑
To look at small distance λ must be small
So p must be large
So E must be large
𝐸 2 = 𝑝2 𝑐 2 + π‘š2 𝑐 4
If 𝑝 ≫ π‘šπ‘
𝐸 = 𝑝𝑐
FUNDAMENTAL: not made out of other particles
Leptons
Electron
Electron neutrino
𝑒−
πœˆπ‘’
Muon
Muon neutrino
πœ‡
−
Tau
𝜏
−
Up
𝑒+
Quarks
2⁄
3
Charm
𝑐+
2⁄
3
Top
𝑑+
2⁄
3
πœˆπœ‡
Tau neutrino
𝜈𝜏
Down
𝑑−
2nd gen
Have a Leptons
3rd gen
1st gen
1⁄
3
Strange
𝑠−
1st gen
2nd gen
1⁄
3
Bottom
𝑏−
3rd gen
1⁄
3
HADRON
Baryons
Mesons
Proton
Neutron
Contains 3 quarks
𝑝+
𝑛0
Baryon number 𝐡 = +1
Pions
πœ‹+
πœ‹0
Contain
πœ‹−
1 quark + 1 antiquark
BOSON
When particles interact, they are affected by one of 4 possible
forces:
Gauge Bosons




Gravity (Graviton): act on energy
Electromagnetism (Photon): charged particles
Strong force (Gluons): quarks
Weak force (W+, W-, Zo) log
In Newtonian physics, we describe these forces using fields
In quantum mechanics, the idea of fields is replaced by the
transfer of particles called gauge bosons
We then call these interactions, instead of forces
Name
Definition
Notes
PARTICLES ACCELERATOR
When the next tube is positive the electron accelerates across the gap
Inside each tube, the electron has constant v
LINACS
High-frequency supply ensure tube has the correct potential to accelerate the eAs particles are accelerated by the E field between the tube their speed increase
The AC frequency is constant
So the time inside each tube must be a constant = ½ period of the AC
So the tube must be longer when v
The tube will increase in length until the speed reach the speed of light (constant) then the tube
lengths become constant
π‘šπœ‹
𝑑
2πœ‹π‘š
𝑇=
π΅π‘ž
π΅π‘ž
𝑓=
2πœ‹π‘š
π΅π‘ž =
Cyclotron
The e- accelerate across the gap end with speed v
Inside the dee, the e- move in a semi-circle
Time inside the dee
𝑑=
So
πœ‹π‘Ÿ
𝑣 πœ‹
π‘œπ‘Ÿ =
𝑣
π‘Ÿ 𝑑
π΅π‘ž =
π‘šπœ‹
𝑑
E field produce a force
Facing dee is always negative (for proton)
Increases the KE of the particles across the gap
βˆ†πΈπΎ = π‘žπ‘‰
B field causes the direction of the particles inside the Dees change
Limitation:
When vο‚Žc, cyclotron stop accelerating particle
Newton’s Law of motion don’t apply when vο‚Žc
Radius of orbit  as energy  but vο‚Ž constant, so time inside dee  so frequency 
Curvature
Some particle tracks curve ‘clockwise’ others ‘anticlockwise’
Some have positive charge, some have negative charge
Fleming’s left-hand rule tells us the sense of curvature
Charge particles gain KE so p 
π‘Ÿ ∝ 𝑝 so r
The curvature decreases along the length
Synchrotron
Accelerate the particles with an electrical field
Synchrotron vs Cyclotron
Particle path is bent with a magnetic field
The particles move in a circle
Radius of path is constant
As KE, B to keep r constant
As particle E, E field get stronger
Because the particles are accelerating, they lose E by
emitting radiation (synchrotron radiation)
The magnetic field causes the track to bend
Uncharged particles leave no track
Electric field:
Accelerate particle
Direction of force indicates sign of charge
Bubble
π‘Ž=
Chamber
𝐸𝑄
π‘š
Magnetic field:
Circular motion
Direction of curvature indicates sign of charge
π‘šπ‘£
π‘Ÿ=
π΅π‘ž
Only moving charged particles leave a track
Pion are charged so leave a track
Pion interact with a stationary charged particle
2 neutral particles created (because no track) to conserve
charge
Track in different direction so momentum conserved
Both particles decayed into opposite charged particle
because charge is conserved
At all collision momentum and charge are conserved
Ad: lots of collision
Dis: There’s momentum before collision so momentum after collision
Fixed target
Particles created must have KE
So not all KE converted into mass
Not many particles are created and their masses are not very big
Ad: Final 𝑝 = 0 so final KE is small
Colliding
beams
All energy goes into making new particle
ο‚Ž can make new massive particles
Dis: Not many collisions
END
TOPIC 9: THERMODYNAMICS
Name
Definition
Formulae
Specific heat
capacity
The amount of heat energy required to change the temperature
Specific
latent heat
The amount of heat energy required per unit mass of a substance
of a unit mass of a substance by a unit temperature
to change the state from … to … at a constant temperature
KINETIC THEORY
Assumption:
Kinetic
model of gas
Internal
energy






A gas is made of lots of particles
Volume of particle << Volume of container
Particles move at random
Particles collide elastically (KE is conserved)
No potential energy between particle (PE=0)
The mean KE of particle is directly proportional to the
temperature
Random distribution of potential and kinetic energy among the
molecules
IDEAL GAS EQUATION
Ideal gas
equation
1
1
𝑝𝑉 = π‘π‘š < 𝑐 2 > = π‘π‘˜π‘‡ = 𝜌 < 𝑐 2 >
3
3
Initial x momentum:
π‘šπ‘£π‘₯
Final x momentum:
−π‘šπ‘£π‘₯
βˆ†π‘ = 2π‘šπ‘£π‘₯
Time between collision:
𝑑=
2𝐿
𝑣π‘₯
N2L, average force on wall
𝐹=
Derive
𝒑𝑽 =
βˆ†πΈ = π‘šπ‘βˆ†πœƒ
βˆ†π‘ 2π‘šπ‘£π‘₯ π‘šπ‘£π‘₯2
=
=
2𝐿
𝑑
𝐿
𝑣π‘₯
Total force on wall
𝟏
π‘΅π’Žπ’„πŸ
πŸ‘
∑
π‘Žπ‘™π‘™ π‘π‘Žπ‘Ÿπ‘‘π‘–π‘π‘™π‘’π‘ 
π‘šπ‘£π‘₯2 π‘š
= ∑ 𝑣π‘₯2
𝐿
𝐿
Mean squared speed
2
< 𝑐 >=
Moving randomly:
∑ 𝑣π‘₯2
∑(𝑣π‘₯2 + 𝑣𝑦2 + 𝑣𝑧2 )
𝑁
=
∑ 𝑣π‘₯2 ∑ 𝑣𝑦2
= ∑ 𝑣𝑧2
3 ∑ 𝑣π‘₯2
𝑁
𝑁 < 𝑐2 >
∑ 𝑣π‘₯2 =
3
< 𝑐2 > =
βˆ†πΈ = πΏβˆ†π‘š
Therefore, total force
𝐹=
π‘š
𝐿
×
𝑁<𝑐 2 >
3
Pressure
𝑃=
𝐹 π‘π‘š < 𝑐 2 >
=
𝐴
3𝐿3
But 𝑉 = 𝐿3 so
1
𝑃𝑉 = π‘π‘š < 𝑐 2 >
3
Internal energy = KE + PE
Fr ideal gas, PE = 0 so Internal energy = KE
Boyle’s Law
Pressure
Law
Charles’ Law
Absolute
zero
1
1
π‘ˆ = ∑ π‘š(𝑣π‘₯2 + 𝑣𝑦2 + 𝑣𝑧2 ) = π‘π‘š < 𝑐 2 >
2
2
2
∴ 𝑃𝑉 = π‘π‘˜π‘‡ = π‘ˆ
3
1
3
∴ π‘ˆ = π‘π‘šπ‘ 2 = π‘π‘˜π‘‡
2
2
For a fixed amount of an ideal gas at a constant temperature:
𝑃1 𝑉1 = 𝑃2 𝑉2
Its pressure is inversely proportional to its volume
For a fixed amount of an ideal gas at a constant volume:
Its pressure is directly proportional to its temperature
For a fixed amount of an ideal gas at a constant pressure:
Its volume is directly proportional to its temperature
The temperature at which the pressure/ volume of a gas become
zero
𝑃1 𝑃2
=
𝑇1 𝑇2
𝑉1 𝑉2
=
𝑇1 𝑇2
1
3
𝐾𝐸 = π‘š < 𝑐 2 >= π‘˜π‘‡
2
2
BLACK BODIES
MaxwellBoltzmann
Distribution
How many molecules will have a speed in a small range of speed
At every temperature above 0K objects radiate energy as
electromagnetic wave
Black bodies
radiator
A blackbody absorbs all the radiation that falls on it
Total energy radiated per second only depends on the surface area A
and the absolute temperature T
StefanBoltzmann
Law
The total amount of energy radiated per second is proportional to
the surface area A and the absolute temperature
𝐸 = πœŽπ΄π‘‡ 4
πœ†π‘šπ‘Žπ‘₯ 𝑇 = 2.898 × 103
= π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘
Wein’s Law
END
TOPIC 10: SPACE
Name
Definition
Note
STELLAR PARALLAX
Intensity/
Flux
𝐼=
𝐿
4πœ‹π‘‘2
𝑑=
1π΄π‘ˆ
πœƒ
The apparent shift in the position of a
nearby star, relative to more distant ones,
due to the moment of the Earth around
the Sun.
Stellar
Parallax
The star is viewed from two positions at 6month intervals
The change in angular position of the star
against backdrop of fixed stars is
measured
Use trigonometry parallax to calculate the
distance
Parsec
The distance that a star would be if it had
a parallax of 1 arcsec
Elliptical
orbit
Over the course of one year the stars will
trace out an elliptical path on the sky.
Stars have orbits not perpendicular to
earth will appear to have elliptical orbits
because only see the projection of the
diameter.
Large
distance
When d is large θ is small so the fractional
uncertainty is large, therefore there is a
large fractional uncertainty in the
calculated value of d.
Since Mars is farther away from the Sun
than the Earth, for a given parallax we can
calculate a larger value of stellar distance.
STANDARD CANDLES
Standard
candle
An astronomical object whose luminosity
is know
Giant stars that become unstable and
pulsate: their diameters oscillate and
therefore they vary in luminosity
Cepheid
variables
Cepheid variables out ward pressure P
and inward gravity compression are out of
sync so the star and temperature pulsates
Determine distance to Cepheid
Measuring period T
𝐿 = 4πœ‹πœŽπ‘… 2 𝑇 4 give luminosity
𝐿
Light flux can be determined 𝐼 = 4πœ‹π‘‘2
𝑑(𝑝. 𝑠. ) =
1
πœƒ(′′)
Inverse square law gives the distance
The explosion of stars that have run out of
fuel for nuclear fusion in their cores.
Type 1a are standard candles
Supernovae
Type 1a supernovae are extremely
luminous they can be seen from a very
large distance
The light curve must be calibrated by
using Cepheid variables to determine the
distance to a galaxy that contains a type
1a supernovae
HR DIAGRAM
HR diagram
A Luminosity-Temperature diagram
Main
sequence
Stars that convert Hydrogen into Helium
via thermonuclear fusion in the core
Blue giants
Large mass, high temp and luminosity
Red giants
Low temp, high luminosity, converting He4 to C-12 and O-16
Core of a red giant star
Do not have fusion reaction
Radius is very small
𝐿 = 4πœ‹πœŽπ‘… 2 𝑇 4 so luminosity is low
White
dwarfs
Surface temperature is high, πœ†π‘π‘’π‘Žπ‘˜ is in
UV spectrum
Emits a lot of light in visible spectrum so
appear white
Stars are very good black bodies.
The total radiations they emit per second
only depend on the surface area and the
absolute temperature.
They obey Stefan’s law:
Star
𝐿 = 4πœ‹πœŽπ‘… 2 𝑇 4
And Wein’s law:
πœ†π‘π‘’π‘Žπ‘˜ 𝑇 = 2.898 × 103
A star position on the HR depend on its
mass and its age
Stars are large ball of gas (mostly
hydrogen, helium)
Life cycle of
the stars
Gravity cause a large cloud of gas and dust
to collapse & heat up
When neutral temperature reach ≈
106 𝐾, nuclear reaction starts in the
centre, H is converted to He
A star is born, its life cycle of a star
depends on its mass
Young star groups have more red giant
stars
Planetary
nebula
Pulsar
Gaseous
nebula
Shell of gas ejected from RG star on its
way to becoming a WD
Rotating neutron star with a very string
magnetic field
Pulsars beam radiation out along their
magnetic axis
Large cloud of gas & dust. They have very
low temperature and density
Name
Definition
Notes
Doppler’s effect
CMBR
Cosmic Microwave Background Radiation:
Come from all part of the sky
Its intensity is almost the same in every direction
Black body radiation produced in the hot Big Bang
Whose wavelength have been stretched by the cosmological expansion
The peak wavelength Is now in the microwave part of the spectrum
It implies that the temperature after Big Bang was very high
If the temperature was exactly uniform across the sky, the density of the universe would be
exactly uniform
Gravity would not be able to form structures such as galaxy, stars and planets
Low temperature region has higher density and will collapse first to form galaxy
Hubble’s Law
The recession velocity of a galaxy is directly
proportional its distance from our galaxy
It implies that in the past the universe was smaller
By extrapolating backward far enough, everything in
the universe was at the same location: a point of
infinite density and temperature, The Big Bang
Hubble’s
parameter
The gradient of the Hubble’s law graph
The present value is 𝐻0 = 71 π‘˜π‘š/𝑠/𝑀𝑝𝑐
Hubble’s constant not very accurate
Because the distances to the galaxies are
underestimated hence gradient is not as steep as in
Hubble’s graph
Dark matter
Material that does not interact via the
electromagnetic force. Its gravity may be responsible
for explaining the rotation curves of galaxies and the
stability of the galaxy clusters
𝑣 = 𝐻0 𝑑
Cosmological
redshift
The increase in wavelength of radiation from distant
galaxies due to the expansion of the universe
Redshift
The fractional increase in wavelength of light emitted
by a source and detected by an observer due to the
relative motion between them
Light from almost all galaxy are redshifted πœ†π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘’π‘‘ >
πœ†π‘™π‘Žπ‘
Due to Doppler effect galaxy are moving away from us
Hubble’s law so distance between galaxy is increasing
So, the universe is expanding
Big Bang
Nucleosynthesis
The early universe was extremely hot and dense, the
condition is suitable for thermonuclear fusion to occur
DARK MATTER
In order to account for the measured shape of the
graph there has to be more mass than can be
accounted for by the visible matter. This extra mass is
called dark matter
Dark matter does not emit electromagnetic radiation,
but it has gravitational effects
The dark matter affects the gravity of the universe,
which affect the rate at which the universe expands,
so it affects whether the universe is open, closed or
flat
Because the total density of the universe is uncertain,
the future of the universe is uncertain
𝑧=
πœ†0 πœ†π‘’ 𝑣
=
πœ†π‘’
𝑐
TOPIC 11: NUCLEAR RADIATION
Name
Definition
Formulae
NUCLEAR DECAY
Nuclear decay
Randomly: It is unpredictable which nucleus will
decay next and when it decays
Spontaneous: the rate of decay cannot be changed
by changing the external conditions (temperature,
pressure, etc.)
Radioactive
isotopes
Isotope has an unstable nucleus, decay and emit
radiation
Alpha decay
Alpha particles:




Beta decay
→
14
6𝐢
14
7𝑁
Beta decay  Z by 1
Beta particles
𝜈: neutrino
Moderately ionizing
Range in air bout 1m
Stopped by thin metal
Deflected by magnetic fields (opposite
direction to alpha)
234
90π‘‡β„Ž
+ 42𝛼
Alpha decay  Z by 2, A by 4
Beta particles are high-speed electron emitted by
the nucleus




Gamma decay
Strongly ionizing
Short range in air
Stopped by paper
Deflected by magnetic fields
238
92π‘ˆ
→
+ −10𝛽 + πœˆΜ…π‘’
πœˆπ‘’ : electron neutrino
πœˆΜ…π‘’ : anti-electron neutrino
Gamma rays are high energy EM radiation (photon)
Gamma rays:




Weakly ionizing
Obey inverse square law in air
Stopped by 1m concrete
Not deflected by magnetic fields
HALF-LIFE
𝑁 = 𝑁0 𝑒 −πœ†π‘‘
Half-life
The time is taken for the number of radioactive
nuclei to reduce into half of its initial value
Decay constant
The probability that a given nucleus will decay in one
second
πœ†=
The rate of decay of unstable nuclei
𝐴 = πœ†π‘
Activity
Unit: Bq (Becquerel)
Rate of
production
The rate of production of C-14 (etc.) decrease
The ratio was greater
Ratio used is from current time not from the past
𝑙𝑛2
𝑇1⁄
2
𝐴 = 𝐴0 𝑒 −πœ†π‘‘
So, the time is underestimated
BACKGROUND RADIATION
Background
radiation
Radioactive isotopes in the environment
Sources of radiation: rocks, air, water, cosmic rays
Background radiation may affect cancer rate,
responsible for some mutations that drive evolution
Before plotting activity graph the count rate
must be corrected for background,
otherwise 𝑇1⁄ will be overestimated
2
END
Name
Definition
Formulae
BINDING ENERGY
Mass defect
Free nucleons have more energy than when they’re trapped in
the nucleus.
2
According to Einstein, 𝐸 = π‘šπ‘ so if the energy of the nucleus
increases the mass must increase
βˆ†π‘š
= π‘€π‘Žπ‘ π‘  π‘œπ‘“ π‘›π‘’π‘π‘™π‘’π‘œπ‘›π‘ 
−π‘€π‘Žπ‘ π‘  π‘œπ‘“ 𝑛𝑒𝑐𝑙𝑒𝑒𝑠
Since the mass of proton/neutron is constant, the mass of the
nucleus < total mass of proton/neutron in it.
Nuclear
binding
energy
The energy needed to separate all nucleons in the nucleus
𝐡. 𝐸. = βˆ†π‘šπ‘ 2
𝐹𝑒 − 56 is the most stable isotope
For A>56 the BE/nu decrease
So required net energy input to undergo fusion
So does not occur in massive stars
FISSION
Nuclear
fission
Split a large nucleus into small nuclei
Release energy because the BE/nucleons of the fragment
increase
ο‚Ž the energy is released in the reaction, provided that we do
not pass the peak
Number of neutrons always increase
Chain
reaction
More than 1 neutron is produced in the reaction.
Each neutron can induce further nuclei to fission
The reaction grows exponentially
Fissile
Nucleus can be split by slow neutron
𝐴𝑐𝑑𝑖𝑣𝑖𝑑𝑦 × πΈ π‘π‘’π‘Ÿ π‘Ÿπ‘’π‘Žπ‘π‘‘π‘–π‘œπ‘›
Rate of
energy
radiation
Rate of
temperature
Most KE released is carried by the alpha particles which
escapes, so it does not heat the metal.
𝑑𝑄
𝑑𝑇
= π‘šπ‘
𝑑𝑑
𝑑𝑑
increase
So, rate of T is likely to be overestimated
Radioactive
waste
Total activity is underestimated
All isotopes produced in the decay will be radioactive, so they
contribute to the total
FUSION
Nuclear
reactor
Pros:
 Lots of energy/kg of fuel
 No CO2 emission
Cons:
 Radioactive waste must be stored for thousands of
years
 Possibility of radiation escape during accident
 High cost of building reactors and decommissioning
Nuclear
fusion
Joining 2 or more light nuclei into a heavier one and release
energy
Sustained
fusion
High energy/ temperature
ο‚Ž The particles have enough kinetic energy to overcome
electrostatic repulsion
ο‚Ž They come close enough for fusion
High density/ pressure
ο‚Ž Ensure that the reaction rate is high
Fusion
reactors
Pros:
 Unlimited supply of fuel
 Little radioactive waste
Cons:
 Very expensive, requires extremely high T, P ο‚Ž
Container problems
 Strong magnetic field required
END
TOPIC 12: GRAVITATION
Name
Definition
Formulae
GRAVITATIONAL FIELDS
A gravitational field is caused by mass & it affects mass
Gravitational fields
Gravitational field
strength
Gravitational field lines show the direction that a positive mass will move in
that field. The field line spacing tells us the field strength
Force acting on unit mass in the field
𝑔=
𝐹
π‘š
β„Ž
GPE
Work done in moving a distance h in the field
∫ 𝐹𝑑π‘₯
π‘œ
= π‘šπ‘”β„Ž
Total energy
𝐸 = 𝐾𝐸 = −
𝐺𝑃𝐸
2
Gravitational
potential
𝛷=−
βˆ†π›· = π‘”β„Ž
βˆ†π›·
𝑔=−
𝑑π‘₯
Gravitational Potential
Change in GPE per unit mass
Change in
gravitational potential
Distance R
The attractive gravitational force between two point mass
Newton’s law of
universal gravitation
Is directly proportional to the product of their mass
And inversely proportional to the square of distance between them
Escape velocities
𝐺𝑀
π‘Ÿ
The speed of the object so that it just reach ∞
𝐺𝑀
π‘Ÿ2
πΊπ‘€π‘š
𝐹= 2
π‘Ÿ
𝑔=
2𝐺𝑀
𝑣𝑒𝑠𝑐 = √
𝑅
KEPLER LAW OF PLANETARY ORBITS
Kepler’s first law
The planets orbit the sun in elliptical orbit with the sun at one focus of the
ellipse
Kepler’s second law
The line joining the planet to the sun sweep out equal area in equal times
Kepler’s third law
If T is measured in year, d is measured in AU,
𝑇 2 = 𝑑3
𝑇2
=(
4πœ‹ 2
) 𝑑3
𝐺𝑀𝑆𝑒𝑛
SATELLITES
𝑣2 =
Near Earth orbit
Geosynchronous
𝐺𝑀
𝑅
Above equator, 𝑇 = 24β„Ž → 𝑑 = 4.2 × 107
BLACK HOLES
Schwarzschild radius
Radius of a black hole of mass M
For Earth 𝑅𝑆 = 8.89 × 10−3 π‘š
END
𝑅𝑆 =
2𝐺𝑀
𝑐2
TOPIC 13: OSCILLATION
Name
Definition
Formulae
SIMPLE HARMONIC MOTION
Simple harmonic
motion
Occurs when there is a force always act toward
equilibrium point and the force is directly
proportional to the displacement from equilibrium
𝐹 = −π‘˜π‘₯
π‘₯ = 𝐴 cos πœ”π‘‘
π‘£π‘šπ‘Žπ‘₯ = π‘₯0 πœ”
𝑣 = −π΄πœ” sin πœ”π‘‘
π‘Žπ‘šπ‘Žπ‘₯ = π‘₯0 πœ”2
π‘Ž = −π΄πœ”2 cos πœ”π‘‘ = −πœ”2 π‘₯
Equation of
simple harmonic
motion
π‘Ž=
𝑑2 π‘₯ 𝑑2 π‘₯
→ 2 = −πœ”2 π‘₯
𝑑𝑑 2
𝑑𝑑
π‘₯ = π‘₯0 cos πœ”π‘‘
π‘₯ = π‘₯0 sin πœ”π‘‘
This equation has 2 solutions that tell us how x
changes with time
π‘₯0 is the maximum displacement from equilibrium
= amplitude
Angular
frequency
π‘˜
𝑔
πœ”=√ =√
π‘š
𝑙
RESONANCE
Occur when the driving frequency is close to the
natural frequency
Resonance
Maximum energy transferred from the driver to
the oscillator
The amplitude of oscillation increases rapidly/ the
oscillation is amplified
The amount of amplification  as damping  (the
width of the curve )
DAMPING
A resistive force that opposes the natural motion
of an oscillator
Damping
Energy is dissipated from the oscillation
So, the amplitude of the oscillation decrease
Light damping
Heavy damping
Critical Damping
With air resistance, T does not change
The amplitude decreases exponentially
No oscillation
The object returns to equilibrium point slowly
The most efficient way of removing energy from
an oscillator
END
𝑠 = 𝑠0 𝑒 −π‘˜π‘‘ cos πœ”π‘‘
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