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A-Level Physics Key Terms Cheat Sheet by

Key terms in Physics A Level - AQA with Engineering


A quantity without direction.
Length­/Di­stance, Speed, Mass, Temper­ature, Time, Energy
A quantity with both direction and magnitude
Displa­cement, Velocity, Force (inc. Weight), Accele­ration, Momentum
When all forces acting on an object are balanced and cancel each other out. There is no resultant force
Free-body Diagram
A diagram of all the forces acting on a body, but not the forces it exerts on other things. The arrows indicate magnitude and direction.
Principle of Moments
For a body to be in equili­brium, the sum of the clockwise moments equals the sum of the anticl­ockwise moments.
The product of the size of the force and the perpen­dicular distance between the turning point and the line of action of the force.
A pair of forces with equal size which act parallel to each other but in opposite direction. E.g. turning a car's steering wheel.
Centre of Mass
The single point from which the body's weight acts through. The object will always balance around this point.
To calculate for uniform objects: Σmx = Mx̄
SUVAT (Constant Accele­ration)
v = u + at
s = 1/2 (u+v)t
v2 = u2 + 2as
s = ut + 1/2 at2
s = vt - 1/2 at2
Displa­cem­ent­-Time Graph
Displa­cement (y) against Time (x).
Gradient = Velocity
Accele­ration = Δgradient
Veloci­ty-Time Graph
Velocity (y) against Time (x)
Gradient = Accele­ration
ΔGradient = ΔAccel­eration
Area = Displa­cement
Variable Accele­ration
Accele­rat­ion­-Time Graph
Accele­ration (y) against Time (x).
Gradient = ΔAccel­eration
0 Gradient = No accele­ration constant velocity.
Constant Gradient = constant accele­ration
Area = Velocity
NB: Remember to treat area below the time axis as negative!
Newtons 1st Law
The velocity of an object will not change unless a resultant force acts on it.
Newtons 2nd Law
F = ma
The accele­ration of an object is ∝ to the resultant force acting upon it. (for objects with a constant mass)
Points to remember:
• Resultant Force is vector sum of all the forces
• Unit = N
• Ensure mass is in kg
• Accele­ration is in the same direction as resultant force.
Newtons 3rd Law
If object A exerts a force on object B, then object B exerts an equal but opposite force on object A
When there is only gravity acting upon an object. i.e. motion with an accele­ration of g (9.81ms-2)
The same SUVAT equations apply, however, u = 0 and a = g {{ng}} NB: 'direc­tion' of motion, dictates the sign of g
Projectile Motion
An object given an initial velocity, then left to move freely under g. There is separate horizontal and vertical motion with time being the only common attribute. Both motion follows SUVAT equations but horizontal motion has no accele­ration.
Force that opposes motion. When in a fluid (liquid or gas) it is drag, drag depends on:
• Viscosity of the fluid
• Speed of object
• Shape of the object

For all frictional forces
• Force is in the opposite direction to motion
• Can never increase speed or induce motion
• They convert kinetic energy heat.
Upwards force on a object in a fluid
Terminal Speed
When frictional forces equal the driving force. For a falling object, when drag equals the force due to their mass.
The product of the mass and velocity of an object. Momentum in any collision is conserved (when no external forces are involved)
Inelastic Collision
Not all of the kinetic energy is conserved. Momentum however is conserved.
Elastic Collision
Kinetic energy is conserved i.e. no energy is dissipated as heat or other energy forms.
An extension of N2L. Impulse is the product of force and time and is equal to the momentum of that body.
FΔt = Δ(mv)
Also equal to the area under a force-time graph.
Work Done
The energy transf­erred from one form to another.
W = Fd
Work Done = The force causing motion x distance moved
The rate of work done over time
P = ΔW/Δt
P = Fv derived from combining P and W = Fs
Force-­Dis­pla­cement Graph
Area = Work Done
Conser­vation of Energy
Energy cannot be created nor destroyed, only converted from one form to another, but the total energy of a closed system will not change.
useful output­/input in terms of energy or power.


ρ = m/V
A property all materials have and is indepe­ndent of both shape and size.
Limit of Propor­tio­nality
The point where Hooke's law no longer applies. On a force-­ext­ension graph, the limit of propor­tio­nality is where the line is no longer straight
Hooke's Law
F = kΔL
The force is propor­tional to the extension of a stretched wire.
k is the stiffness constant a measure of how hard it is to stretch
Elastic Limit
The point on a force-­ext­ension graph where the line begins to curve. Beyond this point, permanent deform­ation occurs where the wire will no longer return to its original shape.
Force-­Ext­ension Graph
Straight section Gradient = k
Loading and unloading plot a loop, if a stretch is elastic, the curve starts and finishes in the same position (the origin). If plastic deform­ation occurs, the unloading line has the same gradient (k) but crosses the x axis at a different point

Area = Elastic Strain Energy

The area between the loading and unloading line (after plastic deform­ation) is equal to the work done in deforming the material
Tensile Stress
The ratio of forced applied and cross-­sec­tional area.
stress = F/A
Tensile Strain
The ratio of extension to original length, it has no units and is just a ratio.
strain = ΔL/L
Youngs Modulus
The ratio of tensile stress and tensile strain
The YM of a material is the constant value up to the limit of propor­tio­nality,
Stress­-Strain Graph
Stress (y) against Strain (x).
Gradient = Young's Modulus
Area = strain energy per unit volume
Yield Point
The point on a stress­-strain graph where the material stretches without any extra load.
When a material breaks after a certain about of force is applied. The line simply stops on a stress­-strain graph. The same thing applies on a force-­ext­ension graph, the line just stops.

Thermal Physics

A temper­ature scale that is in terms of an atoms movements.
°C K
+ 273
Absolute Zero
The lowest theore­tical temper­ature of anything 0 K = -273°C
Internal Energy
The internal energy of a body is the sum of the randomly distri­buted kinetic and potential energies of all its particles
Closed System
A system where no matter or energy is transf­erred in or out of the system
Heat Transfer
Heat is always transf­erred from a hot area/s­ubs­tance to a cold area/s­ubs­tance.
Specific Heat Capacity
The amount of energy required to heat up 1kg of the material by 1°C/1 K
ΔQ = mcΔT
Energy Change is equal to the product of the mass, specific heat capacity and the change in temper­ature.
Specific Latent Heat
The specific latent heat of fusion ( Solid) / vapori­sation ( gas) is the quantity of thermal energy needed­/will be lost to change the state of 1kg of the substance.
Q = ml
where m is the mass and l the latent heat.

When a substance changes state, there is a period where the temper­ature of the material is constant, as the internal energy rises, this is due to the latent heat.
Boyle's Law
At a constant temper­ature, pV is constant. i.e.
= p

On a p-V plot, the higher the line, the higher the temper­ature.
Charles' Law
At a constant pressure: V is directly propor­tional to its absolute temper­ature T
= V
Pressure Law
At a constant volume: p is directly propor­tional to its absolute temper­ature.
= p

Molecular Mass
the sum of the masses of all the atoms that make up the molecule.
Relative Molecular Mass
The sum of the relative atomic masses of all the atoms.
Avogadro Constant
The number of atoms in exactly 12g of carbon isotope 12
= 6.02 x1023 mol-1
Molar Mass
The mass of a material containing N
Ideal Gas Equations
pV = nRT
n = number of moles
R = molar gas constant

pV = NkT
N = number of molecules
k = Boltzmann constant

A way of rememb­ering which n is which. Moles will be small, therefore small n. Number of molecules will be large so, big N.
Kinetic Theory
The pressure exerted by an ideal gas can be derived by consid­ering the gas as individual particles.
pV = 1/3 x Nm(C
is the root mean square speed.

• All molecules in the gas are identical
• Gas contains a large number of molecules
• The volume of the molecules is negligible when compared to the volume of the contai­ner/gas as a whole.
Brownian Motion
Random motion of particles suspended in a fluid helped provide evidence that the movement of the particles was due to the collisions of the fast random­ly-­moving particles, which supported the model of kinetic theory.
Average Kinetic Energy
1/2 x m(C
)2 = 3/2 x nRT/N

1/2 x m(C
)2 = 3/2 x RT/N

Particles and Radiation

Proton & Neutrons
The 2 Baryons that make up the nucleus of an atom. Comprised of 3 quarks. Protons have a relative charge: +1, neutrons: 0. Both have a relative mass of 1 (1.67 x10-27 kg).
A fundam­ental lepton, with a charge of -1. Cannot be broken down into other subatomic particles. Relative mass of 1/2000 (9.11x10-31 kg)
Nuclide Notation A
The general notation of elements.
Proton Number (Z)
The number of protons in an atom. Defines the element. For a neutral atom, proton no. also == the electron number
Nucleon Number (A)
AKA Mass Number - number of total nucleons (protons + neutrons)
Specific Charge
The ratio of a particles charge to its mass. Specific meaning per kg.
S.C. = Charge (Q) / Mass (kg)
Atoms with the same number of protons but a different number of neutrons. Affects the stability of a atom
Strong Nuclear Force
A strong force that holds atoms together at small distances, strong enough to overcome the electr­ostatic repulsion of the protons.
Repulsive: <0.5 fm (0.5 x10-15m)
Attrac­tive: 0.5 to 3 fm
Rapidly falls to ) after 3 fm.
Alpha Decay (α)
Occurs in big atoms (82+ protons). Atoms emits a helium nucleus (2 protons 2 neutrons). Particles is too big to be kept stable by the SNF.
Beta-Minus Decay (β-)
Emission of a electron and anti-e­lec­tro­n-n­eut­rino. Happens in neutron rich particles. In nucleus structure terms, a neutron turns into a proton by changing an d quark to a u quark, emitting an electron and anti-e­lec­tro­n-n­eut­rino.
Beta-Plus Decay (β+)
Emission of a positron and an electron neutrino. One of the atoms protons, changes a u quark to a d quark, changing to a neutron emitting a positron and an electr­on-­neu­trino.
A discrete packet of electr­oma­gnetic radiation with 0 mass.
E = hf = hc/λ
The corres­ponding antipa­rticle to any particle has the same mass and rest energy but opposite charge.
Pair Production
When 2 of the same particles collide at high speed and produce a partic­le-­ant­ipa­rticle pair. The energy of the collisions is converted into the pair. Also occurs when a photon has enough energy to produce an electr­on-­pos­itron pair.
= 2E
(in MeV)
When a particle and antipa­rticle collide producing 2 photons in opposite direct­ions.
= E

This collision is used in PET scanners to detect cancers.
Particles that can feel the strong force. Either a baryon or a meson depending on its quark structure
A hadron consisting of 3 quarks. All are unstable except a free proton - all eventually decay into a proton.
Proton: uud
Neutron: ddu
Baryon Number
A quantum number which is always conserved. Baryons have a B.N. of +1. Antiba­ryons have a B.N. of -1 and all other particles have a B.N of 0.
A hadron consisting of 2 quarks - a quark-­ant­iquark pair. There are 9 possible combin­ations, making either Kaons or Pions.
A fundam­ental particle that doesnt feel the strong force. Interacts via the weak intera­ction.
Lepton Number
Another quantum number that is always conserved. Must be separate for lepton­-el­ectron number and electr­on-muon number.
Strange Particles
Particles that have a property of strang­eness - contain a strang­e/a­nti­-st­range quark.
Created via the strong intera­ction
Decay via the weak intera­ction
Rules of conver­sation mean that strange particles are only produced in pairs.
Another quantum number - however it can change by ±1 or 0 in an intera­ction.
A fundam­ental particle that makes up hadrons. There are 6 types:up/down, top/bo­ttom, strange/charm.
Quark Confin­ement
There is no where to get a quark on its own, when enough energy is provided, pair-p­rod­uction occurs, with one quark remaining in the particle.
Weak Intera­ction
β+ and β- are both examples of weak intera­ctions, which is intera­ction via the weak force, the force acting between leptons.
Feymann Diagram
A diagram of particle intera­ctions, with:
Wavy Lines : Exchange Particle
Straight Lines : Particles in/out of the intera­ction (with arrows indicating direction)

Magnetic Fields

Magnetic Field
A region where a force acts, force is exerted on magnet­ic/­mag­net­ically suscep­tible materials (e.g. iron).
Magnetic Field Lines
Lines that show a magnetic field. They run from north to the south pole of a magnet. The more dense the lines are, the stronger the field
Magnetic Flux Density
The force on one metre of wire carrying a current of 1 A at right angles to the magnetic field. AKA The strength of the magnetic field
B = F/Il
Magnetic flux density is the force by the current meter
Magnetic Field around a wire
When current flows, a magnetic field is induced.
Right hand rule:
• Curl Fingers around "­wir­e".
• Stick up thumb
Thumb:Direction of current
Fingers: Direction of magnetic field
A cylind­rical coil of wire acting as a magnet when carrying electric current. Forms a field like a bar magnet.
Force on a Curren­t-C­arrying Wire
A curren­t-c­arrying wire, running through a magnetic field generates a resultant field of the one induced by the current and the pre-ex­isting one. The direction of the force is perpen­dicular to the current direction and the mag. field.
LeFt-hand Rule
For finding the direction of the Force.
• Thumb upwards
• First finger forwards
• Second finger to the right (perpe­ndi­cular to f.f.)

First Finger:Field
Second Finger:Current
Charged Particles in a mag. field
F = BQv
Circular Path
For a charge travelling perpen­dicular to a field is always perpen­dicular to the direction of motion The condition for circular motion.

F = mv2/r can be combined with F = BQv.
Rearranged for r, this shows that:
• r increases if mass or velocity increases
• r decreases if the mag. field strength is increased or the charge increases
• f = v/2πr
•Combined with r = mv/BQ f = BQ/2πm
Particle Accele­rator
A cyclotron consists of 2 hollow semico­ndu­ctors, with a uniform magnetic field applied perpen­dicular to the plane of the D magnets. An A.C. is applied. Charged particles are fired into the D's. They accelerate across the gap between magnets, taking the same amount of time for the increasing radius.
Magnetic Flux
The number of flux lines through a certain area hence{{n}}Φ = BA
In other words its the amount of flux passing through an area
Electr­oma­gnetic Induction
Relative motion between a conductor and a mag. field, causes an emf to generate at the ends of the conductor as the electrons accumulate at one end.
Flux Linkage
The amount of field lines being cut
NΦ = BANCos(θ)
where θ is the angle between the normal to the coil and the field. (if it is perpen­dic­ular, θ = 0°
Faraday's Law
Induced e.m.f. is propor­tional to the rate of change of flux linkage...
ε = NΔΦ/Δt
Lenz's Law
The induced e.m.f. is always in such a direction that it opposes the change that caused it.
e.m.f in a rotating coil
NΦ = BANCos(ωt)
ε = BANωSi­n(ωt)

Flux Linkage and Induced e.m.f. are 90° out of phase.
is converted into electrical energy, the kinetic energy turns a coil in a magnetic field so that they induce a electric current.
Right-hand Rule
For Generators.
• Thumb upwards
• First finger forwards
• Second finger to the left (perpe­ndi­cular to f.f.)

First Finger:Field
Second Finger:Current
Altern­ating Current
Current that's direction changes over time. The voltage across the resistance goes up and down.
Root Mean Squared (rms) Power
= V
= I
= I
x V
A device that uses electr­oma­gnetic induction to change the size of a voltage for an altern­ating current.

An altern­ating current flowing in the primary coil causes the core to magnet­ise­/de­mag­netise contin­uously in opposite direct­ions. This produces a rapidly changing magnetic flux in the core (made of magnet­ically soft material. The changing flux passes through the secondary coil induces a altern­ating e.m.f. if the same frequency but different voltage (if the no. of turns is different)
Transf­ormer Equations
P.Coil: V
= N
x ΔΦ/Δt
S.Coil: V
= N
x ΔΦ/Δt

Combines to:
= V
Ineffi­cie­ncies in a Transf­ormer
• Eddy Currents (looping currents induced by changing flux) create opposing magnetic fields reducing its strength reduced by laminating the core so that current cannot flow between the cores layers
• Heat Generation due to the resistance in the coils reduced by using a wire with a low resistance
• Magnet­­is­ing­/De­­ma­g­n­etising the core energy is wasted as the core is heated reduced by using a magnet­ically soft core, which has a small hysteresis loop, this the energy required to create­/co­llapse the field is minimised

Efficiency Equations
efficiency = I


Moment of Inertia
A measure of how difficult it is to rotate an object or change its rotational speed

I = Σmr2
This equation means that the moment of inertia is dependent in the masses, and their distri­bution, so a solid disk may have a lower moment of inertia than a hoop.
Rotational Kinetic Energy
The rotational kinetic energy of an object is dependant on its moment of inertia.
= 1/2 x Iω2
Rotational SUVAT
The SUVAT equations can be applied directly to rotational motion, but with rotati­onal's counterparts:
s θ (rads)
u ω

v ω
a α
t t
When a force causes an object to turn, the turning effect is torque.
T = Fr
T = Iα
Work & Power
The work done is the product of the force and the angle turned by:
W = Tθ

Power is the amount of work done in a given time:
P = Tω
as Δθ/Δt = ω

Frictionalk Torque occurs in real world systems therefore:
= T
- T
A flywheel is a heavy wheel that has a high moment of inertia, meaning once spinning it is hard to stop. They are charged as they are spun, turning T into rotational kinetic energy. It is used as a energy storage device if energy is needed, the wheel decele­rates and provides some of its rotational energy to another part of the machine.

Flywheels maximused for energy storage are dubbed flywheel batteries.

Factors that effect storage:
• Mass If the mass is increased, the moment of inertia and hence the r. E

• Angular Speed if the angular speed is increasd, the energy stored increases with angular speed2, so increasing the a.speed, greatly increases energy storage.
• Spoked Wheel this again increases the moment of inertia as the mass is distri­buted further away from the center.
• Material Carbon fibre is generally used as it is strong and allows for higher angular speeds
• Friction Reduction lubric­ation is used to reduce friction as well as superc­ond­ucting magnets to stop contact and therefore friction. Vacuums are also used so air resisi­tance is not a factor.

• Smoothing Torque Flywheels are used to keep systems relying on torque running smoothly
• Breaking especially in F1 cars, flywheels are used to harness some of the force when breaking to allow for faster accele­ration afterwards
• Wind Turbines to provide stable power for days without wind and/or peak times
Angular Momentum
Angular Momentum = Iω

x ω
= I
x ω

Angular Momentum
IS** conserved
Angular Impulse
Impulse = Δ(Iω) = TΔt
1st Law of Thermo­dyn­amics
Q = ΔU + W

If energy is transf­erred to the system: Q = +ve
If work is done on the gas: W = -ve
If the internal energy increases:U = +ve

For closed systems, the first law can be applied, also known as non-flow processes as no gas flows in or out. To apply the law, it is assumed to be an Ideal Gas.
Isothermal (Constant temper­ature) Change
ΔU = 0
Therefore Q = W
There is no change in internal energy... no change in temper­ature therefore:
pV = Constant.

pV plot is a curve, with higher lines indicating a higher temper­ature. The work done is the area under the line.

Expansion is and is positive.
Compression is and is negative.
Adiabatic (No heat transfer) Change
Q = 0
Therefore ΔU = -W
pVγ = constant

Steeper gradient than a isotherm's plot. There is a greater amount of work done for an adiabatic change than a isotherm
Isobaric (Constant Pressure) Changes
W = pΔV
Therefore V/T is constant

No work done.
Isometric (Constant Volume) Changes
W = 0
Therefore Q = ΔU and p/T is constant

Work done = area under straight line
Cyclic Process
A System that undergos a number of combin­ations of processes. They start at a certain pressure and volume and return to it at the end of a cycle.
4-Stroke Petrol Engine
• Induction The piston starts at the top of the cylinder, and moves down increasing the volume of the gas above it. A air-fuel mixture is drawn in through an open inlet valve. Pressure remains constant just above atmospheric.
• Compre­ssion The inlet valve is closed, the piston moves up the cylinder. Work is done on the gas, and the pressure increases. Just before the end of the stoke, a spark ignites the air-fuel mixture. Temper­ature and pressure increase.
• Expansion The explosion expands and pushes the piston back down. Work is done as the gas expands, there is also a net output. Just before the bottom, the exhaust valve opens and the pressure reduces.
• Exhaust The piston moves up the cylinder and the burnt gas leaves through the exhaust valve, the pressure remains constant just above atmosp­heric.
4-Stroke Diesel Engine
Induction Stroke Only air is drawn.
Compression The air is compressed enough to have a temper­ature to ignite diesel fuel just before the end of the stroke, diesel fuel is sprayed in and ignites.
Expansion & Exhaust The same as petrol
Indicated Power
= Area of p-V loop x cycles per second x no. of cylinders
The net work done by the cylinder in one second.
Output Power
The useful power at the crankshaft
P = Tω
Friction Power
The power lost due to friction between moving parts
= P
- P
Engine Efficiency
= Calorific Value x Fuel Flow Rate Mechanical Efficiency = P
Affected by energy lost due to moving parts Thermal Efficiency = P
Heat energy transf­erred into work Overall Efficiency = P
2nd Law of Thermo­dyn­amics
Heat engines must operate between a heat source and a heat sink Engine Efficiency = W/Q
= (Q
- Q
Max Theore­tical Efficiency = (T
- T
Heat Engine
A Source of heat (T


Heat Engine W


Heat Sink (T
Reverse Heat Engine
Hot (T


Heat Engine W


Cold (T
A reverse heat engine where the cold space is the actual fridge. Whilst the hot space is the surrou­ndings, the fridges aim is to extract as much heat from the cold space to the surrou­ndings.
Coeffi­cient of Prefor­mance
= Q
/W = Q
) = T
= Q
/W = Q
) = T


Current (I/A)
The rate of flow of charge. Conven­tio­nally running from + to -. Measured my an Ammeter (in series)
I = ΔQ/Δt
Potential Difference (V/V)
The work done in moving a unit charge between 2 points. 1 V = 1JC-1. Measured by a voltmeter (in parallel)
V = IR / V = W/Q
Resistance (R/Ω)
A measure of how difficult it is to move current around the circuit.
R = V/I
Ohmic Conductor
Under constant physical condit­ions, I is propor­tional to V. On a graph of I (y) against V (x), the gradient is equal to 1/R.
Filament Lamp
A filament lamp has an IV charac­ter­istic of a cubic (s shape) going through the origin. The heat in the filament causes the resistance to increase - the particles in the filament vibrate more, meaning its harder for the curren­t-c­arrying electrons to move through it, therefore resistance increases as the current increases.
A diode only allows current to flow in one direction. The IV charac­ter­istic is virtually no current until the threshold voltage, where the voltage increases expone­nti­ally. The threshold voltage is approx. 0.6V
How difficult it is for current to flow through a material. Depends on:
• Length of the wire
• Cross-­sec­tional area
• Resist­ance.
ρ = RA/L
Unit: Ωm
The lower the resist­ivity, the better it is at conducting electricity.

For Reference: Copper: 1.68x10-8 Ωm
A group of materials that arent as good as conducting as metals, however, if more energy is supplied, the resistance lowers more charge carriers are released.
A metal that can be cooled, and the resist­ivity is reduced. There is no resist­ivity below the critical.
The main uses are for strong electr­oma­gnets, power cables with no energy loss and fast electronic circuits with minimal energy loss.
Power (P/W)
The rate of transfer of energy.
1W = 1JS-1

P= E/t = IV = V2/R = I2R
Energy (E/J)
E = ItV = V2t/R = I2Rt

kWh J
kWh x 3.6x106
Electr­omotive Force (e.m.f.)
The amount of electrical energy the battery provides and transfers to each coulomb of charge.
ε = E/Q
Internal Resistance
The resistance inside cells.
ε = I(R + r)
Kirchh­off's First Law
The total current entering a junction is equal to the total current leaving it, i.e. current is split when it reaches a junction
Kirchh­off's Second Law
The total emf of a series circuit, equals the sum of the pd across each component, i.e. pd is split between components in series but not parallel.
ε = ΣIR
Resistance across Circuits
Series: R
= R
+ R
+ R
+ ...
Parallel: 1/R
= 1/R
+ 1/R
+ 1/R
+ ...
Potential Divider
A circuit with a voltage source and resistors in series. The voltage of one of the resisitors can vary and therefore be used to detect certain changes when thermi­stors and LDRs are used.

Gravit­ational Fields

Force Field
A region in which a body experi­ences a non-co­ntact force.
Newtons Law of Gravit­ation
The force a body experi­ences due to gravity is dependant on its weight, the weight of the object exerting the force and the distance between them An inverse square law.
F = GmM/r2
NB The result of this is the magnitude of the force, the direction is always towards the centre of the mass causing the gravit­ational force.
Gravit­ational Field Strength
The force per unit mass, depending on the location of the body in a field.
g = F/m
Also a vector quantity, directed towards the centre of the mass causing the force.

g = -ΔV/Δr
Earth's g
≈ 9.81 Nkg-1
Radial Field
Point masses have a radial gravit­ational field (such as planets):
g = GM/r2
Gravit­ational Potential
The gravit­ational potential energy that a unit mass would have. It is negative on the surface of a mass and increases with the distance from the mass. It can also be considered as the energy required to fully escape the body's gravit­ational pull
V = -GM/r
Gravit­ational Potential Difference
The energy required to move a unit mass. When an object is moved, work is done against gravity ΔW = mΔV
Lines/­Planes that join points of equal gravit­ational potential similar to contour lines on maps.
Along these lines both ΔV and ΔW are zero, the objects energy isn't changing.
Are smaller objects orbiting a larger object, they are kept in orbit by the force due to the larger body's gravit­ational field.

In terms of planets Orbits are ≈ circular, therefore circular motion equations apply.
Orbital Period Propor­tio­nality
T2 ∝ r3
• Combine F=mv2/r and F = GmM/r2 Solve for v
• T = 2πr/v Sub in v
Escape Velocity
The minimum speed an powered object needs to leave the gravit­ational field of a planet
Synchr­onous Orbit
When an orbiting object has an orbital period equal to the rotational period of the object its orbiting
Geosta­tionary Orbit
An satellite in orbit of a body that remains in the same place it has the same time period. It would have to be over the equator to be a true geosta­tionary orbit
Low Orbiting Satellite
Satellites that orbit between 180 and 2000 km above Earth. They are designed for commun­ication and as they are low-orbit, they're cheaper to launch and require less powerful transm­itters.

EM Radiation and Quantum

Photoe­lectric Effect
The emission of electrons from the surface of a metal in response to an incidence light, where the frequency of the incidence light is above that of the metals threshold frequency.
Threshold Frequency
The lowest frequency of light that can cause electrons to be emitted from the surface of a metal.
Work Function
The minimum quantity of energy which is required to remove an electron to infinity from the surface of a given solid, usually a metal.
Φ = hf
Maximum Kinetic Energy
The energy a photon is carrying minus any other energy loses. These energy loses explain the range of kinetic energies of the photons. The max is equal to hf, with no energy loss.
hf = Φ + 1/2(m)(v
Stopping Potential
The potential difference required to stop the fastest moving electrons travelling at E

= E
Electron Volt
The kinetic energy carried by an electron after it has been accele­rated from rest to a pd of 1 V.
1eV = 1.6 x10-19 J
Ground State
The lowest energy level of an atom/e­lectron inside an atom.
The movement of an electron to a higher level in an atom, requiring energy.
ΔE = E
- E
= hf
An electron moving towards ground state releasing energy equal to the difference between the states in the form of a photon.
Fluore­scent Tubes
The tubes contain mercury vapour, when a high voltage is passed across, producing free electrons, which collide with the mercury electrons exciting them. When they return to the ground state, they release a photon in the UV range. These then collide with the tubes phosphorus coating exciting it's electrons, and then when they return to the ground state they release photons in the visible light range
Line-E­mission Spectra
A series of bright lines against a black backgr­ound, with each line corres­ponding to a wavelength of light.
Line-A­bso­rption Spectra
When light with a continuous spectrum of energy (white light) pass through a cool gas. Most of the electrons will stay in their ground states but some will be absorbed and excite them to higher states, these photons are then missing from the spectrum causing black lines on the continuous spectrum.
When a beam of light passes through a narrow gap and spreads out.
Wave-P­article Duality
An entity behaving with both particle and wave-like behaviour. Light has a relati­onship between wavelength and momentum: DeBrog­lie's Wavele­ngth:
λ = h/mv
Electron Diffra­ction
When electrons are accele­rated and sent through a graphite crystal, they pass through the spaces between the atoms producing a diffra­ction pattern


When a wave is bounced back when hitting a boundary
When a wave changes direction as it enters a different boundary medium. The change in direction is as a result of the wave changing speed in the new medium
When a wave spreads out as it passes through a gap or around a obstacle.
Displa­cement (x/m)
The distance a wave has moved from its undist­urbed positi­on/its starting point. It is a vector quantity
Amplitude (A/m)
The maximum magnitude of displa­cement.
Wavelength (λ/m)
The length of one whole oscill­ation of the wave.
Period (T/s)
The time taken for a whole wave cycle.
T = 1/f
Frequency (f/Hz)
The number of whole waves per second, passing a given point.
f = 1/T
A measur­ement of the position if a certain point along the wave cycle
Phase Difference
The amount by which one wave differs from another
Wave Speed
c = fλ
Transverse Wave
The displa­cement of the partic­les­/field is at a right angle to the direction of energy transfer. e.g. a spring shaking up and down as displa­cement and energy transfer is
Longit­udinal Wave
The displa­cement of the partic­les­/fields is along the line of energy transfer
A wave passing through a filter resulting in a polarised wave that oscillates in one direction only. 2 polarising filters at right angles blocks all light as it blocks both direct­ions. Polarising filters are common sunglasses
Glare Reduction
Polarising filters reduces the amount of reflected light therefore reducing the intensity of the light on your eyes
TV Signals
TV signals are polarised by the rod orient­ation on the transm­itting aerial. If the rods are lined up, you receive a good signal.
When 2 waves pass through each, at the instance where the wave cross, the displa­cement is combined, then each wave continues.
Constr­uctive Interf­erence
When 2 waves meet and their displa­cements are in the same direction, the displa­cements combine to give a bigger one.
Destru­ctive Interf­erence
When 2 waves meet and their displa­cement is in opposite direct­ions, they cancel out 'destr­oying' the displa­cement. The displa­cement of the combined wave is the sum of the individual displa­cem­ents.
Exactly Out of Phase
When 2 points on a wave are a odd multiple of 180°/Ⲡ apart.
In phase
When the phase difference of 2 points is 0 or a multiple of 360°/2Ⲡ.
Stationary Wave
The superp­osition of 2 progre­ssive waves with the same freque­ncy­/wa­vel­ength and amplitude moving in opposite directions
A point on a stationary wave where no movement occurs - zero amplitude. There is total destru­ctive interf­erence.
Points on a stationary wave with maximum amplitude - constr­uctive interf­erence
Resonant Frequency
When the stationary wave produced has an exact number of half-w­ave­lengths
First Harmonic
When the stationary wave is at its lowest possible frequency - a single loop with one antinode and a node at each end. To find the freq of the nth harmonic, multiply the 1st harmonics freq. by n.
f = 1/2l x sqrt(T/μ)
where μ is the mass per unit length, T is the tension in the string and l is the length of the vibrating string.
Second Harmonic
Twice the frequency of the 1st harmonic. With 2 loops, 2 antinodes and 3 nodes (one in the center)
Amount of Diffra­ction
When a wave is passed through a narrow gap.
Gap > Wavelength No diffra­ction
Gap = n x Wavelength Minimal Diffra­ction
Gap = Wavelength Maximum Diffra­ction
Monoch­romatic Light
Light of a signal wavele­ngt­h/f­req­uency and therefore a single colour. Best for producing clear diffra­ction patterns.
White Light Diffra­ction
When white light is diffra­cted, the different wavele­ngths of light diffract by different amounts. The result is a diffra­ction pattern of spectra instead of single coloured fringes
Two-Souce Interf­erence
When waves from 2 sources interfere to produce a pattern. In order to get a clear pattern, the sources must be monoch­romatic and coherant
If the waves produce have the same wavele­ngt­h/f­req­uency and have a fixed phase differ­ence.
Double­-Slit Formula
Young's double­-slit formula relate a waves fringe spacing (w/m), its wavele­ngt­h(λ/m), the slit separa­tio­n(s/m) and the distance from the screen­(D/m) into a single formula
w = λD/s
Diffra­ction Grating
Lots of equally spaced slits very close together, produces a sharp interf­erence pattern, therefore allowing more accurate measur­ements. The formula relates the distance between slits (d/m), the angle to the normal (θ/°), the wavelength (λ/m) and the order of maximum(n)
dSin(θ) = nλ
The order of maximum is the number of bright spots away from the central spot (which has order 0)
Refractive Index
A measure of how optically dense a material is - the more optically dense, the higher refractive index.
n = c/c

where c is the speed of light and c
is the speed of light in the material.

Common Refractive Indexes
Vacuum = 1
Glass ≈ 1.5
Water ≈ 1.33

At a boundary:
= c
= n
/ n

The relative refractive index from material 1 to material 2. Note when using the refractive indexes of the materials its 2/1 rather than 1/2 with the speeds.
Snells Law
) = n
When a ray of light travels from one refractive medium to another.
Critical Angle
The angle of incidence at which the angle of refraction = 90° i.e. Sin(θ
) = n
where n
Total Internal Reflection
When all light is completely reflected back into a medium at a boundary with another medium instead of being refracted. Occurs when θ
> θ
Optical Fibre
A very thin flexible tube of glass/­plastic fibre in which light signals are carried across long distances and around corners by applying TIR. The fibres are surrounded by a cladding with a high refractive index and a core of a lower refractive index. The light is refracted where the mediums meet and travels along the fibre.
Signal Absorbtion
When some of the signals energy is absorbed by the material of the fibre. The final amplitude is reduced.
Signal Dispersion
When the final pulse is broader than expected, which can cause inform­ation loss as it may overlap with another signal.
Modal Dispersion
Light entering at different angles and taking different paths, resulting in signals arriving in the wrong order Single­-mode fibre is used to prevent this - light is only allowed to folllow a very narrow path.
Material Dispersion
Different amounts of dispersion depending on wavele­ngth. Monoch­romatic light prevents this.


Rutherford Scattering
An experiment that proved the current model of the atom that it is mostly empty space.

Rutherford set up an experi­ment, with an alpha emitter pointed at gold foil. He observed the deflection of the particles and it showed that atoms have a concen­trated mass at the centre and are mostly empty space, which disproved the plum-p­udding model which was accepted previously.

It showed that:
• Atoms = mostly empty space
• Nucleus has a large positive charge, as some of the +ve charged alpha particles are repelled and deflected
• Nucleus must be tiny due to few particles being deflected by an angle > 90°
• Mass must be concen­trated in the nucleus
Distance of Closest Approach
= E
= Q
where r is the distance of closest approach
Electron Diffra­ction
λ≈hc/E where the first minimum occurs at:
sinθ ≈ 1.22λ/2R
Nuclear Radius
R = R
Alpha Decay (α)
Charge­(rel): +2
Mass(u): 4
Penetration: low
Ionising: high
Speed: slow
Affected by mag. field: y
Stopped by: paper/­~10cm air

Used for: Smoke alarms if the particles cant reach the detector, the smoke must be stopping them
Beta Decay(β^±)
Charge­(rel): ±1
Mass(u): n/a
Penetration: mid
Ionising: weak
Speed: fast
Affected by mag. field: y
Stopped by: ~3mm of aluminium

Used for: PET Scanners, In production of metals the levels penetr­ating through the metal can be used to control the thickness.
Gamma Decay(γ)
Charge­(rel): 0
Mass(u): 0
Penetration: low
Ionising: very weak
Speed: c (speed of light)
Affected by mag. field: n
Stopped by: several cm of lead.

Used for: PET Scanners produced through annihi­lation, cancer treatment.
Background Radiation
The low level of radiation that always exists. Must be taken into account when measuring radiation.
Sources of Background Rad.
• The Air Radioa­ctive radon gas released from rocks
• Ground­/Bu­ildings Nearly all rock contains radioa­ctive materials
• Cosmic Radiation nuclear radiation from particle collisions due to cosmic rays
• Living things living things are made of carbon, some of which is radioa­ctive carbon-14
• Man-Made Radiation from indust­ria­l/m­edical sources
I = k/x2
Intensity (Wm-2) = constant of propor­tio­nality (W)/di­stance from source (m)
Radioa­ctive Decay
It both sponta­neous and random.

Sponta­neous: Decay is not affected by external factors
Random: It cannot be predicted when the next decay occurs
Decay Constant
The probab­ility of a specific nucleus decaying per unit time. It is a measure of how quickly a isotope will decay.
Activity (Bq)
The number of nuclei that will decay each second.

A = λN
where λ is the decay constant, and N is the number of unstable nuclei in the sample

It can also be written as:

ΔN/Δt = -λN
(ΔN is always a decreasing number hence the neg sign)

A = A
is the activity at t=0
Number of unstable Nuclei (N)
N = N
where N
is the original number of the unstable nuclei

N = nN

where n is the number of moles and N
is Avogadro's constant
Half-Life (T
The average time the isotope takes for the number of nuclei to halve.
= ln2/λ

(Derived from N = N
Uses of Radiation
• Carbon Dating Using the amount of C-14 left in the organic material. Problems are that the material may have been contam­inated, high background count, uncert­ainty in c-14 in the past and sample size may be too small
• Medical Diagnosis Tracers that emit radiation to track things in the body
Nuclei are unstable when:
• Too many/not enough neutrons
• Too many nucleons
• Too much energy

If they nuclei lies on the N=Z line they are generally stable. If they lie above, they undergo β- decay, if they lie below, the undergo β+ decay. If they have a Z number of over ~82 (Protons) they undergo α decay.
Mass Defect
The mass of a nucleus is less than the mass of its consti­tuents. This energy difference is the mass defect and is lost to energy as E = mc2, energy and mass are equiva­lent.
Binding Energy
If you were to pull a nucleus apart, this binding energy would be the energy required to do so, equal to the energy released when the nucleus formed.
Average Binding Energy
Average Binding energy per nucleon = Binding Energy­/Nu­cleon number
Nuclear Fission
When large unstable nuclei randomly split into smaller more stable nuclei. Energy is released as the smaller nuclei have a higher avg. binding energy per nucleon
Nuclear Fusion
When 2 smaller nuclei combine to form a larger nuclei. A lot of energy is released because the new heavier nucleus has a higher avg. binding energy (if the 2 original nuclei are light enough). This is the energy that keeps stars burning
Nuclear Fission Reactors
Control Rods Usually made of carbon, they are lowered and raised to control the rate of fission. The amount of fuel required to produce one fission per fission is the critical mass. Any less (sub-c­rit­ical) then the reaction will eventually fizzle out. Any more, and the reactor could go into meltdown, which is why control rods are used.
Moderator Fuel rods are placed in the moderator, this slows down/a­bsorbs neutrons to control the rate. The choice of moderator needs to slow down the neutrons enough to slow down neutrons enough to keep the rate of fission steady. It slows down neutrons through elastic collis­ions, a moderator with a similar nucleo­n-mass to the neutrons.
Coolant is sent around the reactor to remove heat produced by the fissio. The material is either liquid or gas at room temp. Often it is the same water (heavy­-water) as the moderator and can be used to make steam and turn turbines.
Shielding Reactors are surrounded by thick concrete, which shields and protects from radiation escaping and anyone working there.
Emergency Shut-down All reactors have an emergency shutdown where the control rods are completely lowered into the reactor, thus absorbing all the neutrons produced and slowing the reaction down as quickly as possible.
Waste Unused uranium only produces α so can be easily contained. Spent uranium however emit β & γ radiation. Once removed from the reactor they are cooled and ten stored in sealed containers until the activity is at a low enough level.

Further Mechanics

Objects in circular motion travel through angles, mostly measured in radians.
Rads to Deg:
Angle in deg x π/180
Angular Speed
The angle an object rotates through per second.
ω = θ/t = v/r = 2π/T = 2πf
The number of revolu­tions per second.
f = 1/T
Time Period
The time taken for a complete revolu­tion.
Centri­petal Accele­ration
Objects travelling in a circle are accele­rating as their velocity is changing consta­ntly. The accele­ration is always acting towards the centre of the circle.
a = v2/r = ω2r
Centri­petal Force
Is the resolved force which is always directed towards the centre of the circle.
F = mv2/r = mω2r
Simple Harmonic Motion
An object undergoing SHM is oscill­ating to and fro, either side of an equili­brium position.

It is defined as An oscill­ation in which the accele­ration of an object is directly propor­tional to its displa­cement, which is always directed towards the equili­brium position
Displa­cement (x)
Displa­cement varies as a cosine­/sine wave with a maximum value of A (Amplitude)

x = Acos(ωt)
Velocity (v)
Is the gradient of the displa­cement time graph. Its maximum value is ωA

v = ±ω x sqrt(A2 x2)
= ωA

Accele­ration (a)
Is the gradient of the velocity time graph. Its maximum value is ω2A

a = ω2x
Mass-S­pring System
A mass on a spring is a simple harmonic oscillator. When the mass is pulled­/pushed from the equili­brium position, there is a force directed back towards the equili­brium position.

F = kΔL where k is the spring constant and ΔL is the displa­cement.

The Time period for a M-S System is given by:

T = 2π x sqrt(m/k)
A pendulum is an example of a Simple Harmonic Oscill­ator. The time period for a pendulum is given by:

T = 2π x sqrt(l/g)
Free Vibration
Free vibrations involve no transfer of energy to/from the surrou­ndings. If a mass-s­pring system is stretched, it will oscillate at its natural frequency f
Forced Vibration
Forced Vibration occurs when there is an external driving force. A system can be forced to vibrate by a periodic external force. This is called the driving frequency, f

<< f
Both are in phase
>> f
The oscillator will not be able to keep up and will end up out of control. i.e. completely out of phase.
As f
→ f
, the system gains more and more energy from the driving force, thus the amplitude rapidly increases. The system is now considered to be resona­ting. At resonance, the phase difference between the driver and the oscillator is 90°.
Any oscill­ating system loses energy to its surrou­ndings damping. System are also delibe­rately damped to stop them oscill­ating or minimise resonance.

Light Damping Take a long time for oscill­ation to stop, the amplitude is decreased slowly. Displa­cem­ent­-Time Graph: sharp peak.
Heavy Damping The amplitude decreases rapidly, and oscill­ation takes much less time to stop.D­isp­lac­eme­nt-Time Graph: flat peak.
Critical Damping Oscill­ation is stopped in the shortest amount of time possible.
Over Damping Systems with even heavier damping, they take longer to reach equili­brium than a critically damped system.


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