A-Level Physics Key Terms Cheat Sheet by 0llieC

Scalar

A quantity without direction.
Length­/Di­stance, Speed, Mass, Temper­ature, Time, Energy

Equili­brium

When all forces acting on an object are balanced and cancel each other out.  There is no resultant force

Principle of Moments

For a body to be in equili­brium, the sum of the clockwise moments equals the sum of the anticl­ockwise moments.

Couple

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.

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

Veloci­ty-Time Graph

Velocity (y) against Time (x)
Gradient = Accele­ration
ΔGradient = ΔAccel­eration
Area = Displa­cement

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 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.

Freefall

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

Friction

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.

Terminal Speed

When frictional forces equal the driving force. For a falling object, when drag equals the force due to their mass.

Inelastic Collision

Not all of the kinetic energy is conserved. Momentum however is conserved.

Impulse

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.

Power

The rate of work done over time
P = ΔW/Δt
P = Fv  derived from combining P and W = Fs

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.

Density

ρ = m/V
A property all materials have and is indepe­ndent of both shape and size.

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

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 Strain

The ratio of extension to original length, it has no units and is just a ratio.
strain = ΔL/L

Stress­-Strain Graph

Stress (y) against Strain (x).
Gradient = Young's Modulus
Area = strain energy per unit volume

Brittl­eness

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.

Kelvin

A temper­ature scale that is in terms of an atoms movements.
°C  K
+ 273

Internal Energy

The internal energy of a body is the sum of the randomly distri­buted kinetic and potential energies of all its particles

Heat Transfer

Heat is always transf­erred from a hot area/s­ubs­tance to a cold area/s­ubs­tance.

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.

Charles' Law

At a constant pressure: V is directly propor­tional to its absolute temper­ature T
V

1

/T

1

= V

2

/T

2

Molecular Mass

the sum of the masses of all the atoms that make up the molecule.

Avogadro Constant

The number of atoms in exactly 12g of carbon isotope ¹²

6

C.
N

A

= 6.02 x10²³ mol^-1

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.

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.

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).

Nuclide Notation ^A

Z

X

The general notation of elements.

Nucleon Number (A)

AKA Mass Number - number of total nucleons (protons + neutrons)

Isotope

Atoms with the same number of protons but a different number of neutrons. Affects the stability of a atom

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-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.

Antipa­rticle

The corres­ponding antipa­rticle to any particle has the same mass and rest energy but opposite charge.

Annihi­lation

When a particle and antipa­rticle collide producing 2 photons in opposite direct­ions.
E

min

= E

0

This collision is used in PET scanners to detect cancers.

Baryon

A hadron consisting of 3 quarks. All are unstable except a free proton - all eventually decay into a proton.
Proton: uud
Neutron: ddu

Mesons

A hadron consisting of 2 quarks - a quark-­ant­iquark pair. There are 9 possible combin­ations, making either Kaons or Pions.

Lepton Number

Another quantum number that is always conserved. Must be separate for lepton­-el­ectron number and electr­on-muon number.

Strang­eness

Another quantum number - however it can change by ±1 or 0 in an intera­ction.

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.

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 Field

A region where a force acts, force is exerted on magnet­ic/­mag­net­ically suscep­tible materials (e.g. iron).

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

Solenoid

A cylind­rical coil of wire acting as a magnet when carrying electric current. Forms a field like a bar magnet.

LeFt-hand Rule

For finding the direction of the Force.
• Thumb upwards
• First finger forwards
• Second finger to the right (perpe­ndi­cular to f.f.)

Thumb:Force/Motion
First Finger:Field
Second Finger:Current

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

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

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°

Lenz's Law

The induced e.m.f. is always in such a direction that it opposes the change that caused it.

Generator

E

k

is converted into electrical energy, the kinetic energy turns a coil in a magnetic field so that they induce a electric current.

Altern­ating Current

Current that's direction changes over time. The voltage across the resistance goes up and down.

Transf­ormer

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)

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

s

V

s

/I

p

V

p

 power

out

/power

in

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 SUVAT

The SUVAT equations can be applied directly to rotational motion, but with rotati­onal's counterparts:
s  θ (rads)
u  ω

0

v  ω
a  α
t  t

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

net

= T

applied

- T

frictional

Angular Momentum

Angular Momentum = Iω

I

initial

x ω

initial

= I

final

x ω

final

Angular Momentum IS** conserved

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.

Adiabatic (No heat transfer) Change

Q = 0
Therefore ΔU = -W
pV^γ = constant

Steeper gradient than a isotherm's plot. There is a greater amount of work done for an adiabatic change than a isotherm

Isometric (Constant Volume) Changes

W = 0
Therefore Q = ΔU and p/T is constant

Work done = area under straight line

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.

Indicated Power

P

indicated

= Area of p-V loop x cycles per second x no. of cylinders
The net work done by the cylinder in one second.

Friction Power

The power lost due to friction between moving parts
P

friction

= P

ind

- P

brake

2nd Law of Thermo­dyn­amics

Heat engines must operate between a heat source and a heat sink Engine Efficiency = W/Q

H

= (Q

H

- Q

C

)/Q

H

Max Theore­tical Efficiency = (T

H

- T

C

)/T

H

Reverse Heat Engine

Hot (T

H

)

Q

H


Heat Engine  W

Q

C


Cold (T

C

)

Coeffi­cient of Prefor­mance

COP

ref

= Q

c

/W = Q

c

/(Q

h

-Q

c

) = T

c

/(T

h

-T

c

)
COP

hp

= Q

h

/W = Q

h

/(Q

h

-Q

c

) = T

h

/(T

h

-T

c

)

Current (I/A)

The rate of flow of charge. Conven­tio­nally running from + to -. Measured my an Ammeter (in series)
I = ΔQ/Δt

Resistance (R/Ω)

A measure of how difficult it is to move current around the circuit.
R = V/I

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.

Resist­ivity

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

Superc­ond­uctor

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.

Energy (E/J)

E = ItV = V²t/R = I²Rt

kWh  J
kWh x 3.6x10⁶

Internal Resistance

The resistance inside cells.
ε = I(R + r)

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

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.

Force Field

A region in which a body experi­ences a non-co­ntact 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

Radial Field

Point masses have a radial gravit­ational field (such as planets):
g = GM/r²

Gravit­ational Potential Difference

The energy required to move a unit mass. When an object is moved, work is done against gravity  ΔW = mΔV

Satellite

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.

Escape Velocity

The minimum speed an powered object needs to leave the gravit­ational field of a planet

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

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.

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

0

Stopping Potential

The potential difference required to stop the fastest moving electrons travelling at E

k(max)

eV

s

= E

k(max)

Ground State

The lowest energy level of an atom/e­lectron inside an atom.

De-Exc­itation

An electron moving towards ground state releasing energy equal to the difference between the states in the form of a photon.

Line-E­mission Spectra

A series of bright lines against a black backgr­ound, with each line corres­ponding to a wavelength of light.

Diffra­ction

When a beam of light passes through a narrow gap and spreads out.

Electron Diffra­ction

When electrons are accele­rated and sent through a graphite crystal, they pass through the spaces between the atoms producing a diffra­ction pattern

Reflection

When a wave is bounced back when hitting a boundary

Diffra­ction

When a wave spreads out as it passes through a gap or around a obstacle.

Amplitude (A/m)

The maximum magnitude of displa­cement.

Period (T/s)

The time taken for a whole wave cycle.
T = 1/f

Phase

A measur­ement of the position if a certain point along the wave cycle

Wave Speed

c = fλ

Longit­udinal Wave

The displa­cement of the partic­les­/fields is along the line of energy transfer

Glare Reduction

Polarising filters reduces the amount of reflected light therefore reducing the intensity of the light on your eyes

Superp­ostion

When 2 waves pass through each, at the instance where the wave cross, the displa­cement is combined, then each wave continues.

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.

In phase

When the phase difference of 2 points is 0 or a multiple of 360°/2Ⲡ.

Node

A point on a stationary wave where no movement occurs - zero amplitude. There is total destru­ctive interf­erence.

Resonant Frequency

When the stationary wave produced has an exact number of half-w­ave­lengths

Second Harmonic

Twice the frequency of the 1st harmonic. With 2 loops, 2 antinodes and 3 nodes (one in the center)

Monoch­romatic Light

Light of a signal wavele­ngt­h/f­req­uency and therefore a single colour. Best for producing clear diffra­ction patterns.

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

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

Refractive Index

A measure of how optically dense a material is - the more optically dense, the higher refractive index.
n = c/c

s

where c is the speed of light and c

s

is the speed of light in the material.

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

At a boundary:

1

n

2

= c

1

/c

2

= n

2

/ n

1

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.

Critical Angle

The angle of incidence at which the angle of refraction = 90° i.e. Sin(θ

crit

) = n

2

/n

1

where n

1

>n

2

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 Dispersion

When the final pulse is broader than expected, which can cause inform­ation loss as it may overlap with another signal.

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

Electron Diffra­ction

λ≈hc/E where the first minimum occurs at:
sinθ ≈ 1.22λ/2R

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

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.

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

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

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

0

e^-λt
A

0

is the activity at t=0

Half-Life (T

1/2

)

The average time the isotope takes for the number of nuclei to halve.
T

1/2

= ln2/λ
(Derived from N = N

0

e^-λt)

Instab­ility

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.

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.

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 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.

Radian

Objects in circular motion travel through angles, mostly measured in radians.
Rads to Deg:
Angle in deg x π/180

Frequency

The number of revolu­tions per second.
f = 1/T

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

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

Velocity (v)

Is the gradient of the displa­cement time graph. Its maximum value is ωA

v = ±ω x sqrt(A² x²)
v

max

= ωA

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)

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

n

.

Resonance

As f

d

→ f

n

, 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°.