All formulas and definitions for end of year Flashcards
SI Base; Quantities, Units, Symbol
Time, s, t
Mass, kg, m
Distance, m, (s) d
Amount of atoms, mol, n
Current, A, I
Temperature, K, T
Prefix; names, symbols, powers
pico (p) 10^-12
nano (n) 10^-9
micro (μ) 10^-6
mili (m) 10^-3
kilo (K) 10^3
mega (M) 10^6
giga (G) 10^9
tera (T) 10^12
peta (P) 10^15
exa (E) 10^18
Precision-Uncertainty of measuring equipment
Ruler: 1mm ± 0.5mm
Vernier caliper: 0.01mm ± 0.1mm
Micrometer: 0.001mm ± 0.01mm
Digital scale: 0.01g ± 1g
Stopwatch: 0.1s ± 0.2s *
*or range divided by 2
Evaluating measurements, (the types of errors)
Systematic error: results in all values shifting from true value by the same amount
(high precision and low accuracy)
Random error: results in scattering of data about true value
(high accuracy and low precision)
Accuracy: How close data points are to theoretical value
Precision: How consistent data points are
Uncertainties (calculations for each)
Absolute uncertainty (addition and subtraction):
∆c = ∆a + ∆b
Percentage uncertainty (division and multiplication):
c = a x b
%c = %a + %b
c ± ∆c = ∆c / c x 100 = %c
Powers:
c = a x bˣ
%c = %a + x%b
Data presentation, (rules for sf and dp in answers)
Values:
addition and subtraction; results must have same d.p as values used
multiplication and division; results must have number of s.f as value with least s.f
Absolute uncertainty in 1 s.f
Percentage uncertainty in either 2 or 3 s.f
Precision:
compare precisions and reduce precision of more precise value to match less precise value
final value and uncertainty must have same precision
the last s.f in value must be in the same place as the uncertainty
Speed formula
average speed = distance / time
v = d / t
Average speed definition
the total distance travelled by an object divided by the total time taken
Displacement definition
the distance travelled in a particular direction
Vector quantities
has both a magnitude (size) and direction
Scalar quantities
has only a magnitude (size)
Velocity definition
rate of change of displacement
Velocity formula
change in displacement / time taken
v = s / t
Displacement-time graphs
velocity = gradient of displacement-time graph
Resultant vector
the single vector formed by adding 2 or more vectors
Acceleration definition
the rate of change of velocity of an object
Acceleration formula
a = ∆v / ∆t
a = (v - u) / t
d = 1/2at²
Velocity-time graphs
acceleration = gradient of a velocity-time graph
displacement = area under a velocity-time graph
Equations of motion (Kinematic equations)
v = u + at
s = ( [v + u] / 2 ) x t
Acceleration caused by gravity
9.81ms⁻¹
Free fall definition
when an object accelerates due to gravity in the absence of any other forces such as air resistance
Sinusoidal functions from angle θ
vector component through θ is cosine
vector component away from θ is sine
Resultant force formula
resultant force = mass x acceleration
F = ma
Newton’s second law
resultant force is proportional to rate change of momentum
Inertia definition
a measure of how difficult it is to change the velocity, speed or direction of an object
Weight definition
the force on an object caused by a gravitational field acting on its mass
Centre of gravity definition
the point on a body where the entire weight of the body is considered to act
Weight formula
weight = mass x acceleration of free fall
W = mg
Newton’s first law of motion
an object will remain at rest or in a state of uniform motion unless it is acted upon by a resultant force
Terminal velocity definition
the maximum velocity reached by an object falling under gravity or accelerated by a constant force due to; the net force being zero as the upward force is equal to the weight of the object
Newton’s third law of motion
when 2 bodies interact, the forces they exert on each other are equal in size and opposite in direction
Newton definition
one newton is the force that will give a 1kg mass an acceleration of 1ms⁻² in the direction of the force
Equilibrium definition
an object in equilibrium is either at rest or travelling with constant velocity because its resultant force is zero
Moment of a force
the moment of a force about a point is the product of the force and perpendicular distance from the line of action of the force to the point, the turning effect of a force
Principle of moments
the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about the point provided the body is in equilibrium
Torque definition
the product of one of the forces and the perpendicular distance between the forces
Work done formula
work done = force x distance
W = F x s
W = Fs {cos or sin} θ
work done = energy transferred
Joule definition
the work done when a force of one newton moves a distance of 1m in the direction of the force
Gravitational potential energy definition
the energy a body has gained/lost due to its position in a gravitational field
Gravitational potential energy formula
change in gpe = weight x change in height
∆Ep = mg∆h
Kinetic energy formula
kinetic energy = half mass x speed squared
Ek = 1/2mv²
Efficiency formula
efficiency =
(useful output energy / total input energy) x 100
Principle of conservation of energy
energy cannot be created or destroyed, it can only be changed from one form to another
Power definition
the power of a device is the rate at which it does work, or work done per unit time
Power formula
power = work done / time taken
power = force x velocity
power = change in energy / time
P = W / t
P = F x v
P = ∆E / t
Watt definition
one watt is one joule per second
Linear momentum formula
momentum = mass x velocity
p = mv
Conservation of momentum
the sum or total momentum of the bodies in a closed system is constant
Perfectly elastic collision
in a perfectly elastic collision, the total kinetic energy of all the bodies remains constant
relative speed of approach equals relative speed of separation
Inelastic collision
in an inelastic collision, kinetic energy is not conserved some is transferred to other forms such as heat
total kinetic energy reduces
Resultant force equation (definition and formula)
resultant force is proportional to rate of change of momentum
F = ∆p / ∆t
Density formula
density = mass / volume
ρ = m / V
Pressure formula
pressure = normal force / cross-sectional area
p = F / A
Pressure beneath a liquid formula
change in pressure =
density x acceleration due to gravity x depth
∆p = ρgh
Archimedes’ principle (def)
the upthrust acting on a body is equal to the weight of the liquid or gas that it displaces
Upthrust formula
upthrust = weight of liquid displaced
upthrust = ρgV
Spring constant formula
spring constant = force / extension
k = F / x
Hooke’s law definition
provided the elastic limit is not exceeded, the extension of an object is proportional to the applied force (load)
Elastic deformation
an object that returns to its initial length when the force is removed has deformed elastically
Plastic deformation
an object that does not return to its initial length when force is removed is deformed permanently, it has deformed plastically
Limit of proportionality
the point beyond which the extension (of a spring) is no longer proportional to the force
Elastic limit
the value of stress beyond which an object (such as a spring) will not return to its original dimensions
Strain formula
strain = extension / original length
ε = x / L
Stress formula
stress = normal force / cross-sectional area
ε = F / A
Young’s modulus formula
young modulus = stress / strain
E = σ / ε
Energy stored in a body due to a change in its shape
elastic potential or strain energy
Force-extension graphs
work done/strain energy = area under force-extension graph
spring constant = gradient
Elastic potential energy formula
E = 1/2Fx
E = 1/2kx²
Quantised meaning
a quantity is said to be quantised when it has a definite minimum magnitude and always comes in multiples of that magnitude
Current meaning
the rate of flow of electric charge past a point
Ampere meaning
one coulomb of electric charge moving past a point in a second
Coulomb meaning
one coulomb is the
charge that flows
past a point in a circuit
in a time of 1 second
when the current is 1 A abbreviated to C
Charge equation
∆Q = I∆t
charge = current x time
Elementary charge
e = 1.6 x 10⁻¹⁹C
Current equation
I = Anqv
Potential difference definition
the potential difference (V), between 2 points is the energy transferred per unit charge
as it moves from one point to the other
Voltage equation
V = ∆W/∆Q
Emf definition
the energy transferred per unit charge in driving charge around a complete circuit
Electrical resistance definition
the ratio of potential difference to current (ohm)
Resistance equation
R = V/I
resistance = potential difference / current
Ohm meaning
the ohm is the resistance of a component when a pd of 1V drives a current of 1A through it
Power equations
P = VI
P = I²R
P = V²/R
Kirchhoff’s first law
the sum of the currents entering any point in a circuit is equal to the sum of the currents leaving that same point
Conservation of charge meaning
electric charge can neither be created nor destroyed
Kirchhoff’s first law equation
∑Iᵢₙ = ∑Iₒᵤₜ
Kirchhoff’s second law definition
the sum of the emfs around any loop in a circuit is equal to the sum of the p.d.s around the loop
Kirchhoff’s second law equation
∑E = ∑V
Total resistance of resistors in series
Rₜ = R₁ + R₂ + R₃ + …
Total resistance of resistors in parallel
1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃ + …
Ohm’s Law definition
A conductor obeys Ohm’s law if the current in it is directly proportional to the potential difference across its ends
NTC thermistor
A device whose resistance decreases rapidly when the temperature increases
Threshold voltage
The minimum forward potential difference across a diode at which it starts to conduct
Light-dependant-resistor
A component whose resistance decreases when the light intensity increases
Resistivity meaning
A property of a material; it is a measure of its electrical resistance, defined by ρ = RA/L, unit Ω
Resistance equation
R = ρL/A
resistance = (resistivity x length) / cross sectional area
Internal resistance meaning
The internal resistance of a source of emf is the resistance inherent in the source itself; some energy is transferred into other forms as work is done in driving charge through the source itself
Terminal pd
the potential difference across the terminals of a source and is dependant on the current that is taken from the source
Potential difference across a power source equation
V = E - Ir
Potential divider equation
Vₒᵤₜ = ( R₂ / [R₁ + R₂] ) x Vᵢₙ
where R₂ is the resistance across the component where Vₒᵤₜ is
Emf comparison equation
To compare 2 emfs Eₓ and Eₒ
Eₓ = (AY/AB) x Eₒ
Progressive wave meaning
a wave that carries energy from one place to another
Wave meaning
a periodic disturbance travelling through space, characterised by a vibrating medium
Displacement meaning (waves)
the distance of a point on the wave from its undisturbed or equilibrium position
Amplitude meaning
the maximum displacement of a wave
Wavelength meaning
the distance between 2 adjacent points on a wave oscillating in step with each other
Period meaning
the time taken for one complete oscillation of a point in a wave
Frequency meaning
the number of oscillations per unit time of a point in a wave
Longitudinal wave meaning
a wave in which the particles of the medium oscillate along in the direction in which the wave travels
Transverse wave meaning
a wave in which the particles of the medium oscillate at right angles to the direction in which the wave travels
Compression meaning
the point in a sound wave at which the air pressure is at maximum
Rarefaction meaning
a region in a sound wave where the air pressure is less than its mean value
Phase difference meaning
the fraction of a cycle between 2 oscillating particles, expressed in either degrees or radians
Phase difference calculation
∆Φ = [x / λ] * 180º or 2π
Intensity formula
intensity = power / area
Intensity equation
Intensity ∝ amplitude²
Intensity meaning
intensity is the rate of energy transmitted (power) per unit area at right angles to the wave velocity
Wave speed formula
v = λf
Doppler effect
the change in frequency or wavelength of a wave observed
when the source of the wave is moving towards or away from the observer
(or the observer is moving relative to the source)
Doppler effect formula
f’ = f(V𝓌 / V𝓌 ± Vₛ)
Magnetic field meaning
a force field in which a magnet, a wire carrying current or a moving charge experiences a force
Electromagnetic wave meaning
a transverse wave travelling through space as vibrations of electric and magnetic fields
Wavelength ranges of em waves
Frequency ranges of em waves
Frequency, em wave, Wavelength
3 x 10¹¹ • radio • 10⁴
10¹² • micro • 10⁻²
10¹³ • infrared • 10⁻⁶
visible**
10¹⁵ • ultraviolet • 4 x 10⁻⁸
10¹⁷ • x-ray • 10⁻¹²
10²² • gamma-ray • 10⁻¹⁶
** 4 x 10¹⁴ • red • 7 x 10⁻⁷
** 7 x 10¹⁴ • violet • 4 x 10⁻⁷
Electric field meaning
a force a field in which an electric charged particle experiences a force
Plane polarised meaning
describes a transverse wave with oscillation in just one plane, only transverse waves can be polarised
Malus’ Law formula and conditions for application
I = I₀cos²θ
Only applies to polarised light and if the light is not polarised the it always has half the intensity. With the new intensity value that is half the original you can use the formula
Mass
measure of a body’s resistance to changes in motion
Principle of superposition
when 2 or more waves meet at a point, the resultant displacement is the sum of the displacements of the individual waves
Path difference equation
pd = nλ
whole number n values: constructive interference
half number n values: destructive interference
Double-slit equation
λ = ax/D
Sn = λD/d
a: slit separation*
x: fringe separation
D: slit to screen distance
* can have notation d as well
Wavelength with a diffraction grating equation
d sinθ = nλ
Wavelength formula
λ = c / f
where c is the speed of light for any em wave
Coherence meaning
When 2 or more waves have a constant phase difference
Interference meaning
when 2 or more waves meet at a point, the resultant displacement is the sum of the displacements of the individual waves
Formula for wave minima
θ = nλ / a
a can be written as d
How to solve CRO questions
Given the time-based setting:
1. Count how many full wavelengths they are if the positioning of the waves makes it hard to see
2. Count how many divisions or boxes are in this
3. Place the number of complete waves as the coefficient for T and equate it to the number of divisions multiplied by the time-based setting
4. Solve the equation and hence calculate the speed.
Given the frequency:
1. Calculate the period (T = 1/f)
2. Convert the period into the preferred units
3. Divide the period by the number of divisions per wavelength
4. Calculate and solve
Young’s Modulus for common materials
Copper: 130 Gpa
Steel: 215 Gpa
Iron: 213 Gpa
Stationary wave with both ends fixed/open
λₙ = [2/n] x L
fₙ = Vₙ / 2L
Both ends fixed, node at both ends
Both ends open, antinode at both ends
Stationary wave with one end fixed and one end open
λₙ = [4/n] x L
fₙ = Vₙ / 4L
Node at fixed end and antinode at open end
Solving Barometer and Manometer Questions
Equate the pressures at each boundary
Find the pressure difference at each boundary using the difference in height
Equate these pressures to the original equations
Rearrange then solve the equation
Baryon
Hadron made up from 3 quarks or 3 antiquarks
Meson
a hadron made up of a quark and an antiquark
Down quark to up quark in β⁺ decay
d –> u + ⁰₋₁e + v⁻ *
Force interactions
between proton and electron is EM
electron coming out of nucleus is weak
quark to quark is strong force
Derivation of resistance
Series:
V = IR
Vₜₒₜₐₗ = 1R₁ + IR₂ + IR₃
Rₜₒₜₐₗ = R₁ + R₂ + R₃
Parallel:
I = V / R
Iₜₒₜₐₗ = V / R₁ + V / R₂ + V / R₃
Rₜₒₜₐₗ = (1 / R₁ + 1 / R₂ + 1 / R₃)⁻¹
