EVERYTHINGGGGGG! Flashcards
Differentiate
x by power -1 from power
Integrate
+1 to the power / by power (+c)
Straight line Motion
v=ds/dt
a=dv/dt=d²s/dt²
Constant Acceleration only
v=u+at
s=ut+1/2at²
v²=u²+2as
v—-a
differentiate
s—-v
differentiate
a—-v
integrate (+c)
v—-s
integrate (+c)
ω
angular velocity (rad s⁻¹)
α
angular acceleration (rad s⁻²)
difference between linear and angular velocity equations
s swapped for θ
f
frequency = no of rotations per second (hz)
Equations for centripetal motion
aᵣ= v²/r=rω²
F=mv²/r=mrω²
aᵣ
centripetal acceleration
when t=0
v=x so c=x
s=0 so c=0
In what direction does Centripetal force act
towards the centre of the circle
why would a spinning objects angle decrease when speed decreases
tension (horizontal component) decreases and weight (vertical component) remains constant so angle decreases
calc θ of string
Triangle (tension=x, weight=y, Tanx=x/y)
Find rad from deg
x by 57.3
θ
Angular Displacement
what does centripetal force result in?
centripetal acceleration of the object
aᵣ
centripetal acceleration
what does an unbalanced torque result in?
a change in the angular (rotational)
motion of an object.
MOI
a measure of an objects resistance to angular
acceleration about a given axis.
formula include I=xmr²
Angular Momentum
L=Iω
L=mvr=mr²ω
Conservation of Angular momentum
Eₚ=Eₖ₍ₜᵣₐₙₛₗₐₜᵢₒₙₐₗ₎+Eₖ₍ᵣₒₜₐₜᵢₒₙₐₗ₎
Eₖ=1/2Iω²
gravitational field strength is?
gravitational force acting on a unit mass.
W=mg rearranged to g=W/m
(W=mg can also be substituted into F=GMm/r² to find gfs)
Gravitational Force
F=GMm/r²=mv²/r=mr²ω=mr(2π/T)²
hoops and rings equation
point mass
Gravitational potential is
the work done in moving
unit mass from infinity to that point
V=
Grav potential
Voltage
escape velocity is
the minimum velocity required to allow a mass to
escape a gravitational field to infinity, where the mass achieves zero kinetic energy and
maximum (zero) potential energy.
Difference between General and Special relativity
special relativity deals with motion in inertial (non-accelerating) frames
of reference and that general relativity deals with motion in non-inertial (accelerating)
frames of reference
State the equivalence principle
it is not possible to distinguish between the
effects on an observer of a uniform gravitational field and of a constant acceleration
What is spacetime?
a unified representation of three dimensions of space
and one dimension of time
What leads to the interpretation that mass curves
spacetime, and that gravity arises from the curvature of spacetime
General relativity
escape velocity from the event horizon of a black hole is equal to
the speed of light
where does time appear to be frozen
at the event horizon of a black hole
What is the Schwarzschild radius
distance from its centre
(singularity) to its event horizon
Photon energy and frequency
E=hf
n=
principle quantum number and refractive index
what proves that light behaves like a wave
(double slit experiment)
Tell me about waves
Waves transfer energy.
Wave energy is dependent on the amplitude
of the wave.
Intensity ∝ (amplitude)², where wave
intensity is power per unit area.
Energy transfer is not affected by wave
frequency
As temperature
increases
intensity increases at
every wavelength.
Peak wavelength (λmax) reduces.
Assumptions made in the Bohr model
electrons can
orbit in specific stable orbits
without emitting radiation.
The angular momentum of
electrons is quantised. i.e. Angular
momentum can only take values
that are integer multiples of h/2π.
Centripetal force can be equated to what?
e.g. Derive an equation for the kinetic energy of an electron?
electrostatic force or mag flux density
Electrostatic force (coulombs law)
F=Q₁Q₂/4πε₀r²
State Heisenburg’s uncertainty principle
It is not possible to know the
position and momentum of a
quantum particle simultaneously
(even in theory).
what proves that light behaves like a particle
Photoelectric effect
What is the De Broglie interpretation of the double slit experiment?
the electron goes through both slits
simultaneously as its wavelength is
bigger than the slit separation
What did De Brogli realise about particles
when a particle shows wavelike properties, its wavelength (de Broglie wavelength) is inversely proportional to its momentum
λ=h/p
Not Heisenburg’s principle?
it is not possible to know the lifetime of a quantum particle and the
associated energy change simultaneously
quantum particle uncertainties
ΔxΔpₓ > or equal to h/4π
ΔEΔt > or equal to h/4π
lifetime of quantum particle
consider it an uncertainty in time
B=
Magnetude of a magnetic field (magnetic induction or magnetic flux density)
Measured in T (Tesla)
Define SHM
Displacement is proportional to and in the opposite direction to the acceleration (think of a pendulum)
Show that y=Acosωt is consistent with SHM
double differentiate (gets acceleration)
Substitute y in
Explain how its consistent (compare to a=-ω²y)
Talk about damping
Underdamping: Moves quickly towards the equilibrium but continues to
oscillate
Overdamping: Moves slowly towards the equilibrium and does not oscillate
Critical damping: Moves as quickly as possible towards the equilibrium and does
not oscillate
What do all SHM formulae have in them (excluding angular frequency ω=2πf=2π/T formulae)
y
A=
Amplitude Surface area (in square meters - star stuff)
energy transferred by a
wave and its amplitude
E=kA²
wave motion, phase
difference and phase angle
y=Asin2π(ft-x/λ)
Φ=2πx/λ
How are stationary waves formed?
by the interference of two waves, of the same
frequency and amplitude, travelling in opposite directions. A stationary wave can be
described in terms of nodes and antinodes
Φ=
Phase difference (seperation of 2 points on a wave as a fraction of the λ) (the x co-ordinate in π’s)
L=
Angular momentum (N C-1)
Luminosity (in star stuff)
Inductance (H)
b=
Apparent brightness (in star stuff)
What are Farads a unit of?
Capacitance
Electric field strength
E=F/Q or F=QE
E=
Energy
Electric Field Strength
Define Electric Field Strength
EFS is the electrical force acting on unit POSITIVE charge at a given point
How is a Stationary wave formed
By constructive interference of two waves of the same frequency and amplitude travelling in opposite directions
Coherence?
Constant phase relationship
Same frequency, wavelength and speed
Constructive interference and Destructive
Two coherent waves of equal amplitude meet in phase to form a wave of twice the amplitude
Two coherent waves of equal amplitude meet out of phase they combine to form a wave of 0 amplitude
Div of Amp and Wavelength
Interference of light produced by thin oil films, coated camera lenses and thin wedge interference
Interference caused by youngs double slit
Brewsters angle
Angle of incidence that causes reflected light to be fully plane polarised
When there is a 90 degree angle between the reflected angle and refracted rays
Plane polarised wave
When the electric field oscillations occur in only one plane
Which one is bigger in interference D or d
D
I=
Moment of Inertia (kg m2)
Current (A)
l=
Length (m)
Force acting on a wire
F=IlBsinθ
We get given a mass and not B
Use W=mg
Derive Escape velocity
Ek-Ep=0
1/2mv2-GMm/r=0
Rearrange
What path does light (or a freely moving object) take
A geodesic path (the shortest possible route)
What assumption do we make using Luminosity, Apparent Brightness and other stellar formulae
That the star behaves as a black body
State the principal of quantum tunnelling
a quantum particle can exist in a position that, according to classical physics, it has insufficient energy to occupy.
