1/28
Keywords for each paragraph I might need to write to ensure the best grade
Centre of mass & momentum
Momentum of the system is conserved, no external force, zero momentum at right angles (This would be before collision so you got to say the forces that come out after are “Equal and Opposite”),
Circular Motion
Net centripetal force towards the centre, Verticle Circle Fc = Fr - Fg at bottom and Fc = Fg + Fr at top, Feeling of weight depends on the size of reaction force
Space/Gravity
Feeling of weight is from a support force and since both the ISS and Astronaut are freefalling at the same acceleration the floor doesn’t have a support force, Unbalance centripedal force is required (If balanced the net forces would be 0 and it would fly off on a tangent)
Rotation 1
If you have 2 thrusters on both sides vs 1 on 1 side the 2 can make a torque without a net force changing the orbit, vs 1 can’t
Rotaional Energy 2
Ep = EK(Lin) + EK(Rot). Closer to axis of rotation, angular acceleration, larger rotational inertia, Not much to say you know the rest
Angular momentum
closer to axis of rotation, angular momentum is conserved, EK(Rot) can change whilst momentum is conserved, no external net torque so angular momentum conserved,
Extra stuff!!!
Tension T = m(g-a), Torque is Nm NOT Nm-1, I (Inertia) = kgm2, L = kgm2s-1 (Crucial Remember),
SHM
Frequency/Period is constant, A point of equilibrium is required, and a restoring force which is proportional to the displacement from the equilibrium point. 10 degree approximation is used for T = 2pi x sqrt (l/g) equations.
Resonance
Periodic Driving force, in phase, same direction as the swing’s motion, positive work done, total energy builds up, Ep increase at the top so amplitude increases, this is resonance,
Dampening
Ep transforms to Ek and back, Friction acts against the motion, energy is lost from the system as heat so total energy decreases, the amplitude decreases until object x comes to rest at equilibrium, period stays the same (bc proportional to displacement)
UNITS TO REMEMBER
G = 109
M = 106
k = 103
m = 10-3
𝜇 = 10-6
n = 10-9
Small angle approximation
For within 10 degrees either direction you can us nλ = dx/L
d = slit grating
x = distance between 0th maxima and point your looking for
L = distance between the wall and grating
Interference Patterns, (White light/rainbow formed)
At the centre the path difference from adjacent slits is zero for every wavelength, all colours arrive in phase and constructively interfere to make white light, Violet shortest (smallest angle), Red longest, largest angle on the outside every other colour falls in between forming a complete spectrum in each order on each side, All colours have their own wavelength.
Interference pattern
Diffraction grating will be sharper than slits and brighter maxima, More slits more light gets through so brighter, Grating will be brighter as more waves will Arrive in phase therefore Superimposing constructively to have a brighter maxima, Maxima will be sharper since interference that isn’t the maxima have more waves, and if adjacent slits waves are slightly out of phase, the phase differences add up across all the slits so the overall interference is destructive. , Wide Dark Regions, With only 2 slits the phase difference changes Gradually, so the brightness changes gradually.
Slit Seperation
The closer the slit seperation the d is smaller from nλ = dsin theta, so a larger d gives a smaller angle between maxima’s
Doppler Effect
it moves towards the wavefronts it has already emitted, so each new wavefront starts closer to the one infront, wavefronts are bunched so the wavelenght reaching Dave is shorter, The speed of sound is unchanged, so from v = fλ he hears a higher frequency, the component of velocity towards him quickly changes, so the frequency drops steeply, moving away wavefronts are stretched λ longer, so he hears a constant lower frequency. Driver hears the true frequency throughout because there is no relative motion between her and the horn
If split into parts doppler effect
Talk about At A, then From A to B, then At B, then from B to C, then At C, and the true frequency normally only at B, and at A and C they both hear same frequency, and between points the gradient changes differently due to component of velocity towards the person is different and changes more gradually.
Harmonics and Standing Waves
Harmonics are a whole number multiple of the fundamental, how standing waves form, Sound waves travel down the pipe, reflect off of the closed end and interfere with incoming waves to make nodes, and antinodes, Open ends: waves reflect with no phase change, Closed ends: waves reflect with 180 out of phase, Your blowing makes many frequencies, only the resonant ones constructively interfere to make resonance, the other one interfere with each other quickly destructively interfering, multiple reflections reinforce each other … give standing wave … energy builds up so the pipe resonates.
Nodes, and Antinodes
Antinode = Maximum amplitude and In phase, Node = no amplitude and Out of phase
Beats
A beat is a regular pulsing in loudness, caused by slightly different but similar waves (diff frequencies), they alternately move in and out of phase, constructively loud, destructively quiet
Resonance
x is being shaken by the natural frequency, instrument frequency matches the natural frequency of x, so energy is transferd with few losses, meaning the oscillation builds up, to a maximum amplitude and x shakes/rattles.
Spark when opening switch with inductor
A spark is formed since current almost instantly drops to 0, air gap makes very high resistance this means time constant = L/R becomes very small, Rapid change in current induces a large EMF across the inductor, The circuit is open so it’s not limited to 12.6 V (EMF voltage), This is able to jump the gap and make a spark.
Inductor keywords
Opposes the increase/decrease in current, gradient/gradual ,back EMF,
Capacitors/Capacitance
Capacitor discharges, the charge on its plates decreases, so the voltage across it decreases (in turn so does current), Current is slower … lower rate of current flow means charge is lost more slowly, there fore current, and voltage slow, giving it and exponential decrease, Rate of change is proportional to the remaining amount!!!
Things to know about capacitors
Capacitance in circuit is opposite from resistance, Capacitors can be charged in a circuit separately then reconnected, and look for that possibility. Capacitors in series voltages add up, whilst in parallel they just become 1.
Voltage laws for a battery charging another
Net EMF, so battery charging - normal battery, Net EMF/Total Resistance, this makes current. Also to calculate the terminal voltage across the battery it’s EMF + IR
What is EMF?
EMF - The energy supplied to each coulomb of charge by the battery (before lost to internal resistance) - the terminal voltage when no current is drawn!
Internal Resistance
When no current flows the voltmeter reads EMF, when the voltmeter is measuring the same circuit with current some of the voltage is lost across the internal resistance. More current through the internal resistance means a greater potential drop inside the battery, leaving less voltage for the external circuit.
Electromagnetic induction & Transformers
alternating current in the primary, makes alternating magnetic flux in core, changing flux passes through the secondary and induces an alternating voltage in it (Faraday’s Law). Eddy Currents in Lenz’s law create an opposing magnetic field, opposing the changing magnetic flux, therefore opposing movement of a magnet through a metal ring which has induces a current in the ring, which therefore induces a magnetic field to oppose it. Lenz’s Law. Closer to ring stronger induced field, e.g approaching, increasing field strength opposing, and moving away decreasing strength. Iron rod guides the flux through to the secondary coil, and the iron increases magnetic flux.