THE ULTIMATE PHYSICS SUMMARY SHEET
Author: Minna Pöntinen
- Does not include mechanics
- Be careful, subscripts are usually not used
¤ = change in
# = theta (unless otherwise specified)
WAVES
- each particle oscillates about an equilibrium point
- no matter is transferred, only energy
- a pariodic/continuous wave has a source that is constantly oscillating -> source of any wave is vibration
- crest (the top point), through (the lower point), amplitude (from the top to middle), wavelength (crest to crest)
- f is the number of complete crests (or complete cycles) that pass a given point per unit of time; period
- velocity depends only on the properties of medium of travel
- transverse wave = /\/\/\ = vibr. of particles perpendicular to the direction of the wave’s
- longitudinal wave = ||/\/\|| = vibr. of particles to the same direction of the wave’s (example: light)
Formulae I
- F = -kx
- T = 1/f
- v = lambda*f
- v = sqr [Ft/(m/L)] (wave on a string with a small amplitude)
- 4A/T (particle velocity)
- E = ½kA² (particle’s energy for a sinusoidal wave of frequency f)
- I = (E/T)/A = P/A; A2/A1 = r1/r2
Reflection, interference & standing waves
- Fixed end: the wave changed direction & is transformed upside-down
- Loose end: only direction changes
- Interference: overlapping waves add up (destructive & constructive interference)
- A standing wave doesn’t appear to move
- Must vibrate at a certain frequency
- fundamental = 1st harmonic = f1 = L = ½theta1
- 1st overtone = 2nd harmonic = f2 = L = theta2
- L = n*thetan/2
- The frequency at which standing waves are produced are the natural frequencies (or resonant frequencies) of the cord
Sound
- V = (331 + 0.60T) m/s (velocity of sound in air)
- B (in dB) = 10log1/I
- Pressure in the air is the opposite displacement of air
- Tube open at both ends:
- >< = 1st harm -> L = ½theta1, f1 = v/2L
- ><>< = 2nd harm -> L = theta2, f2 = v/L = 2f1
- Tube closed at both ends (only odd harmonics!):
- > = 1st harm -> L = 1/4theta1, f1 = v/4L
- ><> = 3rd harm -> L = 3/4theta3, f3 = 3v/4L = 3f1
- fbeat = vibrations/time = xHz (beats: the sources of sound are almost at the same frequency)
- f’ = f/[1±(vs/v)] (Doppler shift: + = s away from o, - = so towards o)
- f’ = f*(1±(vo/v)) (Doppler shift: + = o towards s, - = o away from s)
OPTICS
- n = c/v (n = index of refraction; n1 > n2 -> v1 < v2)
- Huygen’s principle: sin#1 = wavel1/AD; sin#2 = wavel2/AD -> sin#1/sin#2 = (wavel1/AD)/(wavel2/AD) = wavel1/wavel2 = v1f/v2f (relative index of refraction)
- Snell’s law: v2/v1 = (c/v1)/(c/v2) = n1/n2 = sin#1/sin#1 -> n1sin#1 = n2sin#2
- From Snell’s law: sin# = n2/n1 -> if n2 # = angle of total internal reflection
WAVE NATURE OF LIGHT
- Young’s double slit experiment -> particle theory was proven to be incorrect -> wave-interference phenomenon happened because of the wave nature of light (light was diffracted through the slits to produce a fringe pattern on the viewing screen)
- Monochromatic light = light of a single wavelength
- colour of light is related to its wavelength: <400 nm = UV light, >750 nm = IR light -> visible spectrum = 400-750 nm
- wavelengthn = wavelength/n (w-length of light in a medium with an index of refraction of n)
- dsin# = m*wavelength (constructive interference; m = 0,1,2...)
- dsin# = (m+½)wavelength (destructive interference)
- the larger m is, the less intensive the fringes are
TEMPERATURE, HEAT & THERMODYNAMICS
- Thermal equilibrium = two objects of different T and in contact come to this in time
- In gases, V inversely proportional to 1/P (Boyle’s law); PV = constant
- L = Lo(1+#*¤T) (thermal expansion (# = coeff. of exp))
- PV = nRT = ideal gas law; R = 8.315 J/mol*K
- PV = NkT (k = Boltzmann’s constant = 1.38*10-23 J/k)
- KE = ½mv = (3/2)kT (T related to the KE of molecules)
Heat
- Heat = energy transfer due to a difference in T
- Internal energy = sum total of all the molecules in an object
- Temperature = a measure of the average KE of molecules
- Mechanical equivalent of heat = 4.186J = 1cal
- convection = transfer of E by the mass movement of molecules over considerable distances
- conduction = E is transferred from higher-KE molecules to lower-KE neighbours when they collide
- radiation = does not require presence of matter; E is transferred as electromagnetic waves
- Q = mc*¤T (specific heat)
- Q = mL (latent heat; value for the heat of fusion & vaporization)
- Q(gain) = mc(Tf-Ti); Q(lost) = mc(Tf-Ti) (if no phase change)
- ¤Q/¤t = kA[(T1-T2)/l] (conduction)
Thermodynamics
- Work = transfer of E that is not due to a diff. in T
- 1st law: ¤U = Q-W (conservation of energy; change in internal E = heat added-work done by system)
- 2nd law: heat runs naturally from a hot object to a cold object, never spontaneously vice cersa
- 3rd law: no device is possible that can transfer a given amount of heat completely into work (never 100% efficient)
- PV = nRT Processes: adiabatic (Q=0), isobaric (const. p), isochoric (const. v), isothermal (const. T)
- E = W/Qh = 1-(Ql/Qh) (efficiency)
- (Th-Tl)/Th = 1-(Tl/Th) (ideal efficiency)
- Refrigerator: Ql/W = Ql-/(Qh-Ql) (efficiency); Tl/(Th-Tl) (ideal eff.)
- Heat pump: Qh/W = Ql-/(Ql-Qh) (efficiency)
- Entropy: entropy is a function of the state of the system, and can be interpreted as a measure of the order or disorder of the system
- Natural processes tend to move towards a state of greater disorder
- ¤S = Q/T (¤ in entropy; T is in kelvins)
ELECTRICITY
- Unlike charges attract, like charges repel
- Conductor (ie. iron), non-conductor (ie. wood)
- Induced charge: 1) |ooo| -> |o++|<-<|++o| 2) |oooo| -> |oo++| |--++|
- F = k[(Q1Q2)/r] (Coulomb’s law; k = 8.988 * 109 Nm²/c²)
- F = 1/4pi*e0 (e0 = 1/4pi*k = 8.85*10-12C²/Nm²)
- E = F/q (electric field)
- E = [kq(Q/r²)]/q = k(Q/r²) (for a single point charge)
- The electric field inside a good conductors is 0 in a static situation
- Any net charge on a good conductor distributes itself on the surface
- The electric field is always perpendicular to the surface outside of the conductor
- |+ -| -> equipotential lines: horiz. lines = el. feld lines, vert. lines = equip. lines (electirc potential is represented by these; among a certain line the potential is the same)
Formulae for electric potential
- 1 electon volt = 1 eV = 1.6*10-19 J
- V = PEa/q
- Vab = Va-Vb = -Wba/q
- W = qVba = Fe*d = qE * d = |¤KE|
- W = qVba; E = Vba/d (relation between el. potential & uniform electric field)
- V = k(Q/r) = 1/4pi*e0 * G/r (electric potential due to point charge)
DC CIRCUITS
- Req = R1 + R2 ... (in series -o-o-)
- 1/Req = 1/R1 + 1/R2 ... (in parallel =o=o)
- V = IR (Ohm’s law)
- P = RI² = VI = V²/R
- Intensity determines the brightness
- Emf = potential difference between the terminals of a source when no current flows to an external circuit
- emf = IR = P/I
- Vab = emf - IR (terminal voltage)
- Vab = emf + IR (when the battery is charged)
- Kirchhoff #1: At any junction point the sum of all currents entering the junction must equal the sum of all currents leaving the juntion
- Kirchhoff #2: The sum of the changes in potential around any closed path of a circuit must be zero
- Wac = Io²*R*(T/2)
- Wdc = I²dc * RT
- Formulae for RMS (the true output) calculations: Irms = Io/sqr2; Vrms = Vo/sqr2; Prms = ½Io²*R (Io²*R = Po)
AC CIRCUITS
- Induced emf is produced by a changing magnetic field
- An induced emf always gives rise to current whoes magnetic field opposes the original change in flux (Lenz’s law)
- Emf is proportional to the rate of change of the magnetic flux
- fluxB = B _|_ A = BAcos# (magnetic flux)
- Emf = -N*(¤fluxB/¤t) (Faraday’s law of induction)
- Emf = ¤fluxB/¤t = B*¤A/¤t = Blv¤t/¤t = Blv (Emf induced in a moving conductor = motional emf)
- E = F/q = qvB/q = vB (¤ in magnetic flux -> electric field)
- A generator changes mech. energy into el. energy; a coil of wire is rotated mechanically in a magnetic field, and the changing flux produces a current
- A motor operates in reverse of the generator
- A transformer changes the magnitude of an ac voltage
Magnetism
Magnetism & magnets
- closely related with electricity
- magnets have always a north and south pole; like poles repel each other
- breaking a magnet in half results in the production of two new magnets
- the Earth’s magnetic field is much like a bar magnet’s
Magnetic field
- magnetic field between two large poles is nearly uniform (except at the edges)
- a magnetic field is imagined to surround a magnet -> magnetic field lines
- magnetic field lines point from north to south magnetic poles
- magnetism is produced by electric current
- 1st right hand rule: grasp the wire -> thumb points in the direction of + current and fingers curl on the wire in the direction of the magnetic field
- magnetic field into paper = q, towards the reader = u
Electric current & magnetism
- a magnet excerts force on a current-carrying wire
- the direction of the force is always perperndicular to the direction of the surrent and also perpendicular to the direction of the magnetic field
- 2nd right hand rule: hand in front of you, thumb up, index finger to the front, middle finger to the left -> thumb = F, index finger = I, middle finger = B
- SI unit for B is T or tesla (1 T = 1N / Am)
Formulae
- F = IlBsinx (force on an electric current in a magnetic field) (I = current in wire, l = length of wire, B = strength of magnetic field, x = angle at which the current lies in relation to the magnetic field)
- when the current is perpendicular to the field lines, the force is stronger, and when parallel to field lines, the weakest
- force changes only direction of velocity, not magnitude
- F = qvBsinx (force on an electric charge moving in a magnetic field; the force is zero if the particle moves parallel to the field lines (x = 0°))
- B % I/r; B = FoI / 2Pr (magnetic field due to a straight wire)
- Fo = constant / permeability of free space = 4P * 10-7 T*m/A
- force between two parallel wires (magnetic field B1 produced by current I1):
B1 = Fo / 2P * I1/L
- force per unit length l on the conductor carrying current I2 = F/I = I2B2
Definitions & stuff
- One ampere is defined as that current flowing in each of two long parallel conductors 1 m apart, which results in a force of exactly 2 * 10^7 N/m of length of each conductor.
- The coulomb is one ampere-second: 1 C = 1 A*s
- The magnetic field created by a solenoid: the more closely the coils are spaced, the more uniform the produced magnetic field is
RELATIVITY
Theory
Special theory of relativity
- Postulates of the special theory of relativity (by Einstein in 1905):
1) The laws of physics have the same form in all inertial reference frames
2) Light propagates through empty space with a definite speed c independent of the speed of the source or observer
- Experimental support: Michelson-Morley experiment with an inferometer: the speed of the earth in relation to the “ether” is zero
- Special theory of relativity holds true within inertial (nonaccelerating) reference frames
- Velocity of light, 3*108 m/s is the “speed limit” of the universe
- All inertial ref. frames are equal
- Clocks moving relative to an observer are measured by that observer to run more slowly (as compared to clocks at rest)
- The L of an object is measured to be shorter when it is moving relative to the obs. than when it is at rest; the moving objects are shortened in the direction of the motion
- The correspondence principle: the two theories (StoR & GtoR) must correspond where their realms of validity overlap
- Two events can not be said to be simultaneous (depends on the observer)
General theory of relativity
- GToR deals with accelerating rfs
- Gravitational mass = inertial mass
- An observer can not deduct by measurement whether he is in accelerating motion or inside a gravitational field
- Large bodies of mass bend the four-dimensional space time
- If a star is massive enough collapses a black hole can be born (even light can’t escape)
- Light always travels along the shortest distance or geodesic
- Light is bent in gravitational field
- Gravitational redshift: the frequency of monochromatic light decreases as it leaves a heavenly body -> clocks run slower near a massive body of mass
Formulae
- # = sqr[1-(v²/c²)]
- The Lorenz transformation: x’ = x - vt/#; t’= (t-vx/c²)/#
- Length contraction: L = Lo/# (-> Muon decay in atmosphere)
- Time dilation: T = To/# (-> Muon decay in atmosphere)
- Relativistic mass: m = mo/#
- Relativistic momentum: p = mov/#
- Gravitational time dilation: T = To / sqr[1-(2GM/Rc²)]
- -”- near the surface of the earth: T = To / sqr[1-(2gR/c²)]
- Energy-mass relationship: e = mc²
- Rest mass energy of a particle = E = moc²
- KE of a high-speed particle = KE = mc²-moc² = [(1/#) -1]moc²
- Relativistic energy of a particle = E = mc² = sqr(p²c²+moc²c4)
Relativistic addition of velocities
- A = rest observer, B = moving observer ->, C = projectile fired by B ->
- u’ = v of projectile as seen by B, u = v of projectile as seen by A
- u = v+u’/[1+(vu’/c²)]
- u’ = u-v/[1-(uv/c²)]