Physics - OAK PARK USD



Physics Annotated Formula Sheet

|Formula |Symbol and Units |

|Displacement |d = displacement in m (meter) |

|d = x - xo |x = position in m |

|+ or – depending on direction |vav = average velocity in m/s |

| |t = change in time in s (second) |

| |a = acceleration in m/s2 |

| |v = instantaneous velocity in m/s |

|Constant velocity | |

|vav = d/t | |

|Accelerated motion | |

|a = (vt – vo)/t | |

|Kinematic formulas | |

|d = vot + ½at2 | |

|d = ½(vo + vt)t | |

|vt = vot + at | |

|vt2 = vo2 + 2ad | |

|Graphing constant velocity in one dimension |

|d |v |a |

| | | |

| | | |

| | | |

|t |t |t |

|Graphing accelerated motion in one dimension |

|d |v |a |

| | | |

| | | |

| | | |

|t |t |t |

|Vector addition |

|y Rx Bx= BcosθB |

| |

|By = BsinθB |

|B |

|Ry R |

|A |

|Ay = AsinθA |

| |

|Ax = AcosθA |

|x |

|Ax + Bx = Rx |

|Ay + By = Ry |

|R = (Rx2 + Ry2)½ |

|tan θ = Ry/Rx ∴ θ = tan-1(Ry/Rx) |

|add 180o to θ when Rx is negative |

|Projectile motion (g = gravitational acceleration, -10 m/s2) |

|vertical motion use accelerated motion formulas |

|horizontal motion use constant velocity formula |

|direction |d |vo |vt |a |t |

|vertical |dy |vyo |vyt |-g |t |

|horizontal |dx |vx | | |

|Uniform circular motion |vc = perimeter velocity in m/s |

|vc = 2πr/T |r = radius of circle in m |

|ac = vc2/r |T = period of motion in s |

|ac is directed toward center |ac = centripetal acceleration in m/s2 |

|Newton's Laws of Motion |

|Object stay in same motion unless acted upon by a force |

|Acceleration if proportional to force/mass |

|For every action there is an equal, but opposite reaction |

|Accelerating force |F = force in N (Newton) |

|F|| = ma |m = mass in kg (kilogram) |

| |a = acceleration in m/s2 |

|Spring force |Fs = spring force in N |

|Fs = kx |k = spring constant in N/m |

| |x = distance stretched in m |

|Force of gravity (weight) |Fg = force of gravity in N |

|Fg = mg |m = mass in kg |

| |g = 10 m/s2 |

|Formula |Symbol and Units |

|Normal force, Fn, is the ⊥ force on the object by the surface |

|Force of friction |Ff = force of friction in N |

|For static friction: Ff ≤ μsFn |μ = coefficient of friction |

|For kinetic friction: Ff = μkFn |Fn = force normal in N |

|Accelerating forces problems. |

|Fn Fp |

| |

| |

|Fp-⊥ |

|Ff |

|Fp-|| |

| |

| |

|Fg |

|Fn |

|Fp |

| |

| |

| |

|Ff θ Fg−⊥ |

|Fg |

| |

|Fg-|| |

|θ |

|Label all forces |

|resolve non-||, non-⊥ forces into || and ⊥ components |

|Σ F|| = ma (m is all moving mass) |

|Σ F⊥ = 0 |

|Masses hanging from a pulley, |m = mass of A and B in kg |

|where mA > mB |g = 10 m/s2 |

|(mA – mB)g = (mA + mB)a |a = acceleration of system in m/s2 |

|Centripetal force |Fc = centripetal force in N |

| |m = mass in kg |

|Fc = mac = mv2/r |ac = centripetal acceleration in m/s2 |

| |v = perimeter velocity in m/s |

| |r = radius of circle in m |

|Force of gravity between planets |Fg = force of gravity in N |

|Fg = GMm/r2 |G = 6.67 x 10-11 N•m2/kg2 |

| |M, m = mass in kg |

| |r = distance between centers in m |

| |v = perimeter velocity in m/s |

|Force of gravity is centripetal | |

|GMm/r2 = mv2/r | |

|Center of mass |cm = center of mass in m |

|cm = m1r1 + m2r2 + ... |m = mass in kg |

|(m1 + m2 + ...) |r = distance from 0 position in m |

|Non-accelerating force problems where forces act through cm. |

|Draw free body diagram |

|Resolve all forces into x-components and y-components |

|Σ Fx = 0 |

|Σ Fy = 0 |

|3 forces, two of which are perpendicular: draw vector sum diagram and solve |

|for missing sides of right triangle |

|Non-accelerating force problems where forces act away from cm. |

|[pic] |

|Draw free body diagram |

|Determine axis of rotation that eliminates an unknown |

|ΣΠF x r = Σ ΘF x r (torque) |

|Σ F→ = Σ F ← |

|Σ F ↑ = Σ F ↓ |

|Formula |Symbol and Units |

|Work: W = F||d |W = work in J (Joule) |

|+ or – , but no direction |F|| = force in N |

| |d = distance parallel to F in m |

| |P = power in W (Watt) |

| |K = kinetic energy in J |

| |m = mass in kg |

| |v = velocity in m/s |

| |Ug = gravity potential energy in J |

| |g = 10 m/s2 |

| |h = height above surface in m |

| |G = 6.67 x 10-11 N•m2/kg2 |

| |M = planet mass in kg |

| |r = distance center-center in m |

| |Us = spring potential energy in J |

| |k = spring constant in N/m |

| |x = distance stretched in m |

|Power: P = W/t = Fvav | |

|W can be any energy form | |

|Kinetic energy: K = ½mv2 | |

|Gravitational potential energy near a | |

|surface | |

|Ug = mgh | |

|Gravitational potential energy between| |

|planets | |

|Ug = -GMm/r | |

|Spring potential energy | |

| | |

|Us = ½kx2 | |

|Energy problems |

|1. determine initial energy of the object, Eo |

|2. determine energy +/– due to a push or pull: Wp = ±F||d |

|3. determine energy removed by friction: Wf = Ffd |

|4. determine resulting energy, E' = Eo ± Wp – Wf |

|5. determine d, h, x or v |

|6. general equation: K + U ± Wp – Wf = K' + U' |

|½mv2 + mgh + ½kx2 ± Fpd – Ffd = ½mv'2 + mgh' + ½kx'2 |

|Linear momentum |p = linear momentum in kg•m/s |

|p = mv |m = mass in kg |

| |v = velocity in m/s |

| |J = impulse in N•s |

| |F = force in N |

| |t = time in s |

| |K = kinetic energy in J |

|Impulse | |

|J = FΔt = mΔv = Δp | |

|Kinetic energy to momentum | |

|K = p2/2m | |

|Stationary → separation | |

|0 = mAvA' + mBvB' | |

|Inelastic collision | |

|mAvA + mBvB = (mA + mB)v' | |

|conservation of p, but not K | |

|Elastic collision | |

|mAvA + mBvB = mAvA' + mBvB' | |

|vA + vA' = vB + vB' | |

|conservation of p and K | |

|Collision in two dimensions |

|px: mAvAx + mBvBx = (mA + mB)vx' or mAvAx' + mBvBx' |

|py: mAvAy + mBvBy = (mA + mB)vy' or mAvAy' + mBvBy' |

|Ballistic pendulum problems |

|bullet strikes block and sticks |

|mvm + 0 = (m + M)v' |

|block swings or slides |

|swing (K = Ug): ½(m + M)v'2 = (m + M)gh ∴ h = v'2/2g |

|slide (K = Wf): ½(m + M)v'2 = μ(m + M)gd ∴ d = v'2/2μg |

|Moment of Inertia (angular inertia): I =|I = moment of inertia in kg•m2 |

|mr2 |m = mass in kg |

|point mass in a circular orbit |r = radius of circular path in m |

| |L = angular momentum in kg•m2/s |

| |ϖ = angular velocity in rad/s |

| |p = linear momentum in kg•m/s |

| |v = linear velocity in m/s |

|Angular momentum | |

|L = Iϖ = rp = rmv | |

|point mass in a circular orbit | |

|Conservation of angular momentum: r1v1 =| |

|r2v2 | |

|Matter energy equivalence |E = energy in J |

|E = mc2 |m = mass in kg |

| |c = 3 x 108 m/s |

|Binding energy, BE | |

|mnuclide + mBE = mp + mn | |

|Nuclear reactions |

|proton: 11p, neutron 10n, electron 0-1e, positron 01e |

|alpha: α = 42He, beta: β = 0-1e |

|conservation of mass # & charge: 23892U → 42He + 23490Th |

|nuclear process: mproducts – mreactants = mBE < 0 (E = Δmc2) |

|half life: 1 → ½ → ¼ take same amount of time t½ |

|Formula |Symbol and Units |

|Simple harmonic motion (SHM) |T = period in s |

|Time to complete one cycle |m = mass in kg |

|T = 2π(m/k)½ |k = spring constant in N/m |

| |A = amplitude in m |

| |vo = velocity at midpoint in m/s |

|displacement |0 |±A |

|velocity, v |vo = 2πA/T = A(k/m)½ |vA = 0 |

|acceleration, a |ao = 0 |aA = vo2/A = A(k/m) |

|potential energy, U |Uo = 0 |UA = ½kA2 |

|kinetic energy, K |Ko = ½mvo2 |KA = 0 |

|Period of a simple pendulum |T = period in s |

| |L = length of pendulum in m |

|T = 2π(L/g)½ |g = gravity acceleration in m/s2 |

|Mechanical wave |

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|amplitude, A: maximum height of a crest or depth of a trough measured from the |

|midpoint (m) |

|wavelength, λ: distance between any two successive identical points of the wave |

|(m) |

|frequency, f: the number of complete waves that pass a given point per unit time |

|(Hz or s-1) |

|period, T: the time it takes for one wave to pass (s) |

|T = 1/f |

|velocity, vw: speed of the waveform, vw = λ/T = λf (m/s) |

|transverse wave (string): disturbance Ε wave Δ |

|longitudinal wave (sound): disturbance Δ wave Δ |

|Interference |

|amplitudes combine (superposition principle) |

|constructive interference when amplitudes are added |

|destructive interference when amplitudes are subtracted |

|beats, fbeats = |fA – fB| |

|Velocity of a wave on a string |vw = velocity of wave in m/s |

| |Ft = force of tension in N |

|vw = (Ft/α)½ |α = linear density in kg/m |

|Harmonics |

|[pic] |

|Determining nth harmonic |λ = wavelength in m |

| |L = length of string in m |

|λn = 2L/n |n = number of harmonic |

|fn = nf1 |f = frequency |

|Doppler effect |f' = perceived frequency in s-1 |

|f’ = f(vw ± vo)/(vw ± vs) |f = generated frequency in s-1 |

|approaching: f' > f (+vo, –vs) |vw = wave velocity in m/s |

|receding: f' < f (–vo, +vs) |vo = observer velocity in m/s |

|approximation formula |vs = source velocity in m/s |

|Δf/f ≈ v/vw | |

|approaching: f’ = f + Δf | |

|receding: f’ = f – Δf | |

|Formula |Symbol and Units |

|Angle of reflection |θi = incoming ray ⊥ to surface |

|θi = θr |θr = reflected ray ⊥ to surface |

|phase shift when ni < nr |n = index of refraction |

|Wave velocity in a vacuum |c = 3 x 108 m/s |

|c = fλ |f = frequency of wave in s-1 (Hz) |

| |λ = wavelength in m |

| |n = index of refraction (no units) |

| |vn = velocity at n in m/s |

|Refraction within a medium | |

|vn = c/n | |

|fn = f1 | |

|λn = λ1/n | |

|Angle of refraction (Snell's law) |ni = source medium n |

|nisinθi = nRsinθR |θi = incident angle ⊥ to surface |

|ni < nR: bend toward normal |nR = refracting medium n |

|ni > nR: bend away from normal |θR = refracted angle ⊥ to surface |

|n ∝ to f ∴ color separation = dispersion (prism) |

|total reflection when ni > nR and θi ≥ θc = nlow/nhigh |

|Parabolic mirror radius of curvature r|r = radius of curvature in m |

|= 2f |f = focal length in m |

|lens/mirror equation |do = object distance to l/m in m |

|1/do + 1/±di = 1/±f |di = image distance to l/m in m |

|+di for real image (-di virtual) |f = focal length in m |

|+f for converging (-f diverging) |M = magnification (no units) |

| |hi = height of image in m |

| |ho = height of object in m |

|magnification equation | |

|M = hi/ho = -di/do | |

|do > +f |do < +f |–f |

|[pic] |[pic] |[pic] |

|[pic] |[pic] |[pic] |

|Interference with two slits |θ = angle from slits to band in m |

|tanθ = x/L |x = center to band distance in m |

|sinθc = mλ/d |L = slits to screen distance in m |

|sinθd = (m + ½)λ/d |m = band order (no units) |

|θc for bright band (θd for dark) |λ = wavelength of light in m |

| |d = distance between slits in m |

| |W = width of light spot |

| |d' = width of slit |

|Interference with one slit | |

| | |

|W = 2λL/d' | |

|Thickness of a film, T (λf = λ1/n) |

|Interference |ni < nf < nr |nf > ni and nr |

|Bright |T = ½λf |T = ¼λf |

|Dark |T = ¼λf |T = ½λf |

|EM Radiation |

|High energy has short λ, high f (low energy has long λ, low f) |

|Transverse wave ∴ polarizable |

|Doppler shift: moving away = shift to longer λ (red shift) |

|Photon energy |E = Energy in J |

|E = hf = mc2 |h = 6.63 x 10-34 J•s |

|UV > violet ... red > infrared |f = frequency in s-1 |

| |m = relativistic mass in kg |

| |c = 3 x 108 m/s |

| |λ = wavelength in m |

| |p = momentum in kg•m/s |

|Photon momentum | |

|p = mc = h/λ = E/c | |

|Particle wavelength (De Broglie) | |

|λparticle = h/p | |

|Atomic energy levels (Bohr model) |En = electron energy in eV |

|En = -B/n2 |B = 13.6 eV for hydrogen |

| |n = energy level (1, 2, etc.) |

| |EeV = photon energy in eV |

| |λnm = wavelength in nm |

|Energy absorbed by an atom | |

|EeV = En-high – En-low | |

|EeV = 1240 eV•nm/λnm | |

|Photoelectric effect |Kelectron = kinetic energy in eV |

|Kelectron = Ephoton - φ |Ephoton = 1240 eV•nm/λnm |

| |φ = work function in eV |

| |me = 9.11 x 10-31 kg |

| |v = electron velocity in m/s |

|Kinetic energy of an electron | |

| | |

|Kelectron = ½mev2 | |

|Formula |Symbol and Units |

|Density |ρ = density in kg/m3 |

| |m = mass in kg |

|ρ = m/V |V = volume in m3 |

| |ρkg/m3 = ρg/cm3 x 103 |

|Specific gravity |s.g. = specific gravity (no units) |

|s.g. = mair/(mair – mfluid) |mair = mass measured in air |

|ρobject = s.g. x ρfluid |mfluid = submerged mass |

|Pressure on a surface |P = pressure in Pa (Pascals) |

|P = F/A |F = force in N |

| |A = Area in m2 |

| |PPa = Patm x 105 |

|Force on a hydraulic piston | |

|Fin/Ain = Fout/Aout | |

|Pressure in fluid at a depth |P = pressure in Pa |

| |ρf = density of fluid in kg/m3 |

|P = ρfgh |g = 10 m/s2 |

| |h = depth in m |

|Upward force on a submerged object |Fb = buoyant force in N |

|(Archimedes principle) |ρf = density of fluid in kg/m3 |

| |g = 10 m/s2 |

|Fb = ρfgVo |Vo = object's submerged volume |

|Fluid flow in a pipe |V/t = volume flow rate in m3/s |

| |A = area at a position in m2 |

|V/t = Av = Constant |v = velocity at a position in m/s |

|Solve plumbing, lift & tank leak |P = pressure on fluid in Pa |

|problems (Bernoulli's equation) |ρ = density of fluid in kg/m3 |

| |g = 10 m/s2 |

|P + ρgy + ½ρv2 = Constant |y = elevation in m |

| |v = velocity in m/s |

|Thermal expansion |ΔL = change in length in m |

| |α = expansion coefficient in o C-1 |

|ΔL = αLoΔT |Lo = original length in m |

| |ΔT = temperature change in o C |

|Kinetic energy of gases |K = kinetic energy in J |

| |R = 8.31 J/mol•K |

|K = 3/2RT |T = Temperature in K |

| |v = velocity in m/s |

| |M = molar mass in kg |

| |P = pressure in Pa |

| |V = volume in m3 |

| |n = number of moles |

| |TK = ToC + 273 |

|Velocity of gas molecules | |

| | |

|v = (3RT/M)½ | |

|Ideal gas law | |

|PV = nRT | |

|PV diagram |

|+Win (-Wout) toward y-axis, -Win (+Wout) away from y-axis |

|+ΔT and +ΔU away from origin (P x V) |

|PV (heat engine) problems |ΔU = internal energy change in J |

|ΔU = 3/2nRΔT = 3/2ΔPV = 3/2PΔV |n = number of moles |

|Win = -PΔV = Area |R = 8.31 J/mol•K |

|ΔU = Qin + Win |Qin = heat added to system in J |

|For complete cycle: ΔU = 0 |Win = work on the system in J |

|Process |ΔT | ΔU = Qin + |

| | |Win |

|IsometricΕ(ΔV = 0) |ΔPV/nR |3/2ΔPV |ΔU |0 |

|IsobaricΔ(ΔP = 0) |PΔV/nR |3/2PΔV |ΔU – Win |-PΔV |

|Isothermic (ΔT = 0) |0 |0 |-Win |-Qin |

|Adiabatic (Q = 0) |? |Win |0 |ΔU |

|Efficiency of a heat engine |ec = ideal efficiency (no units) |

|ec = (Thigh – Tlow)/Thigh |T = temperature in K |

|e = |Wcycle|/Qin |e = actual efficiency (no units) |

|Rate of heat flow through a barrier |Q/t = rate of heat flow in J/s |

| |A = area of barrier in m2 |

|Q/t ∝ A(TH – TL)/L |TH = high temperature in o C |

| |TL = low temperature in o C |

| |L = thickness of barrier |

| |Q = heat in J |

| |m = mass in kg |

| |c = specific heat in J/kg•K |

|Heat gain/loss by a material | |

| | |

|Q = mcΔT | |

|Formula |Symbol and Units |

|Conducting sphere: excess charge on outer surface, E = 0 inside |

|Electric force between charges |Fe = electric force in N |

|Fe = k|Qq|/r2 |k = 9 x 109 N•m2/C2 |

|attract for unlike (repel for like) |Q, q = charge in C (Coulombs) |

| |r = Q1 to Q2 distance in m |

| |E = electric field in N/C or V/m |

|Electric field around a charge | |

|E = k|Q|/r2 | |

|away from +Q (toward -Q) | |

|Electric field around multiple charges |

|Calculate E for each charge |

|Combine E (add for same direction, subtract for opposite direction, use |

|Pythagorean and tanθ = y/x for ⊥ fields) |

|E = 0 between like charges and closer to lesser |Q| |

|E = 0 outside unlike charges and closer to lesser |Q| |

|Force on q in electric field E |Fe = electric force in N |

|Fe = |q|E |q = charge in C |

|+q: E → , Fe →; (–q: E →, Fe ← |E = electric field in N/C |

|Electric potential energy between |Ue = electric potential energy in J |

|charges Ue = kQq/r |k = 9 x 109 N•m2/C2 |

|+Ue for like (-Ue for unlike) |Q, q = charge in C (Coulombs) |

| |r = Q1 to Q2 distance in m |

| |V = potential (voltage) in V (volts) |

|Electric potential (voltage) around a | |

|charge V = kQ/r | |

|+V for +Q (-V for –Q) | |

|Electric potential around multiple charges |

|Calculate V for each charge |

|Combine V (add +V and subtract -V) |

|V = 0 between unlike charges and closer to lesser |Q| |

|V = 0 infinitely far away from like charges |

|Electric potential energy on a charge |Ue = electric potential energy in J |

|in an electric potential |q = charge in C |

|Ue = qV |V = voltage (potential) in V |

| |m = mass in kg |

| |v = velocity in m/s |

|Kinetic energy equals loss in Ue | |

|K = -ΔUe | |

|½mv2 = |qΔV| | |

|Electric field between capacitor |V = voltage in V |

|plates V = E/d |E = electric field in V/m |

|Direction if from Vhigh → Vlow |d = distance between plates |

|Current flow |I = current in A (amperes) |

|I = Q/t |Q = charge in C |

| |t = time in s |

|Resistance in wires |R = resistance in Ω (ohms) |

| |ρ = resistivity in Ω•m |

|R = ρL/A |L = length in m |

| |A = cross-section area in m2 |

|Battery terminal voltage |V = terminal voltage in V |

|V = E ± IR |E = emf in V |

|+ when battery is recharging |I = current in A |

|– when battery is discharging |R = internal resistance in Ω |

|Voltage loss (Ohm's law) |V = voltage in V |

|V = IR |I = current in A |

| |R = resistance in Ω |

| |P = power in watts W |

|Power consumed | |

|P = IV = V2/R = I2R | |

|Capacitor capacitance |C = capacitance in F (farads) |

|C = єoA/d |єo = 8.85 x 10-12 C2/N•m2 |

| |A = plate area in m2 |

| |d = plate separation in m |

| |Q = charge in C |

| |V = voltage in V |

| |UC = stored energy in joules J |

|Capacitor store charge | |

|Q = CV | |

|Capacitor store energy | |

| | |

|UC = ½QV = ½CV2 = ½Q2/C | |

|Variable Capacitor problems |

|Adjust A or d |Capacitance |Battery Connection |

|Area |Distance |C = єoA |Connected |Disconnected |

|(A) |(d) |d | | |

| | | | Q = C x V | Q = C x V |

|↑ |↓ |

|Circuit Element Symbols |

| | | |

|Summary Chart for Circuit Elements in Series and Parallel |

|Element |S/P |Formula |Constant |Variable |

|Resistor |Series |Rs = R1 + R2 |Is |Vn = IsRn |

| |Parallel |1/Rp = 1/R1 + 1/R2 |Vp |In = Vp/Rn |

|Capacitor |Series |1/Cs = 1/C1 + 1/C2 |Qs |Vn = Qs/Cn |

| |Parallel |CP = C1 + C2 |Vp |Qn = CnVp |

|Kirchhoff’s Circuit Rules |

|loop rule: ΔV = 0 for any complete circuit |

|junction rule: Iin = Iout for any junction |

|General steps for solving a circuit problem |

|Determine overall resistance: combine Rp until all Rs |

|Determine the overall current of the circuit: I = Vtot/Rtot |

|Determine voltage loss in series resistors: V = ItotR |

|Determine voltage in parallel components: Vp = Vtot – Σ Vs |

|Determine I and P for each resistor: I = V/R, P = IV |

|Determine Q and UC for each capacitor: Q = CV, Uc = ½QV |

|Measuring I and V |

|I: place ammeter between battery and circuit element (series) |

|V: attach voltmeter to each side of circuit element (parallel) |

|Magnetic force on a moving charge: |FB = force in N |

|FB = qvB |q = charge in C |

| |v = velocity in m/s |

| |B = magnetic field in T |

| |m = mass in kg |

| |r = radius of circular path in m |

| |I = current in A |

| |L = length of wire in m |

|Magnetic forces are centripetal | |

|qvB = mv2/r | |

|palm toward center of circle path | |

|Magnetic force on current wire | |

|FB = ILB | |

|Direction F B | |

| | |

| | |

|I, v | |

|Magnetic field near a wire |B = magnetic field in T (teslas) |

|I out I in |k' = 2 x 10-7 T•m/A |

|B↓?↑ B = k'I/r ↑Υ↓B |I = current in A |

| |r = ⊥ distance from wire m |

| |μo = 4π x 10-7 T•m/A |

| |N = number of turns |

| |L = length in m |

|Magnetic field in a solenoid | |

|B out B in | |

|I↓?↑ B = μoI(N/L) ↑Υ↓I | |

|Magnetic force between wires | |

|FB = k'I1I2L/r | |

|Direction: I1 Ι I2 = attraction | |

|Permanent Magnetics |

|Magnetic field lines go from north pole to south pole |

|Earth's north magnetic pole is at the south geographic pole |

|Magnetic flux |ΦB = flux in Wb (weber) |

| |A = enclosed area ⊥ to B in m2 |

|ΦB = A x B |B = magnetic field in T |

| |E = emf in V |

| |ΔΦB = change in flux in Wb |

| |t = time in s |

| |v = velocity of rod in m/s |

| |L = distance between rails m |

| |B = magnetic field in T |

|Induced emf in a wire loop | |

| | |

|E = ΔΦB/t | |

|Induced emf in a moving rod | |

| | |

|E = vLB | |

|Direction of induced current |

|B |ΔΦ |Induced Current |

|thumb |(increase: flip, decrease: no flip) |I = E/R |

|Up |increase |clockwise |

| |(rotate || to ⊥, move B closer) | |

| |decrease |counter clockwise |

|Down |increase |counter clockwise |

| |decrease |clockwise |

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