Physics - Oak Park Independent
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 |
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|t |t |t |
|Graphing accelerated motion in one dimension |
|d |v |a |
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|t |t |t |
|Vector addition |
|y Rx Bx= BcosθB |
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|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 |
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|Fp-⊥ |
|Ff |
|Fp-|| |
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|Fg |
|Fn |
|Fp |
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|Ff θ Fg−⊥ |
|Fg |
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|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 | |
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|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 | |
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|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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