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# Physics formulae

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### Physics formulae

1. 1. PHYSICS FORMULAEDensity is mass per unit volumeDensity = mass / volumevelocity = displacement / timeForce = rate of change of momentumMomentum = mass . velocityPower is rate of work donePower = work / timeUnit of power is wattPotential energy (P)PE = m.g.hm = massg = acceleration due to gravity (9.81m/s2)h = heightKinetic energy (P)P = (1/2).m.v2m = massv = velocityOhms lawV=I.R
2. 2. V = voltage appliedR = ResistanceI = currentElectric power (P) = (voltage applied) x (current)P = V . I = I2 . RV = voltage appliedR = ResistanceI = currentOPTICSIndex of refractionn = c/vn - index of refractionc - velocity of light in a vacuumv - velocity of light in the given material
3. 3. Density is mass per unit volume velocity = displacement / timeDensity = mass / volumeForce = rate of change of momentum Momentum = mass . velocityPower is rate of work done Kinetic energy (P)Power = work / time P = (1/2).m.v2Unit of power is watt m = mass v = velocityPotential energy (P)PE = m.g.hm = massg = acceleration due to gravity (9.81m/s2)h = heightGravity (Force due to gravity) Acceleration due to gravity at a depth d from earthFg : Force of attraction surface is :G : Gravitational constantM1 : Mass of first object dM2 : Mass of second object gd = g(1- ) R G M1 M2Fg = r2Acceleration due to gravity at height h from earth Escape velocitysurface is : Escape velocity from a body of mass M and radius rh is very much smaller than R is 2hgh = g(1- ) R
4. 4. For example if you want to calculate the escape velocity of a object from earth then, M is the mass of earth r is radius of earthOPTICS Under constant acceleration linear motion v = final velocityIndex of refraction u = initial velocityn = c/v a = acceleration t = time taken to reach velocity v from un - index of refraction s = displacementc - velocity of light in a vacuumv - velocity of light in the given material v=u+at s = ut + (1/2)a t 2 s = vt - (1/2)a t 2 v2 = u2 + 2 a sFriction force (kinetic friction) Linear MomentumWhen the object is moving then Friction is defined as Momentum = mass x velocity:Ff = μ FnwhereFf = Friction force, μ= coefficient of frictionFn = Normal force
5. 5. Capillary action Simple harmonic motionThe height to which the liquid can be lifted is given Simple harmonic motion is defined by:by: d2x/dt2 = - k x 2γcosθh= ρgrγ: liquid-air surface tension(T)(T=energy/area)θ: contact angleρ: density of liquidg: acceleration due to gravityr: is radius of tubeTime period of pendulum Waves 1 f= T 2π ω= T
6. 6. v=f.λ where ω = Angular frequency, T=Time period, v = Speed of wave, λ=wavelengthDoppler effect Relationship between observed Resonance of a stringfrequency f and emitted frequency f0: nv v frequency = f =f = f0( ) 2L v + vs Where,Where, L: length of the stringv=velocity of wave n = 1, 2, 3...vs=velocity of source. It is positive if source of wave ismoving away from observer. It is negative if source ofwave is moving towards observer.Resonance of a open tube of air(approximate) Resonance of a open tube of air(accurate) nv nvApproximate frequency = f = frequency = f = 2L 2(L+0.8D)
7. 7. where, where,L: length of the cylinder L: length of the cylindern = 1, 2, 3... n: 1, 2, 3...v = speed of sound v: speed of sound d:diameter of the resonance tubeResonance of a closed tube of air(approximate) Resonance of a closed tube of air(accurate) nv nvApproximate frequency = f = frequency = f = 4L 4(L+0.8D)Where, Where,L: length of the cylindern = 1, 2, 3... L: length of the cylinderv = speed of sound n: 1, 2, 3... v: speed of sound d:diameter of the resonance tubeIntensity of sound Braggs law nλ = 2d sinθ Sound Powerintensity of sound = where area n = integer (based upon order) λ = wavelength d = distance between the planes I θ = angle between the surface and the rayintensity of sound in decibel= 10log10 I0
8. 8. IdB = 10log10 I0whereI=intensity of interest in Wm-2I0=intensity of interest in 10-12Wm-2de Broglie equation Relation between energy and frequency h h E = hνλ= = where p mv E = Energy h = Plancks constant ν = frequencywherep = momentumλ = wavelengthh = Plancks constantv = velocityDavisson and Germer experiment Centripetal Force (F) h m v2λ= F= = m ω2 r rwhere
9. 9. e = charge of electronm = mass of electronV = potential difference between the plates thru whichthe electron passλ = wavelengthCircular motion formula Torque (it measures how the force acting on the object can rotate the object)v=ωr Torque is cross product of radius and Force Torque = (Force) X (Moment arm) X sin θ T = F L sin θ v2 whete θ = angle between force and moment armCentripetal acceleration (a) = rForces of gravitation Stefan-Boltzmann Law The energy radiated by a blackbody radiator perF = G (m1.m2)/r2 second = Pwhere G is constant. G = 6.67E - 11 N m2 / kg2 P = AσT4 where, σ = Stefan-Boltzmann constant σ = 5.6703 × 10-8 watt/m2K4Efficiency of Carnot cycle Ideal gas law PV=nRT Tc P = Pressure (Pa i.e. Pascal)η= 1- V = Volume (m3) Th n = number of of gas (in moles)
10. 10. R = gas constant ( 8.314472 .m3.Pa.K-1mol-1] ) T = Temperature ( in Kelvin [K])Boyles law (for ideal gas) Charles law (for ideal gas)P1 V1 = P2V2T (temperature is constant) V1 V2 = T1 T2 P (pressure is constant)Translational kinetic energy K per gas molecule Internal energy of monatomic gas(average molecular kinetic energy:) 3 3 K= nRTK= kT 2 2 n = number of of gas (in moles) -23k = 1.38066 x 10 J/K Boltzmann’s constant R = gas constant ( 8.314472 .m3.Pa.K-1mol-1] )
11. 11. Root mean square speed of gas Ratio of specific heat (γ) 3kT CpV2rms = γ= m Cvk = 1.38066 x 10-23 J/K Boltzmann’s constant Cp = specific heat capacity of the gas in a constantm = mass of gas pressure process Cv = specific heat capacity of the gas in a constant volume processInternal energy of ideal gas In Adiabatic process no heat is gained or lost by the system.Internal energy of ideal gas (U) = cv nRT Under adiabatic condition PVγ = Constant TVγ-1 = Constant where γ is ratio of specific heat. Cp γ= Cv
12. 12. Boltzmann constant (k) Speed of the sound in gas Rk= R = gas constant(8.314 J/mol K) Na T = the absolute temperature M = the molecular weight of the gas (kg/mol) γ = adiabatic constant = cp/cvR = gas constantNa = Avogadros number.Capillary action Resistance of a wireThe height to which the liquid can be lifted is given ρLby R= Ah=height of the liquid liftedT=surface tensionr=radius of capillary tube ρ = resistivity L = length of the wire 2T A = cross-sectional area of the wireh= ρrgOhms law Resistor combinationV=I.R If resistors are in series then equivalentV = voltage applied resistance will beR = Resistance Req = R1 + R2 + R3 + . . . . . . + RnI = currentElectric power (P) = (voltage applied) x (current) If resistors are in parallel then equivalentP = V . I = I2 . R resistance will beV = voltage applied 1/Req = 1/R1 + 1/R2 + 1/R3 + . . . . . . + 1/RnR = ResistanceI = current
13. 13. In AC circuit average power is : In AC circuit Instantaneous power is :Pavg = VrmsIrms cosυ PInstantaneous = VmIm sinωt sin(ωt-υ)where, where,Pavg = Average Power PInstantaneous = Instantaneous PowerVrms = rms value of voltage Vm = Instantaneous voltageIrms = rms value of current Im = Instantaneous currentCapacitors Total capacitance (Ceq) for PARALLEL CapacitorQ = C.V Combinations:where Ceq = C1 + C2 + C3 + . . . . . . + CnQ = charge on the capacitor Total capacitance (Ceq) for SERIES CapacitorC = capacitance of the capacitor Combinations:V = voltage applied to the capacitor 1/Ceq = 1/C1 + 1/C2 + 1/C3 + . . . . . . + 1/CnParallel Plate Capacitor Cylindrical Capacitor A LC = κ ε0 C = 2 π κ ε0 d ln (b/a)where whereC = [Farad (F)] C = [Farad (F)]κ = dielectric constant κ = dielectric constantA = Area of plate L = length of cylinder [m]d = distance between the plate a = outer radius of conductor [m]ε0 = permittivity of free space (8.85 X 10-12C2/N m2) b = inner radius of conductor [m] ε0 = permittivity of free space (8.85 X 10-12 C2/N m2)
14. 14. Spherical Capacitor Magnetic force acting on a charge q moving with velocity v ab F = q v B sin θ whereC = 4 π κ ε0 F = force acting on charge q (Newton) b-a q = charge (C)where v = velocity (m/sec2)C = [Farad (F)] B = magnetic fieldκ = dielectric constant θ = angle between V (velocity) and B (magnetic field)a = outer radius of conductor [m]b = inner radius of conductor [m]ε0 = permittivity of free space (8.85 X 10-12C2/N m2)Force on a wire in magnetic field (B) In an RC circuit (Resistor-Capacitor), the timeF = B I l sin θ constant (in seconds) is:where τ = RCF = force acting on wire (Newton) R = Resistance in ΩI = Current (Ampere) C = Capacitance in farads.l = length of wire (m)B = magnetic fieldθ = angle between I (current) and B (magnetic field)In an RL circuit (Resistor-inductor ), the time constant Self inductance of a solenoid = L = μn2LA(in seconds) is: n = number of turns per unit lengthτ = L/R L = length of the solenoid.R = Resistance in ΩC = Inductance in henries
15. 15. Mutual inductance of two solenoid two long thin Energy stored in capacitorsolenoids, one wound on top of the otherM = μ0N1N2LA 1N1 = total number of turns per unit length for first E= CV2solenoidN2 = number of turns per unit length for second 2solenoidA = cross-sectional areaL = length of the solenoid.Coulombs Law Ohms lawLike charges repel, unlike charges attract.F = k (q1 . q2)/r2 V = IRwhere k is constant. k = 1/(4 π ε0) ≈ 9 x 109N.m2/C2 whereq1 = charge on one body V = voltageq2 = charge on the other body I = currentr = distance between them R = RésistanceElectric Field around a point charge (q) Electric field due to thin infinite sheetE = k ( q/r2 ) σwhere k is constant. k = 1/(4 π ε0) ≈ 9 x 109N.m2/C2 E=q = point charger = distance from point charge (q) 2 ε0 where E = Electric field (N/C) σ = charge per unit area C/m2 ε0 = 8.85 X 10-12 C2/N m2
16. 16. Electric field due to thick infinite sheet Magnetic Field around a wire (B) when r is greater than the radius of the wire. σE= μ0 I ε0 B=where 2πrE = Electric field (N/C) whereσ = charge per unit area C/m2 I = currentε0 = 8.85 X 10-12 C2/N m2 r = distance from wire and r ≥ Radius of the wireMagnetic Field around a wire (B) when r is less Magnetic Field At the center of an arcthan the radius of the wire. μ0 I υ μ0 I r B=B= 4πr 2 2πR wherewhere I = currentI = current r = radius from the center of the wireR = radius of wirer = distance from wireand r ≤ Radius of the wire (R)
17. 17. Bohrs model Emitting Photons(Rydberg Formula) 1 1 nh Ephoton = E0( - )L= n12 n22 2πwhereL = angular momentum wheren = principal quantum number = 1,2,3,...n n1 < n 2h = Plancks constant. E0 = 13.6 eVHalf life of radioactive element Average life of radioactive element ln(2) 1t1/2 = τ= λ λ