Toomey



Harold’s Physics“Cheat Sheet”3 May 2021Mechanics:Linear TranslationMechanics:Angular / Rotational MotionElectricity / MagnetismFluid Mechanics / Thermo-dynamicsAtomic and Nuclear / Waves and OpticsKinematicsPosition(m)(rad)Horizontal / 1-D:x= x0+vx0t+12at2Vertical:y= y0+vy0t-12gt2x= x0+vtx=vdts=rθθ=θ0+ω0t+12αt2θ=θ0+ωtθ=ωdt10-100=googolth10-24=yocto?10-21=zepto?10-18=atto?10-15=femto?10-12=pico?10-9=nano?10-6=micro?10-3=milli? 10-2=centi? 10-1=deci? 100=1 101=deca?102=hecto?103=kilo?106=mega?109=giga?1012=tera?1015=peta?1018=exa?1021=zetta?1024=yotta?10100=googol101000=googolplexFluid Mechanics:P1+ρgy1+12ρv12=P2+ρgy2+12ρv22(Conservation of Mass)ρ=mV?l=αl0?TWaves:f(x,t)=A sin?(2πft-xλ+?)+kOptics:f=vλ1do+1di=1fRefraction:(bend)n=cvSnell’s Law:n1sinθ1=n2sinθ2n1n2=v2v1Diffraction:(spread out)?L=dsinθmλ=dsinθx(t)=Acosωt+?x(t)=Acos2πft+?Velocity(m/s)Angular Velocity / Angular Frequency(rad/s)v=dt=?x?t=dxdtv= v0+atv2=v02+2a(x-x0)v=v0+v2v=adtf=1Tω=θt=?θ?t=dθdtω=ω0+αtω2=ω02+2α(θ-θ0)ω=ω0+ω2ω=αdtω=2πT=2πfω=km (spring)ω=gl (pendulum)Speed of Light:c≈3.00×108 msFluid Mechanics:A1v1=A2v2vrms=3RTMvrms=3kBTμWaves and Optics:v=fλReflection:(throw back)Critical angle:sinθc=n1n2Maxima for a thin film:2d=λ2n,3λ2n,5λ2n…v=ωrv=ω × rv(t)=-Aωsinωt+?v(t)=-Aωsin2πft+?Acceleration(m/s2)(rad/s2)Linear:a=vt=?v?t=dvdta=Fm=FnetmTangential (linear):a=at=α rGravity (g)Angular:α=ωt=?ω?t=dωdtα=τI=τnetICentripetal (center):ac= v2r=ω2rConstants:Gravitational ConstantG=6.67430×10-11 Nm2kgGravity Acceleration (Earth) g=9.80665 ms2=32.1740 fts2Speed of Light in Vacuumc=2.99792458×108 msElectron-Volt1eV=1.602176462×10-19 JCharge of an Electrone=-1.602176462×10-19 C Mass of an Electronme=9.1093837015×10-31 kgMass of a Protonmp=1.67262192369×10-27 kgMass of a Neutronmn=1.67492749804×10-27 kgElectric Permittivityε0=1μ0c2=8.85418782×10-12C2Nm2Magnetic Permeabilityμ0=4π×10-7TmAAvogadro’s NumberNA=6.02214076×10231molBoltzmann ConstantkB=1.380649×10-23 JKCoulomb’s Law Constantke=14πε0=8.987551×109 Nm2C2Faraday ConstantF=9.648533289×104 CmolPlanck’s Constanth=6.6267004×10-34 JsNet:anet2=at2+ac2a=-Aω2cosωt+?a(t)=-Aω2cos2πft+?Jerk (Jolt)(m/s3)(rad/s3)j=at=?a?t=dadtζ=αt=?α?t=dαdtDynamicsMass(kg)/Moment of Inertia (kg?m2)m = actual massI = effective massI=mr2I=r2dmI=r?r dmmp≈mnNAMagnification:M=dido=hihoMTelescope=-fobjective lensfeyepieceMomentum(kg?m/s)(kg?m2/s)p=mv?p=m?vConservation of Linear Momentum:pi=pfmvi=mvfp=ω× m?p=J=t1t2F dtElastic Collision = bounce off each otherInelastic Collision = stick togetherL=IωL=rmvConservation of Angular Momentum:Li=LfIωi=IωfL=r × pL=mr × vL=r × v dm?L=τ dtNAFluid Mechanics:?p=ρgAtomic and Nuclear:λ=hpForce(N = kg?m/s2)/Torque(J = N?m)F=maFg=mgF=Fnet=maF=pt=?p?tF=dpdt=ddt(mv)Ff≤μNHooke’s Law:Fs=-kΔxFG=-Gm1m2r2FG=-Gm1m2r2 rτ=rFsinθτ=τnet=Iατ=rF=Iατ=r × Fτ=dLdt=IdωdtF=macF=mv2rF=mrω2Electricity:Coulomb’s Law:F=kq1q2r2F=14π?0 q1q2r2F=E qMagnetism:FB=qvBsinθFB=BIlsinθFB=qv × BFB=Il × BF=I dl× BFluid Mechanics:F=PAP=FA=ρhgFbuoy=ρVgPV=nRT=NkBTR=8.31Jmol?KkB=1.38×10-23 JKNAImpulse(N?s)(N?m?s)J=F ?t=?p=m ?vJ=?p=F dtH=τ ?t=?L=I ?ωH=?L=τ dtNANANAYank(N/s2)/Rotatum(J/s)Y=m JY=Ft=?F?t=dFdtP=I ζP=r × YP=τt=?τ?t=dτdt=IζNANANAEnergyWork(J = N?m)W=FdW=F ?xcosθW=F?drW=τ ?θθ-θ0W=τ ?θcosθW=τ?dθW=QVThermodynamics:W=-P ?Ve=WQHec=TH-TCTHNAKineticEnergy(J)Translational:K=KE=12mv2Rotational:K=KE=12Iω21 eV=1.60×10-19 JFluid Mechanics:Bernoulli’s Equation:P1+ρgy1+12ρv12=P2+ρgy2+12ρv22Thermodynamics:Kavg=32kBTAtomic and Nuclear:Kmax=hf-?PotentialEnergy(J)?Ug=mghUG=-Gm1m2rG=6.67×10-11 Nm2kg2Coiled Spring:Us=-12kΔx2UE=qVUE=14π?0 q1q2rUc=12QVUc=12CV2UL=12LI2Fluid Mechanics:P=P0+ρghContinuity of Mass:ρ1A1v1=ρ2A2v2Continuity of Volume:A1v1=A2v2Thermodynamics:?U=Q+WAtomic and Nuclear:E=hfE=mc2?E=(?m)c2Relativity:E=mc2 11-v2c2HeatEnergy(J)Conservation of Energy:Ei=EfEi=EfE=W+Q+K+?Ug+UG+Us+UE+Uc+UL+…=constantThermodynamics:H=kA?TLQ=mHfQ=mHv?E=Q=mC?TmC?T=mCTf-TiCH2O=4180 J Jkg °KTf=m1C1?T1i+m2C2?T2im1C1+m2C2NAPower(W)P=Wt=FvP=?E?t=dEdtP=FvcosθP=F?vP=Wt=τωP=?W?t=dWdtP=τωcosθP=τ?ωP=IVP=I2RP=V2RP=pQwhere:P = pressure Nm2Q = volumetric flow rate m3sNAEngineering ApplicationPeriod / Frequency(Hz)T=1ff=1TT=1f=2πωTs=2πmkTp=2πlgT=2πbFor:y=sinbθy=cosbθNAWaves and Optics:f=vλDoppler Effect:fr=fsv±vrv?vsCenterof Mass(m)xCM=m1x1+m2x2m1+m2xCM=miximix=1M 0Mx dmwhere M=0Mdmand dm=ρ dz dy dxrCM=mrmNANANARigid BodiesFy=mg=0(Down = ‘?‘)τ=Fy xCM=0(CW = ‘?‘)Conservation of ChargeQi=Qf(Circuits)Conservation of Massmi=mf(Chemistry)Conservation of EnergyEi=Ef(Physics)ElectricityElectricityElectricField(V/m)(N/C)E=FqEavg=-VdE= -?V?r=-dVdrGauss’s Law:E?dA=Q?0E=ρJCapacitance(F)C=QVC=?0AdC =κ?0AdCp= iCi1Cs= i1CiPotential(V)V=IRV=QCV=kiqiriV=14π?0iqiriResistance(Ω)R=VIR=ρlARs= iRi1Rp= i1RiCurrent(A)I=?Q?t=dQdtI=VRI=NevdAe=-1.602176462×10-19 CInductance(H)L=NΦIL=VLdIdtL=μ0N2AlLs= iLi1Lp= i1LiMagnetismMagnetismMagneticField(T)B=μ02π IrSolenoid:Bs=μ0nIwhere n=Nl turns per meterB=μ04π qv × rr3B=μ04π qv × rr2μ0=4π ×10-7(T?m)AAmpere’s Circuit Law:B?dl= μoI+μ0ε0d?EdtGauss’s Law for Magnetism:B?dA=0dB=μ04π I dl × rr3EMF(V)Faraday’s Law of Induction:E?dl=- ??B?tε=-LdIdtMagneticFlux(Wb)?B=BAcosθ?B=B?AGauss’s Law for Magnetism:?B=B?dAEMF(V)εavg= - ??B?tε=E?ds= - d?Bdtε=Blv ................
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