医学物理学-chapter2b_14_p

Summarytothelastlecture1.unitvectorsandproductsofvectors2.definitionofforce:F=dP/dt3.theNewton’slawsofmotion;4.workandkineticenergy:5.conservativeforceandpotentialenergy.6.ConservationofenergyPleasevisitatthefollowingwebsite:://physics.med.stu.edu.cn/Coursework:notebookusedandhandintime?2.4Momentumanditsconservation（守恒）pddtF2.4.1Impulse（冲量）Fromthedefinitionofforce,wehave:Fdtistheamountofforceaccumulation(积聚)withinthetimeperioddtandiscalledImpulse:12122121VmVmpppddtFIttttImpulse=thechangeofmomentumattTheoremofmomentum2.4.2momentumconservation0dtpdFAlsofromNewton’ssecondlawofmotion,iftheexternal(外部的)forceiszero,thenwehaveIfthesystemcontainsmanyparticles,thenconstant21pppThisistheconservationallawofmomentum.2.4.3Collisions(碰撞)fipp•Isolatedsystem(孤立系统：无外力)：momentumshouldbeconserved.•Forelastic(弹性的)andhorizontal(水平的)collisions,thekineticenergyshouldbeconserved.kfkiEE2.5CircularMotion(圆周运动)2.5.1Rotationalkinematics(转动运动学)RsHaveyouevernoticedthebasicangularquantities?Angulardisplacement:(角位移)angularvelocity:;angularaccelerationAngulardisplacementcanbe:A.positive,B.negative,C.eitherpositiveornegative;D.noneoftheabovezRot.dir.Ref.dirRot.planeaxisPxOsRAnti-clockwise:ispositiveClockwise:isnegativeDisplacementx←→AngulardisplacementVelocitydx/dt←→d/dtangularvelocityd/dt(2.20)Radian(弧度):zRot.dir.Ref.dirRot.planeaxisPxOsRRsWhatistheunitofangulardisplacement?Foracircularmotion,whatistherelationofvand?OPzrvv=R(2.21)dtdRdtdsItisknownthats=RWhatdoesvreallymean?Thevelocityvisthedistancetraveledinonesecond.Ifwewritev=2RfWhatdoesfmean?Itisthenumberofrevolutionpersecond.(每秒转动的圈数)Consideringv=R,wehaveR=2RfTherefore,weobtain:=2forf=/2(2.22)Theletterfstandsforfrequencyinrevolution(转数)persecond.Accelerationa=d2x/dt2←→=d2/dt2dtddtddtddtd22Thisrelationisnotonlyvalidforthecircularmotionbutalsoforanykindofcurvemotion.Asv=R,tangentialacceleration:RdtdRdtRddtdva)(Forcircularmotion,accelerationcanbedividedintotwocomponents:tangentialandcentripetal(向心的)acceleration.222)(RRRRvaRantnaaantO2.4.2AngularmomentumanditsconservationWhatisangularmomentum(角动量)?Byyourknowledge,itisA.MomentumtimesangleB.AmomentumaboutrotationC.quantityaboutarotationalspeedD.noneoftheabove•Theangularmomentumisdefinedaspparticle’slinearmomentum;rthepositionvectorprLOPzrvmItsdirection？prFig.2.2sinsinmrvrpLItsmagnitude？A.SameasrB.SameaspC.randpD.noneoftheaboveIfaparticlewithmassmmovesinthex-yplane,itspathcanbedescribedbyalineequation2xyDoestheparticlehaveangularmomentumtoO?2xyOxyA.YesB.NoDocalculateittobeasacoursework2.ConservationofAngularmomentumTheconservationofaphysicalquantityisdefinedasthatitdoesnotchangewithtime.IfLisconserved,then0dtLdExample:Asingleparticlemovesinacentralforcefield.Isitsangularmomentumconserved?prL?dtLdprOprdtddtLd0)(FrvmvdtpdrpdtrdThusL=constantQuestion1:Thinkingaboutthephenomenathatsomebodyisridingabicycle.Whenhe(she)ridesfast,thebicycleissteady,whenheridestooslow,thebicycleiseasytofalldown.Why?Angularmomentiskeptconstantbygravityasmuchaspossible!(classroomshow:spinningtop).Question2:Isthespinningtoprelatedtotheangularmomentumconservation?A.YesB.NoC.notsure2.4.3Torque(力矩)androtationallawTorqueisdefinedasFrA.force×itsarmtoOB.FrOConsideraparticlewithmassmattachedtotheendofastringandanappliedforceFactingontheparticleperpendicularlytothestring.Whichoneiscorrect?∴=r(ma)=rm(r)(purerotation)=mr2=II=mr2iscalledmomentofinertiaorrotationalinertia.=IiscalledrotationallawrFrFFr90sinIFWhenthespool*(轮轴)ispulledtotheright,willitrolltowardtheA.rightB.leftC.other,dependson…Rotationalinertia21iNiirmI2mrIdmrIrmINiii2120morlimorDiscretemassesContinuousmassesForasystemwhichcontainmanydiscretemassesSothedefinitionoftherotationalinertiaforcontinuousmassesbecomes)dimensions-3(for22dVrdmrI)dimensions-2(for22dsrdmrIdimension)-1(for22dlrdmrITheSIunitofrotationalinertiaiskgm2Themomentofinertiaforspecificshapes1.Thinhoop(铁环)aboutsymmetryaxis22dlrdmrIWhereislinedensitywhichcanbefoundas:RdlRM2SodlRMdldmRr2,220222MRdlπMRdlRdmrIR2.Diskorcylinderaboutsymmetryaxis;drr2rR22dsrdmrIπrdrRMdsdm22Canwetaketheabover2asaconstantR2?A.Yes.B.No.Why?204203202222214122)2(MRrπRMdrrRMrdrrπRMdsrdmrIRRR3.Thinrodaboutperpendicularaxisthroughcenter2121MLdrLMdrdmdrrdmrI22drr2/022/0222LLdrrLMdrrITherotationalkineticenergyParticle’skineticenergy:221iikvmEThekineticenergyofrotationofthebodyshouldbethesumofkineticenergiestakenoveralltheparticlesthatmakeupthebody.222222221121)(21212121IrmvmvmvmEiiiikThirdlectureendshereTheangularmomentumofarigidbodyvrmprLIfvisatangentialvelocity,anditisperpendiculartor,wecouldusetheformularvWehaveImrrmrvmrL2rv(第四次课从本页到Continuityequation）OPzrvmForrotations,thedirectionofisdefinedasright-handrule.Itshouldbethesameasa