點(diǎn)的運(yùn)動(dòng)學(xué)課件

點(diǎn)的運(yùn)動(dòng)學(xué)

§6–1Descriptionofthemotionofaparticleusingavectorofposition§6–2Descriptionofthemotionofaparticleusingrectangularcoordinates§6–3DescriptionofthemotionofaparticleusingnaturalcoordinatesChapter6:KinematicsofaParticle1.Equationofmotion,trajectory(path)2.Velocityofaparticle3.Accelerationofaparticle§6-1DescriptionofthemotionofaparticleusingavectorofpositionKinematics3一.運(yùn)動(dòng)方程，軌跡二.點(diǎn)的速度三.加速度運(yùn)動(dòng)學(xué)§6-1

點(diǎn)的運(yùn)動(dòng)矢量分析方法41.Equationofmotion,trajectory(path)2.Velocityofaparticle§6-2DescriptionofthemotionofaparticleusingrectangularcoordinatesKinematics5一.運(yùn)動(dòng)方程軌跡二.點(diǎn)的速度

運(yùn)動(dòng)學(xué)§6-2點(diǎn)的運(yùn)動(dòng)的直角坐標(biāo)法63.Accelerationofaparticle

Note:x,y,zare

continuousfunctionsoftimeTheequationofthetrajectory,F(x,y,z)=0,canbedeterminedbyeliminatingtheparametert.Kinematics7

三.加速度.

[注]這里的x,y,z

都是時(shí)間單位連續(xù)函數(shù)。當(dāng)消去參數(shù)

t后,可得到F(x,y,z)=0

形式的軌跡方程。運(yùn)動(dòng)學(xué)8§6-3DescriptionofthemotionofaparticleusingnaturalcoordinatesThepositionofamovingparticleisdeterminedbymeasuringthedisplacementalongitspathfromareferencepoint.

1.Curvilinearcoordinate,naturalcoordinatesystem1)Equationofmotion:S=f(t)Inaddition,polarcoordinateandcolumncoordinatecanalsobeusedtodescribethemotionofaparticle.Kinematics9§6-3點(diǎn)的運(yùn)動(dòng)的自然坐標(biāo)法

以點(diǎn)的軌跡作為一條曲線形式的坐標(biāo)軸來(lái)確定動(dòng)點(diǎn)的位置的方法叫自然坐標(biāo)法。運(yùn)動(dòng)學(xué)一.弧坐標(biāo),自然軸系1.弧坐標(biāo)的運(yùn)動(dòng)方程S=f(t)補(bǔ)充：極坐標(biāo)法(對(duì)平面曲線運(yùn)動(dòng)時(shí)可用)同理可導(dǎo)出柱坐標(biāo)下的點(diǎn)的運(yùn)動(dòng)方程102.velocityofaparticle2)NaturalcoordinatesystemOsculatingplanetangentPrincipalnormalNormalplaneKinematics11二.點(diǎn)的速度2.自然軸系運(yùn)動(dòng)學(xué)12①Tangentialacceleration

----representstherateofchangeofspeedoftheparticle3.Accelerationofaparticle②Normalacceleration-----representstherateofchangeofspeeddirectionoftheparticleKinematics13①切向加速度

----表示速度大小的變化運(yùn)動(dòng)學(xué)三.點(diǎn)的加速度②法向加速度

-----表示速度方向的變化14TheleftfigureshowsthatKinematics15由圖可知運(yùn)動(dòng)學(xué)16Teachyourselfintheclass:①Writetheequationsofmotionofaparticleusingcolumncoordinates.②What’sthedifferencebetweenand?Examineitforrectilinearandcurvilinearcases,respectively.

isvalidforallcases.,therateofchangeofthevalueofthevelocity,isonlythetangentialcomponentoftheacceleration forthecurvilinearcase.Answer:Kinematics17運(yùn)動(dòng)學(xué)課堂自學(xué).①用柱坐標(biāo)法給出點(diǎn)的運(yùn)動(dòng)方程。②與有何不同?就直線和曲線分別說(shuō)明。(直線.曲線都一樣),為速度的大小變化率,在曲線中應(yīng)為切向加速度。柱坐標(biāo)法方程18③DeterminethetypesofmotionoftheparticleMinthefollowingcases.<1>,<2>, <3><4>,<5><6> <7><8><9> <10> (uniformrectilinearmotion)(uniformcircularmotion)(uniformrectilinearmotionorrest)(rectilinearmotion)(uniformmotion)(circularmotion)(uniformmotion)(rectilinearmotion)(uniformcurvilinearmotion)(uniformlyacceleratedmotion)Kinematics19運(yùn)動(dòng)學(xué)③指出在下列情況下,點(diǎn)M作何種運(yùn)動(dòng)?<1>,<2>, <3><4>,<5><6> <7><8><9> <10> (勻變速直線運(yùn)動(dòng))(勻速圓周運(yùn)動(dòng))(勻速直線運(yùn)動(dòng)或靜止)(直線運(yùn)動(dòng))(勻速運(yùn)動(dòng))(圓周運(yùn)動(dòng))(勻速運(yùn)動(dòng))(直線運(yùn)動(dòng))(勻速曲線運(yùn)動(dòng))(勻變速曲線運(yùn)動(dòng))20

④Theparticlesaremovingalongacurvedpath,drawthedirectionofitsaccelerationinthefollowingcases. <1>M1ismovingwithauniformvelocity;<2>M2ismovingwithapositiveacceleration;<3>M3ismovingwithanegativeacceleration.⑤Examinewhetherthefollowingmotionsarepossibleanddeterminetheirtypesinthepossiblecases.(acceleratedmotion)(impossible)(uniformcurvilinearmotion(impossibleorchangetoacceleratedrectilinearmotion)(impossibleorchangetodeceleratedrectilinearmotion)(impossible)(deceleratedcurvilinearmotion)Kinematics21

④點(diǎn)作曲線運(yùn)動(dòng),

畫出下列情況下點(diǎn)的加速度方向。

<1>M1點(diǎn)作勻速運(yùn)動(dòng)

<2>M2點(diǎn)作加速運(yùn)動(dòng)

<3>M3點(diǎn)作減速運(yùn)動(dòng)⑤判斷下列運(yùn)動(dòng)是否可能出現(xiàn),若能出現(xiàn)判斷是什么運(yùn)動(dòng)?運(yùn)動(dòng)學(xué)(加速運(yùn)動(dòng))(不可能)(勻速曲線運(yùn)動(dòng))(不可能或改作 直線加速運(yùn)動(dòng))(不可能或改作直線減速運(yùn)動(dòng))(不可能)(減速曲線運(yùn)動(dòng))22⑥<1>Ifthevelocityofaparticletravelingalongastraightlineiszero,thenitsaccelerationmustbezerotoo.<2>Whenaparticleperformsacurvilinearmotion,anditsvelocityhasaconstantvalueisitsaccelerationzero?Solution:<1>notalways.Ifaparticlehaszerovelocity,itsaccelerationmaynotbezero.(forexample,attheacmeofaupcastedobject.)<2>Theaccelerationisnotzero.Acentripetalaccelerationalwaysexistsforaparticletravelingalongacurvedpath.⑦Whatarethephysicalmeaningsofthetangentialandthenormalaccelerations?answer：representstherateofchangeofthemagnitudeofthevelocity

representstherateofthechangeofthedirectionofthevelocityKinematics23⑥<1>點(diǎn)作直線運(yùn)動(dòng)時(shí),若其速度為零,其加速度也為零

<2>點(diǎn)作曲線運(yùn)動(dòng)時(shí),若其速度大小不變,加速度是否一定為零運(yùn)動(dòng)學(xué)答:<1>不一定.

速度為零時(shí)加速度不一定為零(自由落體上拋到頂點(diǎn)時(shí))<2>加速度不一定為零，只要點(diǎn)作曲線運(yùn)動(dòng)，就有向心加速度⑦切向加速度和法向加速度的物理意義？答：表示速度大小的變化 表示速度方向的變化24⑧PointMmovesalongahelicalcurvefromtheoutsidetotheinsideanditsdistancefromtheorigin