点的运动学课件

点的运动学

§6–1Descriptionofthemotionofaparticleusingavectorofposition§6–2Descriptionofthemotionofaparticleusingrectangularcoordinates§6–3DescriptionofthemotionofaparticleusingnaturalcoordinatesChapter6:KinematicsofaParticle1.Equationofmotion,trajectory(path)2.Velocityofaparticle3.Accelerationofaparticle§6-1DescriptionofthemotionofaparticleusingavectorofpositionKinematics3一.运动方程，轨迹二.点的速度三.加速度运动学§6-1

点的运动矢量分析方法41.Equationofmotion,trajectory(path)2.Velocityofaparticle§6-2DescriptionofthemotionofaparticleusingrectangularcoordinatesKinematics5一.运动方程轨迹二.点的速度

运动学§6-2点的运动的直角坐标法63.Accelerationofaparticle

Note:x,y,zare

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

三.加速度.

[注]这里的x,y,z

都是时间单位连续函数。当消去参数

t后,可得到F(x,y,z)=0

形式的轨迹方程。运动学8§6-3DescriptionofthemotionofaparticleusingnaturalcoordinatesThepositionofamovingparticleisdeterminedbymeasuringthedisplacementalongitspathfromareferencepoint.

1.Curvilinearcoordinate,naturalcoordinatesystem1)Equationofmotion:S=f(t)Inaddition,polarcoordinateandcolumncoordinatecanalsobeusedtodescribethemotionofaparticle.Kinematics9§6-3点的运动的自然坐标法

以点的轨迹作为一条曲线形式的坐标轴来确定动点的位置的方法叫自然坐标法。运动学一.弧坐标,自然轴系1.弧坐标的运动方程S=f(t)补充：极坐标法(对平面曲线运动时可用)同理可导出柱坐标下的点的运动方程102.velocityofaparticle2)NaturalcoordinatesystemOsculatingplanetangentPrincipalnormalNormalplaneKinematics11二.点的速度2.自然轴系运动学12①Tangentialacceleration

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

----表示速度大小的变化运动学三.点的加速度②法向加速度

-----表示速度方向的变化14TheleftfigureshowsthatKinematics15由图可知运动学16Teachyourselfintheclass:①Writetheequationsofmotionofaparticleusingcolumncoordinates.②What’sthedifferencebetweenand?Examineitforrectilinearandcurvilinearcases,respectively.

isvalidforallcases.,therateofchangeofthevalueofthevelocity,isonlythetangentialcomponentoftheacceleration forthecurvilinearcase.Answer:Kinematics17运动学课堂自学.①用柱坐标法给出点的运动方程。②与有何不同?就直线和曲线分别说明。(直线.曲线都一样),为速度的大小变化率,在曲线中应为切向加速度。柱坐标法方程18③DeterminethetypesofmotionoftheparticleMinthefollowingcases.<1>,<2>, <3><4>,<5><6> <7><8><9> <10> (uniformrectilinearmotion)(uniformcircularmotion)(uniformrectilinearmotionorrest)(rectilinearmotion)(uniformmotion)(circularmotion)(uniformmotion)(rectilinearmotion)(uniformcurvilinearmotion)(uniformlyacceleratedmotion)Kinematics19运动学③指出在下列情况下,点M作何种运动?<1>,<2>, <3><4>,<5><6> <7><8><9> <10> (匀变速直线运动)(匀速圆周运动)(匀速直线运动或静止)(直线运动)(匀速运动)(圆周运动)(匀速运动)(直线运动)(匀速曲线运动)(匀变速曲线运动)20

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

④点作曲线运动,

画出下列情况下点的加速度方向。

<1>M1点作匀速运动

<2>M2点作加速运动

<3>M3点作减速运动⑤判断下列运动是否可能出现,若能出现判断是什么运动?运动学(加速运动)(不可能)(匀速曲线运动)(不可能或改作 直线加速运动)(不可能或改作直线减速运动)(不可能)(减速曲线运动)22⑥<1>Ifthevelocityofaparticletravelingalongastraightlineiszero,thenitsaccelerationmustbezerotoo.<2>Whenaparticleperformsacurvilinearmotion,anditsvelocityhasaconstantvalueisitsaccelerationzero?Solution:<1>notalways.Ifaparticlehaszerovelocity,itsaccelerationmaynotbezero.(forexample,attheacmeofaupcastedobject.)<2>Theaccelerationisnotzero.Acentripetalaccelerationalwaysexistsforaparticletravelingalongacurvedpath.⑦Whatarethephysicalmeaningsofthetangentialandthenormalaccelerations?answer：representstherateofchangeofthemagnitudeofthevelocity

representstherateofthechangeofthedirectionofthevelocityKinematics23⑥<1>点作直线运动时,若其速度为零,其加速度也为零

<2>点作曲线运动时,若其速度大小不变,加速度是否一定为零运动学答:<1>不一定.

速度为零时加速度不一定为零(自由落体上抛到顶点时)<2>加速度不一定为零，只要点作曲线运动，就有向心加速度⑦切向加速度和法向加速度的物理意义？答：表示速度大小的变化 表示速度方向的变化24⑧PointMmovesalongahelicalcurvefromtheoutsidetotheinsideanditsdistancefromtheorigin