Ch1 Kinematics

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1、KinematicsKinematicsWewillstartwiththesubjectofKinematics:“Howdowedescribethemotionofobjects?”a)inoneandtwodimensions.b)asafunctionoftime.ThenextchapterwillbeDynamics:“Whatcausesthechangeinthemotionofobjects?”Abstract1Quantitiestodescribeaparticle’smotion21Dmotion:Freefall32Dmotion:P

2、rojectilemotion4Circularmotion5Relativemotion1.PointparticleTreattheobjectasapointparticlewithoutshapeandsizebutwithmass.
Idealmodel.
Acomplexobjectcanberegardedasagroupofpointparticles.111．1．．Position．PositionzDefinitionAvectorthatextendsfromareferencepointOtoP(x,y,z)ktheparticle.rg

3、Obyij



ar=xi+yj+zkxmanitude：r=x2+y2+z2xyzdirection：cosa=,cosb=,cosg=rrrMotionEquations



r=x(t)i+y(t)j+z(t)kx=x(t)y=y(t)z=z(t)Fxyz(,,)=0消去t¾¾¾®Gxyz(,,)=0——TrajectoryEq.(TrajectoryEq.(轨道方程TrajectoryEq.(轨道方程)))222．2．．Displacement．Displacement

D=rr¢-=rrt(+D-t)rt()zPD

4、DDsP¢DDDrrr¢¢¢Oyx

DisplacementanddistanceDisplacementanddistance：Displacementanddistance：Dr¹DsPositionandDisplacement•Positionisdefinedintermsofaframeofreference•Onedimensional,sogenerallythex-ory-axis•Displacementmeasuresthechangeinposition•RepresentedasDx(ifhorizontal)orDy(ifverti

5、cal)•Vectorquantity(i.e.needsdirectionalinformation)•+or-isgenerallysufficienttoindicatedirectionforone-dimensionalmotion333．3．．Velocity．Velocity3.1velocityzPDDDsAveragevelocity：DDDrP¢


r
Drrt(+Dt)-rt()v==r¢DtDtOyInstantaneousvelocity:


Drdrxv=lim=Dt®0Dtdtds
magnitudemagnitude：magn

6、itude：v=------------Speed------Speeddt
direction:Tangenttothepath3.2Componentnotationofvelocity




r=rt()=xti()+ytj()+ztk()

drdx
dy
dz



v==i+j+k=vi+vj+vkxyzdtdtdtdtmagnitude:v=v2+v2+v2xyzvvvxyzdirection:cosa=,cosb=,cosg=vvavvv444．4．．Acceleration．AccelerationzvP4.1Acceleratio

7、nP¢rv¢Averageacceleration：r¢



Dvv(t+Dt)-v(t)Oya==DtDtInstantaneousacceleration：x

2
v
Dvdvdra=lim==2DDDvDt®0Dtdtdtv¢
Note:thedirectionofvelocityandaccelerationarenotnecessarilythesame.4.2Componentnotationofacceleration





v=vt()=vti()+vtjvtk()+()xyz

dvdv
dv
dv



xyza==i+j+k=ai+

8、aj+akxyzdtdt