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1、Chapter10&11RotationalMotionAboutaFixedAxisTorque,RotationalInertiaandLawWorkandRotationalKineticEnergyRollingAngularMomentumandConservationofAngularMomentum10-1.AngularQuantities(P235)Angulardisplacement(角位移):Angularvelocity:Angularacceleration:1.Angularvariables(radian
2、measure)xyOor2.RelationoflinearandangularvariablesThedistancealongacirculararc:Differentiatingaboveequationwithrespecttotime(ragainholdsconstant)Thelinearspeed(withrheldconstant):Thetangentialcomponentat:Theradialcomponentan:Theyarevalidonlyifanglesareexpressedinradian.a
3、nisalsocalledaR,radialacceleration,inourbook.q-q0w=w0+atwq-q0=w0t+at2tw2=w02+2a(q-q0)aq-q0=(w0+w)tw0q-q0=wt-at2v=v0+atx-x0x-x0=v0t+at2vv2=v02+2a(x-x0)tx-x0=(v0+v)tax-x0=vt-at2v0Equationsofmotionforconstantlinearaccelerationareanalogoustotheonesofconstantangularaccelerati
4、on:linear missingangularequationvariableequation3.Kinematicsequationsforuniformlyacceleratedrotationalmotion(P238)Example:Theflywheelofasteamenginerunswithaconstantangularvelocityof150rev/min.Whensteamisshutoff,thefrictionofthebearingsandoftheairstopsthewheelin2.2h.Answe
5、r:(b)Howmanyrotationsdoesthewheelmakebeforestopping?(a)whatistheconstantangularacceleration,inrev/min2,ofthewheelduringtheslowdown?(c)Attheinstanttheflywheelistuningat75rev/min,whatisthetangentialcomponentofthelinearaccelerationofaflywheelparticlethatis50cmfromtheaxisofr
6、otation?(d)Whatisthemagnitudeofthenetlinearaccelerationoftheparticlein(c)?10-2SeveralConceptsRelatedtoRotation(a)Arigidbodyisonethatcanrotatewithallitspartslockedtogetherandwithoutanychangeinitsshape(刚体是一种特殊的质点系统).(b)Themotionofarigidbodyreducestoatranslationofitscentero
7、fmassaddsarotationrelativetocenterofmass..O(c)Translationismotionalongastraightline.Feature:ABA'B'A''B''(d)RotationisthemotionastheFig.showing.protationaxisFeature:Anypointmovesaroundonesameaxis.zABA′B′Thefeaturesofrotationaboutafixedaxis:Thelocationanddirectionofrotatio
8、naxisarefixedrelativetoainertialreferenceframe.Everypointofbodymovesinacirclewhosecenterliesonrotationa
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