Chapter8:Momentum,Impulse,&Collisionslinearmomentum:Newton’ssecondlawintermsofmomentum:impulse:UnderwhatSPECIFICconditionislinearmomentumconserved?(Theanswerdoesnotinvolvecollisions.)Listthetypesofcollisionsandwhatdefinestheminthetablebelow.

collisions properties

Whatistheonlycollisionduringwhichyoucananalyzetheenergyandwhy?Whatisalwaystrueabouttherelativevelocitiesbetweenobjectsbeforeandafteracollision?centerofmass:

Whyisthecenterofmassofacollectionofparticlesoranextended,rigidbodysignificant?Examples:8*IalsorecommendyoudoatleastoneproblemfromeachsectionattheendofthechapterinyourUniversityPhysicsbook.Ex:8.1Acannonballisfiredwithaninitialvelocityvatanangle𝜃withthehorizontal.Atthetopofthetrajectory,theshellexplodesintotwofragmentsofequalmass.Onefragment,whosespeedimmediatelyaftertheexplosioniszero,fallsvertically.Howfarfromthecannondoestheotherfragmentland?Ignoreairresistance.

(Ifv=20m/s,𝜃=60°,thenx=53m.)

𝜃v

explosion

Ex:8.2Abodyofmassmismovingthroughspaceinonedimensionwithaspeedof2vwhen,duetoaninternalexplosion,itbreaksintothreeparts.Onepart,withamassof!

!𝑚movesawayfromthepointofexplosionwithaspeedofvperpendicular

totheoriginaldirectionofvelocity.Asecondpartwithamassof!!𝑚movesinthe

negativedirectionoftheoriginalvelocitywithaspeedof5v.a.Whatisthevelocityofthethirdpart?b.Howmuchenergyisreleasedintheexplosion?Ignoreeffectsduetogravity.(Ifm=20.0kg,v=100m/sinthepositivex-direction,thena.v3x=1.00x103m/s,v3y=-167m/s,orv3=1.01x103m/s,𝜃=9.48°belowthex-axis;b.∆K=3.23x106J.)

Ex:8.3Afteracompletelyinelasticcollision,twoobjectsofthesamemassandsameinitialspeedmoveawaytogetherathalftheirinitialspeed.Findtheanglebetweentheinitialvelocitiesoftheobjects.Ignoreexternalforcessuchasgravity.(𝜃=120°)

Chapter9:RotationofRigidBodiesrigidbody:angularvelocity:Howdoyoudeterminethedirectionofangularvelocity?angularacceleration:Howdoyoudeterminethedirectionofangularacceleration?(Wedidnotcoverthisinclass.)Listtheconstantangularaccelerationequations.Givetheequationoflinearspeedintermsofangularspeed.Givetheequationoflinearaccelerationintermsofangularacceleration.Givetheequationofcentripetalaccelerationintermsofangularvelocity.momentofinertia:rotationalkineticenergy:

Whatisspecialaboutthegravitationalpotentialenergyforanextendedbodythatisdifferentthanthegravitationalpotentialenergyforapointparticle?parallelaxistheorem:Examples:9*IalsorecommendyoudoatleastoneproblemfromeachsectionattheendofthechapterinyourUniversityPhysicsbook.Ex:9.1Awheelhasaconstantangularaccelerationof3.0rad/s2.Duringacertain4.0sinterval,itturnsthroughanangleof120rad.Assumingthatthewheelstartedfromrest,howlonghasitbeeninmotionatthestartofthis4.0-sinterval?(t=-8s;Thewheelstartedfromrest8secondsbeforethestartofthe4.0-sinterval.)

Ex:9.2Aflywheelwithadiameterof1.20misrotatingatanangularspeedof200rev/min.a.Whatistheangularspeedoftheflywheelinradianspersecond?(𝜔=20.9rad/s)b.Whatisthelinearspeedofapointontherimoftheflywheel?(v=12.5m/s)c.Whatconstantangularacceleration(inrevolutionsperminute-squared)willincreasethewheel’sangularspeedto1000rev/minin60.0s?(𝛼=800rev/min2)d.Howmanyrevolutionsdoesthewheelmakeduringthat60.0s?(𝜃=600rev)

Ex:9.3Calculatetherotationalinertiaofawheelthathasakineticenergyof24,400Jwhenrotatingat602rev/min.(I=12.3kg∙m2)

Ex:9.4Calculatetherotationalinertiaofameterstickwithmass0.56kgaboutanaxisperpendiculartothestickandlocatedatthe20cmmark.(Treatthestickasathinrod.)(I=9.7x10-2kg∙m2)

Chapter10:DynamicsofRotationalMotionWhatisthedifferencebetweentranslationalandrotationalmotion?torque:Howdoyoudeterminethedirectionoftorque?GivetheequationfortherotationalanalogofNewton’ssecondlawforarigidbody.Givetheequationforthekineticenergyduetorollingwithoutfriction.Givetheequationfortheconditionforrollingwithoutslipping.Listtheequationsforthesummationofforces(inequilibrium,withlinearacceleration,andwithcentripetalacceleration)andthesummationoftorques(inequilibriumandwithangularacceleration).

Givetheequationforworkdonebyaconstanttorque.Givetheequationfortherotationalanalogofthework-energytheorem.Givetheequationforpowerduetoatorque.angularmomentum:Howdoyoudeterminethedirectionofangularmomentum?UnderwhatSPECIFICconditionisangularmomentumconserved?Givetheequationfortheangularmomentumofarigidbodyrotatingaroundasymmetryaxis.precession:precessionangularspeed:

Examples:10*IalsorecommendyoudoatleastoneproblemfromeachsectionattheendofthechapterinyourUniversityPhysicsbook.Ex:10.1Athinuniformrodhaslength2.0mandcanpivotaboutahorizontal,frictionlesspinthroughoneend.Itisreleasedfromrestatangle𝜃=40°abovethehorizontal.Usetheprincipleofconservationofenergytodeterminetheangularspeedoftherodasitpassesthroughthehorizontalposition.(𝜔=3.1rad/s)

pin

𝜃

Ex:10.2A140-kghooprollsalongahorizontalfloorsothatthehoop’scenterofmasshasaspeedof0.150m/s.Howmuchworkmustbedoneonthehooptostopit?(W=-3.15J)Ex:10.3Atoneinstant,force𝑭 = 4.0! 𝑁actsona0.025-kgobjectthathaspositionvector𝒓 = (2.0!− 2.0𝒌)m and velocity vector𝒗 = (−5.0!+ 5.0𝒌)m/s. About theoriginandinunitvectornotation,whatarea.theobject’sangularmomentumandb.thetorqueactingontheobject?(a.𝑳=0;b.𝝉=(8.0N∙m)!+(8.0N∙m)𝒌)

Ex:10.4A3.0-kgparticlewithvelocity𝒗=(5.0m/s)!–(6.0m/s)!isat𝑥 = 3.0 𝑚,𝑦 = 8.0 𝑚.Itispulledbya7.0Nforceinthenegativex-direction.Abouttheorigin,whatarea.theparticle’sangularmomentum,b.thetorqueactingontheparticle,andc.therateatwhichtheangularmomentumischanging?(a.𝑳=(-1.7x102kg∙m2/s)𝒌;b.𝝉=(56N∙m)𝒌;c.!𝑳

!"=(56N∙m)𝒌)