《大学物理简明教程》 课件 5-1 Rotational kinematics

Anglesinradians

(1rad=360°/2

=57.3°)

CircularMotionThechangeofangleCircularMotionTherateofchangeofangleis

angularvelocity(angularspeed)Thelinearspeed

Aconstantlineartangentialspeed(v)atanyinstantAconstantangularvelocity,

(inrads-1)

vUniformCircularMotionExampleWhatistheangularspeedoftheroundabout?

v=r=(/10)x1ms-1

≈0.314ms-1

Achildren’sroundaboutisspinningat3revolutionsperminute(rpm).b)Iftheroundaboutis2mindiameter,whatspeedisachildstandingontheoutsideedgetravellingat?3rpm=3x2radmin-1

=/10rads-1or

3rpmmeanschildgoesroundcircumferenceoncein20secs

speed=distance/time

=2r/t=2x1/20=/10ms-1

ThechangeofangularvelocityTherateofchangeofangle

angularaccelerationTherateofchangeoflinearspeed

isthetangentialaccelerationtangentlineradialdirection

DisplacementVelocityAccelerationForceMomentumLinearKineticEnergyMassAnglechangeAngularVelocityAngularAccelerationMomentofForce(Torque)AngularMomentumRotationalKineticEnergyMomentofinertiaFormotioninacircle,thereareangularequivalentsforthequantitiesforlinearmotion.LinearCircularCircularMotionvsLinearMotion

(aorαisconstant)

ConstantLinearAccelerationConstantAngularAccelerationRotationalKinematicEquations====rrrrExampleA30cmradiuswheelstartsfromrestandrotatesthrough10revolutionswithconstantangularaccelerationof30rads-2.Howlongdoesittaketomakethe10revolutions?Whatwastheangularvelocityafterrotating10revolutions?

A30cmradiuswheelstartsfromrestandrotatesthrough10revolutionswithconstantangularaccelerationof30rads-2.Howlongdoesittaketomakethe10revolutions?Whatwastheangularvelocityafterrotating10revolutions?

ExampleArotating5metrelongbarstartswithanangularvelocityof30rads-1

anddeceleratestoastopafterrotatingfor60revolutions.Howfastisthemiddlepointofthebarmovinginitially(inm/s)?Whatistheangularacceleration?

5mvr02=302+2α(377)

α

=-(302)/2(377)=-1.2rads-2b)

=60x

2=377

radω0=30rads-1Aparticlehasaconstantangularvelocity.(orinotherwords,inuniformcircularmotion)Isitaccelerating?Aconstantangularvelocityimpliesaconstantspeedbutnotaconstantdirection.Theobjectischangingitsvelocity

rvxCentripetalAccelerationThereisanacceleration

Massmr

xCentripetalAcceleration

O

AB

CentripetalAcceleration

O

AB

CentripetalAccelerationIftheparticlehasamassmandisbeingaccelerateditmustbesubjectto