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rotational motion theory

rotational motion theory

Grade:11

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Komal
askIITians Faculty 747 Points
7 years ago
Rotational motion

Themotionofarigidbodywhichtakesplaceinsuchawaythatallofitsparticlesmoveincirclesaboutanaxiswithacommonangularvelocity;also,therotationofaparticleaboutafixedpointinspace.Rotationalmotionisillustratedby thefixedspeedofrotationoftheEarthaboutitsaxis; thevaryingspeedofrotationoftheflywheelofasewingmachine;therotationofasatelliteaboutaplanet; themotionofanioninacyclotron;and themotionofapendulum.Circularmotionisarotationalmotioninwhicheachparticleoftherotatingbodymovesinacircularpathaboutanaxis.Suchmotionisexhibitedbythefirstandsecondexamples.ForinformationconcerningtheotherexamplesSeeHarmonic motion,Particle accelerator,Pendulum

Thespeedofrotation,orangularvelocity,remainsconstantinuniformcircularmotion.Inthiscase,theangulardisplacementΘexperiencedbytheparticleorrotatingbodyinatimetisΘ=ωt,whereωistheconstantangularvelocity.

Aspecialcaseofcircularmotionoccurswhentherotatingbodymoveswithconstantangularacceleration.Ifabodyismovinginacirclewithanangularaccelerationofαradians/s2,andifatacertaininstantithasanangularvelocityω0,thenatatimetsecondslater,theangularvelocitymaybeexpressedasω=ω0+αt,andtheangulardisplacementasΘ=ω0t+½αt2.SeeAcceleration,Velocity

ArotatingbodypossesseskineticenergyofrotationwhichmaybeexpressedasTrot= ½Iω2,whereωisthemagnitudeoftheangularvelocityoftherotatingbodyandIisthemomentofinertia,whichisameasureoftheoppositionofthebodytoangularacceleration.Themomentofinertiaofabodydependsonthemassofabodyandthedistributionofthemassrelativetotheaxisofrotation.Forexample,themomentofinertiaofasolidcylinderofmassMandradiusRaboutitsaxisofsymmetryis½MR2.

TheactionofatorqueListoproduceanangularaccelerationαaccordingtotheequationbelow,whereIω,theproductofmomentofinertiaandangularvelocity,iscalledtheangularmomentumoftherotatingbody.ThisequationpointsoutthattheangularmomentumIωofarotatingbody,andhenceitsangularvelocityω,remainsconstantunlesstherotatingbodyisacteduponbyatorque.BothLandIωmayberepresentedbyvectors.

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