EXAMPLE1Amansiteonaturnchairholdingapairofdumbbells,each5kg,atadistanceof0.6mfromaxisofrotationofthechair.Heisgivenanangularvelocityof5rad/s,afterwhichhepullsthedumbbellsinuntiltheyareonly0.2mdistantfromtheaxis.Themomentofinertiaofthemanabouttheaxisofrotationis5kgm2andmaybeconsideredconstant.(a)WhatistheInitialanglemomentofthesystem?(b)Whatistheangularvelocityofsystemafterdumbbellsarepulledintowardtheaxis?(c)Computerthedifferenceofkineticenergyofsystembeforeandafterpullingdumbbells.
EXAMPLE1Solution:(a)(b)Fromtheconservationlawofangularmomentum(c)
EXAMPLE2Awheelisonahorizontalaxis,Theradiusofsystemisr=0.10m.A5.0kgofblockattachedtoastringiswrappedaroundtheaxisandreleasedfromrest.Itfallsadistanceof1.0min10s.(a)Whatisthetensioninthestring?(b)Whatisthemomentofinertiaofthewheelandaxis?
EXAMPLE2Solution:(a)Fromthen(b)From
Waterflowssteadilyfromareservoir,asinFig.17.Theelevationofpoint1is10.0m;ofpoint2andpoint3itis1.0m.Thecrosssectionareaatpoint2is0.04m2andatpoint3itis0.020m2.Theareaofthereservoirisverylargecomparedwiththeareasofthepipe.a)Computethegaugepressureatpoint2.b)Computethedischargerateincubicmeterspersecond.EXAMPLE3123
EXAMPLE3123Solution:(a)(b)
EXAMPLE4Whetherthepressureinbottleoftransfusionispositiveornegativeandwhatisthevelocityattheendoftube?h1h2Solution:
EXAMPLE5Abodyofmass100ghangsfromalongspiralspring.Whenpulleddown10cmbelowitsequilibriumpositionandreleased,itvibrateswithaperiodof2s.(a)Whatisitsvelocityasitpassesthroughtheequilibriumposition?(b)Whatistheaccelerationwhenitis5cmabovetheequilibriumposition?(c)Whenitmovingupwar