ⅢTheLawofGravitation[例1]AsshowninFig,athinrodwithasmallmassandalengthlcanrotateintheverticalplaneabouttheaxisgoingthroughthemid-pointOandperpendiculartotheplane.Whenthethinrodisrestingathorizontalposition,asmallinsectverticallydropswithaspeedvoontherodisatadistancel/4frompointO,andthenstartstocrawlawayfromOtowardpointAattheendoftherod.Assumethatthemassoftheinsectandthemassoftherodbotharem.Ifwewanttorotatethethinrodwithaconstantangularvelocity,whatisthespeedatwhichtheinsectshouldbecrawlingtowardtheendoftherod?SowecangetthefollowequationWhentheinsectisatpointPthemomentofinertiaofthesystemAbouttherotationalaxisis[例2]已知：两平行圆柱在水平面内转动，解一：因摩擦力为内力，外力过轴，外力矩为零，则：I1+I2系统角动量守恒，以顺时针方向旋转为正方向：问题：（1）式中各角量是否对同轴而言？（2）I1+I2系统角动量是否守恒？分别以m1,m2为研究对象，受力如图：[例3]杂技演员M从h高处下落,弹起N.设跷板长l,质量为m.C为转动支点.M、N质量都为m.M与板为完全非弹性碰撞.问N可弹起多高?[例4]A150.0kgrocketmovingradiallyoutwardfromEarthhasaspeedof3.70km/sWhenitsengineshutsoff200kmaboveEarth’ssurface.(a)Assumingnegligibeairdrag,findtherocket’skineticenergyoftherocketis1000kmabovetheEarth’ssurface.(b)Whatmaximumheightabovethesurfaceisreachedbytherocket?P31936CombiningtheEq(1)-(3),wecangetsolution[例6]AtankisfilledwithwatertoaheightH.Aholeispunchedinoneofthewallsatadepthhbelowthewatersurface.(a)Showthatdistancexfromtheresultingstreamstrikesthefloorisgivenby(b)Couldaholebepunchedatanotherdepthtoproduceasecondstreamthatwouldhavethesamerange?(c)Atwhatdepthshouldtheholebeplacedtomaketheemergingstreamstrikethegroundatthemaximumdistancefromthebaseofthetank?p344.54(b)Assumingaholebepunchedatanotherdepthtoproduceasecondstreamthatwouldhavethesamerange,wecanwritethefollowequationIftheemergingstreamstrikesthegroundatthemaximumdistancefromthebaseofthetank,wecanget(A,B水平流线)由以上方程解得: