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1、TheHoppingHoopRevisitedAuthor(s):TimothyPritchettSource:TheAmericanMathematicalMonthly,Vol.106,No.7(Aug.-Sep.,1999),pp.609-617Publishedby:MathematicalAssociationofAmericaStableURL:http://www.jstor.org/stable/2589490.Accessed:01/04/201303:07YouruseoftheJSTORarchiveindicatesyouracce
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4、3.157.160.23onMon,1Apr201303:07:13AMAllusesubjecttoJSTORTermsandConditionsTheHoppingHoopRevisitedTimothyPritchettInthisMONTHLY,T.Tokieda[1]recentlyprovidedanoveldiscussionofthehoppinghoopproblemdescribedbyLittlewood[2].Unfortunately,theanalysisin[1]isincorrect.Weshowthatifthe"nosl
5、ipping"conditionimposedin[1]and[2]isstrictlyadheredto,thehoopneverbecomesairborne.Essentialfortheobservedhopofthehoopisaphaseinwhichthereisslippageatthepointofcontactofthehoopwiththesupportingsurface.Inordertoexposethisandothersubtletiesnotconsideredin[1],wetreatasomewhatmoregener
6、alproblem.TheviewofLittlewood'shoppinghoopproblempresentedhereisconsciouslydifferentfromthatgivenin[1].InofferingthisalternativewayofthinkingaboutLittlewood'shoppinghoop,wehopetodeepenthereader'sintuitiveunderstandingofpreciselywhythehoophops.Weconsiderherearigidcircularhoopofradi
7、usRandmass(1-A)Mthat,atleastinitially,rollswithoutslippingalongaflatsurface.AnadditionalobjectofmassAMisrigidlyattachedtotherimofthehoop,withthepointofattachmentcoincidingwiththecentroidoftheobject.Here,Misthetotalmassofthecombinedsystemconsistingofthehoopandtheattachedobject.Thep
8、arameterAistheratiooftheobjectmas
