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Dndxh are familiar with the c985 i as n

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Unformatted text preview: U •V = U xVx + U yV y + U zVz = UV cosθ Obi.d.nd^xh are familiar with the C98.5). I As n becomesarger,the sum getsevencloderlo I (s€eprobl€fimethods l If you I a.t ExerciseC 9X.5 Obi.d.nd^xhUV sin θ I mag U × V = he sums nvolv€d eex.mpks unders I a.tr| uch mor€iinteested tate tyou get oiut of thesexacdyand mioree an rt[ilr m \ 1,'D, , , q hat Db C 9.l b racke understandingoVdreUrocess fVerify that theoruantity incourse,but in yo calculatinS f oint i o the squatE m f y I a cylinder V + z UrrrL)rrt.(l\V f −p o quired at this pq ann biectthan I memoro ˆ ˆ U × V = x U yVz − U zV y + y UI zVx −rU x Jz!'r \ ,rˆ , x y r 'rr' lr,r y x resultsthat wc found. For easyfuture r€ memorizint the paiticular at p mblemC 96.1. MR1 feten or dist mornentsoI inertia for vSinceasimplc obiccb in tablehavelis iMR. 2 arious . inenia L = r × P = mr ω (cMR1 lar motihavelisted (azimIuthally symmetric) ny obicrt's momentofC9.lIf yo ircu on) = I Obi.d.nd^xh ω E x e ryou eC 9amiliar with thepartides imanteFal €alculus,you canou s If c i s are f X . 5 methodsofuch mor cit follows that ifyw€g n i n oF, I a.tr| nteested that the c ate eva dL \ 1,'D, , ,i q ate the sumsinvolv€d exacdyand moreeasilyuof dre process fhis ii not T nertia1 picresw ith v ariousinEgrals.o quired a omcnts icalcula understandingsint mC9.15s equalto 0.. Db = r × F C 9.l τ= cylinder i quation i Verify at this pquantity in squatE racketsn e= quiredthat the oint in the course,but€rtia isareinteEstedin . he prc<6s,w b of in if you I thetpaiticular resultsthatsle r + 12 a cylinder, r J ! ' r \ , r , r r r L ) r r t . ( l \ + t (aslong mbo memorizint I r'rr' trlr d at p or dist at p mblemC 96.1.MR1 for btation6 around toI inertiaaor variou or dist havelisted mornentshe same f xis),b€c iMR. iML, dθ s V 2π pi inenia imply amiliar w of nrt,' method I ll ˆ iMR. T = Sinceany obicrt's momentof€'e is ou are fa portion ith tthesoverSinr θ = ; ω= ω; ω = If y sis simply a sum lle ufi oan Obi.d.nd^xh I nteested hat fhe€get o n...
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