Axis. Axis. Axis. Solid cylinder (or disk) about. Hoop about. Annular cylinder (or ring) about central axis. central axis.


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1 Insucos: Fiel/che/Deweile PYSICS DEPATENT PY 48 Em ch 5, 5 Nme pin, ls fis: Signue: On m hono, I he neihe gien no eceie unuhoie i on his eminion. YOU TEST NUBE IS TE 5DIGIT NUBE AT TE TOP OF EAC PAGE. Coe ou es nume on ou nswe shee use lines 76 8 on he nswe shee fo he 5igi nume. Coe ou nme on ou nswe shee. DAKEN CICES COPETEY. Coe ou UFID nume on ou nswe shee. Pin ou nme on his shee n sign i lso. 3 Do ll scch wok nwhee on his em h ou like. Cicle ou nswes on he es fom. A he en of he es, his em pinou is o e une in. No cei will e gien wihou oh nswe shee n pinou. 4 Blcken he cicle of ou inene nswe compleel, using # pencil o lue o lck ink. Do no mke n s mks o some nswes m e coune s incoec. 5 The nswes e oune off. Choose he closes o ec. Thee is no penl fo guessing. If ou eliee h no lise nswe is coec, lee he fom lnk. 6 n in he nswe shee sepel. Use g = 9.8 m/s Ais oop ou cenl is Ais Annul cline o ing ou cenl is Ais Soli cline o isk ou cenl is I = I = + I = Ais Soli cline o isk ou cenl imee Ais Thin o ou is hough cene pepenicul o lengh Ais Soli sphee ou n imee I = 4 + I = I = 5 Ais Thin spheicl shell ou n imee Ais oop ou n imee Ais Sl ou pepenicul is hough cene I = 3 I = I = +
2 PY48 Em Fomul Shee Vecos k j i k j i ˆ ˆ ˆ ˆ ˆ ˆ gniues: Scl Pouc: gniue: cos = ngle eween n Veco Pouc: k j i ˆ ˆ ˆ gniue: sin = smlles ngle eween n oion Displcemen: imension 3 imensions Aege Veloci: e im e 3 im Aege Spee: s e = ol isnce/ Insnneous Veloci: im 3 im elie Veloci: BC AB AC 3 im Aege Acceleion: e im e 3 im Insnneous Acceleion: im 3 im Equions of oion Consn Acceleion Newon s w n Weigh m F ne m = mss Weigh ne he sufce of he Eh = W = mg use g = 9.8 m/s gniue of he Ficionl Foce s = sic coefficien of ficion, k = kineic coefficien of ficion Sic: N s s F f m Kineic: N k k F f F N is he mgniue of he noml foce Unifom Cicul oion ius, Tngenil Spee =, Angul Veloci Cenipel Acceleion & Foce: m m F Peio: T Pojecile oion hoionl sufce ne Eh, = iniil spee, = iniil ngle wih hoionl nge: g sin eigh: g sin Time of fligh: g f sin Quic Fomul If: c Then: c 4
3 PY48 Em Fomul Shee Wok W, echnicl Eneg E, Kineic Eneg KE, Poenil Eneg U W KE = m Wok: W F = F Powe: P F Cons n F = = Kineic Eneg: WokEneg Theoem: KE = KE W Poenil Eneg: U = F f i+ WokEneg: Weenl = KE + U + Eheml + Einenl Gi Ne he Sufce of he Eh is up: Sping Foce: F echnicl Eneg: ine omenum: = k Cene of ss CO: Ne Foce: F omen of Inei: Angul omenum: U = k F = mg U = mg U F = Wok: W =  U E = KE+ U Isole n Conseie Ssem: E= KE+ U = E = E ine omenum, Angul omenum, Toque f p p p = m F = Kineic Eneg: KE = Impulse: J = p= m F P N o = m i i= CO N = mi i o i= N o ne = = oco Po = oco = i= I = N i= m i i p iscee I = Toque: = m Conseion of ine omenum: if unifom p i CO Pllel Ais: = N pi o i= I = ICO + h f τ = F = Wok: W = τ i p = = hen p = consn n p f = pi τ = = hen = consn n f = i F ne Conseion of Angul omenum: if ne oionl Vles ω Angul Posiion: Angul Veloci: ω = Angul Acceleion: α = = Toque: τ ne = Iα Angul omenum: = Iω Kineic Eneg: E o = Iω = Powe: P= τω I Ac engh: s= Tngenil Spee: = ω Tngenil Acceleion: =α olling Wihou Slipping: CO = CO = ω CO = α KE = CO + I CO ω oionl Equions of oion Consn Angul Acceleionα ω = ω + α = + ω + ω = ω + α α i f i
4 . Ne he sufce of he Eh, lock wih mss = kg is plce gins sping on ficionless incline wih ngle = 3 s shown in he figue. The lock is no connece o he sping. The sping hs sping consn of k = 96 N/m n iniill compesse cm. The sping is hen elese. ow f in m long he incline fom he elese poin will he lock el? k. Ne he sufce of he Eh, lock wih mss = kg is plce gins sping on ficionless incline wih ngle = 3 s shown in he figue. The lock is no connece o he sping. The sping hs sping consn of k = 94 N/m n iniill compesse cm. The sping is hen elese. ow f in m long he incline fom he elese poin will he lock el? k 3. Ne he sufce of he Eh, lock wih mss = kg is plce gins sping on ficionless incline wih ngle = 3 s shown in he figue. The lock is no connece o he sping. The sping hs sping consn of k = 39 N/m n iniill compesse cm. The sping is hen elese. ow f in m long he incline fom he elese poin will he lock el? k 4. A kg lock slies long hoionl ficionless sufce wih n iniil spee = m/s. When he lock eches he poin =, ile hoionl foce wih mgniue h epens on ccoing o he fomul F =, whee = N/m, is pplie o he lock s shown in he figue. Wh is he spee of he lock in m/s when i eches he poin = = 5 m? F = = is A kg lock slies long hoionl ficionless sufce wih n iniil spee = m/s. When he lock eches he poin =, ile hoionl foce wih mgniue h epens on ccoing o he fomul F =, whee = N/m, is pplie o he lock s shown in he figue. Wh is he spee of he lock in m/s when i eches he poin = = 5 m? F = = is A kg lock slies long hoionl ficionless sufce wih n iniil spee = 4 m/s. When he lock eches he poin =, ile hoionl foce wih mgniue h epens on ccoing o he fomul F =, whee = N/m, is pplie o he lock s shown in he figue. Wh is he spee of he lock in m/s when i eches he poin = = m? F = = is A 4kg picle moes long he is une he influence of conseie foce. The poenil eneg is gien U = 3, whee = 8. J/m 3. Wh is he mgniue of he cceleion of he picle in m/s when i is he poin = m?
5 8. A 4kg picle moes long he is une he influence of conseie foce. The poenil eneg is gien U = 3, whee = 8. J/m 3. Wh is he mgniue of he cceleion of he picle in m/s when i is he poin = 3 m? A 4kg picle moes long he is une he influence of conseie foce. The poenil eneg is gien U = 3, whee = 8. J/m 3. Wh is he mgniue of he cceleion of he picle in m/s when i is he poin = 4 m? Sing fom es ne he sufce of he Eh, 5kg e slies m own eicl pine ee, n hs spee of 6 m/s jus efoe hiing he goun. Wh ws he mgniue of he ege ficionl foce in N cing on he e uing he slie? Sing fom es ne he sufce of he Eh, 5kg e slies m own eicl pine ee, n hs spee of 8 m/s jus efoe hiing he goun. Wh ws he mgniue of he ege ficionl foce in N cing on he e uing he slie? Sing fom es ne he sufce of he Eh, 5kg e slies m own eicl pine ee, n hs spee of m/s jus efoe hiing he goun. Wh ws he mgniue of he ege ficionl foce in N cing on he e uing he slie? Ne he sufce of he Eh, unifom limp ope of mss n lengh hngs oe ficionless peg heigh oe he goun, s shown in he figue. If he ope is elese fom es wih 3/4 of is lengh on one sie n /4 of is lengh on he ohe sie, wh is he spee of he ope when he fis en his he goun? 3g/8 3 g 3 5 3g 4 3g 5 g 4. Ne he sufce of he Eh, unifom limp ope of mss n lengh hngs oe ficionless peg heigh oe he goun, s shown in he figue. If he ope is elese fom es wih /3 of is lengh on one sie n /3 of is lengh on he ohe sie, wh is he spee of he ope when he fis en his he goun? 3 g 3g/ g 4 3g 5 g
6 5. Ne he sufce of he Eh, unifom limp ope of mss n lengh hngs oe ficionless peg heigh oe he goun, s shown in he figue. If he ope is elese fom es wih 3/5 of is lengh on one sie n /5 of is lengh on he ohe sie, wh is he spee of he ope when he fis en his he goun? 5 3g 3g/8 3 3 g 4 3g 5 g 6. A kg picle moes long he is une he influence of conseie foce. The poenil eneg funcion of he picle is gien he fomul U = +5, whee is he cooine in m s U is mesue in Joules. Wh is he fhes poin in he posiie iecion h he picle cn ech in m if = m is kineic eneg is 5 J? A kg picle moes long he is une he influence of conseie foce. The poenil eneg funcion of he picle is gien he fomul U = +5, whee is he cooine in m s U is mesue in Joules. Wh is he fhes poin in he posiie iecion h he picle cn ech in m if = m is kineic eneg is J? A kg picle moes long he is une he influence of conseie foce. The poenil eneg funcion of he picle is gien he fomul U = +5, whee is he cooine in m s U is mesue in Joules. Wh is he fhes poin in he posiie iecion h he picle cn ech in m if = m is kineic eneg is 5 J? Ne he sufce of he Eh, ll of mss hngs eicll on sing of lengh s shown in he figue. A lump of mu wih mss m n hoionl spee collies wih he ll. The mu sicks o he ll cusing i o swing on is sing. If m =, wh mimum eicl heigh oes he mull ssem ech fe he collision? Befoe Afe.5 /g. /g 3.56 /g 4.5 /g /g Bll. Ne he sufce of he Eh, ll of mss hngs eicll on sing of lengh s shown in he figue. A lump of mu wih mss m n hoionl spee collies wih he ll. The mu sicks o he ll cusing i o swing on is sing. If m =, wh mimum eicl heigh oes he mull ssem ech fe he collision? Befoe Afe. /g.5 /g 3.56 /g 4.5 /g /g Bll
7 . Ne he sufce of he Eh, ll of mss hngs eicll on sing of lengh s shown in he figue. A lump of mu wih mss m n hoionl spee collies wih he ll. The mu sicks o he ll cusing i o swing on is sing. If m = /, wh mimum eicl heigh oes he mull ssem ech fe he collision? Befoe Afe.56 /g.5 /g 3. /g 4.5 /g /g Bll. A.5kg ll is oppe fom es heigh = m oe he sufce of he Eh, s shown in he figue. I sikes he siewlk = n epeiences n upw foce h epens on ime ccoing o he fomul F =, whee is consn. If = 98 N/s n he ll is in conc wih he siewlk fo.45 secons, wh mimum heigh h in m is eche he ll when i eouns fom he siewlk? is Dop eoun h A.5kg ll is oppe fom es heigh = m oe he sufce of he Eh, s shown in he figue. I sikes he siewlk = n epeiences n upw foce h epens on ime ccoing o he fomul F =, whee is consn. If = 98 N/s n he ll is in conc wih he siewlk fo.5 secons, wh mimum heigh h in m is eche he ll when i eouns fom he siewlk? is Dop eoun h A.5kg ll is oppe fom es heigh = m oe he sufce of he Eh, s shown in he figue. I sikes he siewlk = n epeiences n upw foce h epens on ime ccoing o he fomul F =, whee is consn. If = 98 N/s n he ll is in conc wih he siewlk fo.5 secons, wh mimum heigh h in m is eche he ll when i eouns fom he siewlk? is Dop eoun h A kg lock wih spee = 5 m/s sliing long hoionl ficionless sufce collies wih secon lock es wih mss of 3 kg. The wo locks sick ogehe o fom single ojec wih mss of 5kg n coninue o slie. ow much kineic eneg in J is los uing he collision ue o he heing up of he locks? A kg lock wih spee = m/s sliing long hoionl ficionless sufce collies wih secon lock es wih mss of 3 kg. The wo locks sick ogehe o fom single ojec wih mss of 5kg n coninue o slie. ow much kineic eneg in J is los uing he collision ue o he heing up of he locks? A kg lock wih spee = 5 m/s sliing long hoionl ficionless sufce collies wih secon lock es wih mss of 3 kg. The wo locks sick ogehe o fom single ojec wih mss of 5kg n coninue o slie. ow much kineic eneg in J is los uing he collision ue o he heing up of he locks?
8 8. Sn fom sion hoppe flls consn e = 3 kg/s on moing el wih mss s shown in he figue. The el is suppoe ficionless olles n he el n he sn h hs fllen on he el moe wih consn spee V ue o consn hoionl eenl foce F e pplie o he el. If F e = 6 N, wh is he consn spee V in m/s? oppe Sn ss m Bel ss V F e 9. Sn fom sion hoppe flls consn e = 3 kg/s on moing el wih mss s shown in he figue. The el is suppoe ficionless olles n he el n he sn h hs fllen on he el moe wih consn spee V ue o consn hoionl eenl foce F e pplie o he el. If F e = 9 N, wh is he consn spee V in m/s? oppe Sn ss m Bel ss V F e 3. Sn fom sion hoppe flls consn e = 3 kg/s on moing el wih mss s shown in he figue. The el is suppoe ficionless olles n he el n he sn h hs fllen on he el moe wih consn spee V ue o consn hoionl eenl foce F e pplie o he el. If F e = N, wh is he consn spee V in m/s? oppe Sn ss m Bel ss V F e 3. A ce c ccelees unifoml fom spee of 4 m/s o spee of 58 m/s in 6 secons while eling oun cicul ck of ius 59 m. When he mgniue of he c s ol cceleion ecomes 5 m/s, wh is is spee in m/s? A ce c ccelees unifoml fom spee of 4 m/s o spee of 58 m/s in 6 secons while eling oun cicul ck of ius 65 m. When he mgniue of he c s ol cceleion ecomes 5 m/s, wh is is spee in m/s? A ce c ccelees unifoml fom spee of 4 m/s o spee of 58 m/s in 6 secons while eling oun cicul ck of ius 79 m. When he mgniue of he c s ol cceleion ecomes 5 m/s, wh is is spee in m/s? A hin o oflengh n mss is loce on he is fom = o = s shown in he figue. I hs nonunifom line mss ensi h ies wih ccoing o he fomul λ = λ, whee λ is consn. Wh is he momen of inei of he o ou he is =? is is
9 35. A hin o oflengh n mss is loce on he is fom = o = s shown in he figue. I hs nonunifom line mss ensi h ies wih ccoing o he fomul λ = λ, whee λ is consn. Wh is he momen of inei of he o ou he is =? is is 36. A hin o oflengh n mss is loce on he is fom = o = s shown in he figue. I hs nonunifom line mss ensi h ies wih ccoing o he fomul λ = λ 3, whee λ is consn. Wh is he momen of inei of he o ou he is =? is is 37. An sonu is eing ese in cenifuge. The cenifuge hs ius n, in sing fom es =, oes wih consn ngul cceleion α. If he mgniue of he ngenil cceleion is equl o he mgniue of he il cceleion i.e., cenipel cceleion = s, wh is he mgniue of he ngul eloci in /s of he cenifuge = 3 s? An sonu is eing ese in cenifuge. The cenifuge hs ius n, in sing fom es =, oes wih consn ngul cceleion α. If he mgniue of he ngenil cceleion is equl o he mgniue of he il cceleion i.e., cenipel cceleion = s, wh is he mgniue of he ngul eloci in /s of he cenifuge = 4 s? An sonu is eing ese in cenifuge. The cenifuge hs ius n, in sing fom es =, oes wih consn ngul cceleion α. If he mgniue of he ngenil cceleion is equl o he mgniue of he il cceleion i.e., cenipel cceleion = s, wh is he mgniue of he ngul eloci in /s of he cenifuge = 6 s? Ne he sufce of he Eh soli ojec of mss n ius olls smoohl long hoionl sufce wih spee V CO = V n hen up mp h mkes n ngle of wih he hoionl sufce s shown in he figue. If he ojec eches mimum heigh = 3V /4g efoe olling ck own he incline, wh is is momen of inei? V / /3 3 4 /3 5 3 /5 4. Ne he sufce of he Eh soli ojec of mss n ius olls smoohl long hoionl sufce wih spee V CO = V n hen up mp h mkes n ngle of wih he hoionl sufce s shown in he figue. If he ojec eches mimum heigh = V /3g efoe olling ck own he incline, wh is is momen of inei? V /3 / 3 4 /3 5 3 /5
10 4. Ne he sufce of he Eh soli ojec of mss n ius olls smoohl long hoionl sufce wih spee V CO = V n hen up mp h mkes n ngle of wih he hoionl sufce s shown in he figue. If he ojec eches mimum heigh = V /g efoe olling ck own he incline, wh is is momen of inei? V / 3 /3 4 /3 5 3 /5 43. A poin picle wih mss n spee V is moing in he plne s shown in he figue. A he momen i cosses he is = =, is eloci eco poins n ngle of 45 elie o he is n he mgniue of is ngul momenum ou he oigin, i.e., = = is. Wh is he mgniue of is ngul momenum ou poin P loce on he is isnce = 4 fom he oigin his sme momen? / P O is is 44. A poin picle wih mss n spee V is moing in he plne s shown in he figue. A he momen i cosses he is = =, is eloci eco poins n ngle of 45 elie o he is n he mgniue of is ngul momenum ou he oigin, i.e., = = is. Wh is he mgniue of is ngul momenum ou poin P loce on he is isnce = fom he oigin his sme momen? / P O is is 45. A poin picle wih mss n spee V is moing in he plne s shown in he figue. A he momen i cosses he is = =, is eloci eco poins n ngle of 45 elie o he is n he mgniue of is ngul momenum ou he oigin, i.e., = = is. Wh is he mgniue of is ngul momenum ou poin P loce on he is isnce = 3 fom he oigin his sme momen? / P O is is 46. A hin hoionl kg o of lengh oes hoionll oun is en wih n ngul eloci ω s shown in he figue. A.5 kg mouse oiginll es on he f en of he o isnce fom he is of oion moes o new esing posiion isnce fom he is of oion. If he new ngul eloci of he mouseo ssem is.5ω, wh is he isnce? Ais of oion ouse 47. A hin hoionl kg o of lengh oes hoionll oun is en wih n ngul eloci ω s shown in he figue. A.5 kg mouse oiginll es on he f en of he o isnce fom he is of oion moes o new esing posiion isnce fom he is of oion. If he new ngul eloci of he mouseo ssem is.75ω, wh is he isnce? Ais of oion ouse
11 48. A hin hoionl kg o of lengh oes hoionll oun is en wih n ngul eloci ω s shown in he figue. A.5 kg mouse oiginll es on he f en of he o isnce fom he is of oion moes o new esing posiion isnce fom he is of oion. If he new ngul eloci of he mouseo ssem is.5ω, wh is he isnce? Ais of oion ouse 49. A hoionl unifom wih lengh n weigh of N is hel in plce hinge one en n wie ngle = 3 he ohe en s shown in he figue. Thee is lock wih weigh W = 3 N on he isnce fom he wll. If he mimum ension he wie cn suppl wihou eking is 4 N, wh is he lges lue of he isnce such h he wie will no ek? /3 / 3 /3 4 /4 5 3/4 A C com B 5. A hoionl unifom wih lengh n weigh of N is hel in plce hinge one en n wie ngle = 3 he ohe en s shown in he figue. Thee is lock wih weigh W = 3 N on he isnce fom he wll. If he mimum ension he wie cn suppl wihou eking is 5 N, wh is he lges lue of he isnce such h he wie will no ek? / /3 3 /3 4 /4 5 3/4 A C com B 5. A hoionl unifom wih lengh n weigh of N is hel in plce hinge one en n wie ngle = 3 he ohe en s shown in he figue. Thee is lock wih weigh W = 3 N on he isnce fom he wll. If he mimum ension he wie cn suppl wihou eking is 6 N, wh is he lges lue of he isnce such h he wie will no ek? /3 /3 3 / 4 /4 5 3/4 A C com B 5. A mn wih weigh of 75 N is es on he goun n is using he pulle ssem shown in he figue o lif weigh W off he goun. Assuming h he pulles oe wihou ficion n wihou he ope slipping, wh is he mimum weigh W in N he cn lif? W
12 53. A mn wih weigh of 5 N is es on he goun n is using he pulle ssem shown in he figue o lif weigh W off he goun. Assuming h he pulles oe wihou ficion n wihou he ope slipping, wh is he mimum weigh W in N he cn lif? W 54. A mn wih weigh of 5 N is es on he goun n is using he pulle ssem shown in he figue o lif weigh W off he goun. Assuming h he pulles oe wihou ficion n wihou he ope slipping, wh is he mimum weigh W in N he cn lif? W 55. An eension le consiss of wo unifom plnks of equl lengh. The op plnk hs mss op n he oom plnk hs mss oom. A winow wshe emps o len his eension le gins ficionless eicl wll s shown in he figue. e fins h he le slips on he goun when i is plce n ngle,, less hn 3 o he goun, u emins in plce when he ngleis geehn 3. If oom = op, wh is he coefficien of sic ficion eween he le n he goun? op oom An eension le consiss of wo unifom plnks of equl lengh. The op plnk hs mss op n he oom plnk hs mss oom. A winow wshe emps o len his eension le gins ficionless eicl wll s shown in he figue. e fins h he le slips on he goun when i is plce n ngle,, less hn 3 o he goun, u emins in plce when he ngleis geehn 3. If oom = 3 op, wh is he coefficien of sic ficion eween he le n he goun? op oom An eension le consiss of wo unifom plnks of equl lengh. The op plnk hs mss op n he oom plnk hs mss oom. A winow wshe emps o len his eension le gins ficionless eicl wll s shown in he figue. e fins h he le slips on he goun when i is plce n ngle,, less hn 3 o he goun, u emins in plce when he ngleis geehn 3. If oom = 4 op, wh is he coefficien of sic ficion eween he le n he goun? op oom
13 58. Ne he sufce of he Eh, pee consiss of o wih lengh n negligile mss suppoe is ens eicl opes of equl lengh s shown in he figue. Ech ope cn wihsn mimum ension of T m efoe eking. When hnging es, pee is cn hol on wih ech hn isnce of /4 fom he ens of he o, n neihe ope eks. owee, if she kes one hn off, n oes no moe he ohe hn, she fins h one ope eks cusing he o fll. Wh is he minimum possile mss? Tpee 4T m /3g 5T m /4g 3 3T m /g 4 T m /g 5 T m /g 59. Ne he sufce of he Eh, pee consiss of o wih lengh n negligile mss suppoe is ens eicl opes of equl lengh s shown in he figue. Ech ope cn wihsn mimum ension of T m efoe eking. When hnging es, pee is cn hol on wih ech hn isnce of /5 fom he ens of he o, n neihe ope eks. owee, if she kes one hn off, n oes no moe he ohe hn, she fins h one ope eks cusing he o fll. Wh is he minimum possile mss? Tpee 5T m /4g 4T m /3g 3 3T m /g 4 T m /g 5 T m /g 6. Ne he sufce of he Eh, pee consiss of o wih lengh n negligile mss suppoe is ens eicl opes of equl lengh s shown in he figue. Ech ope cn wihsn mimum ension of T m efoe eking. When hnging es, pee is cn hol on wih ech hn isnce of /3 fom he ens of he o, n neihe ope eks. owee, if she kes one hn off, n oes no moe he ohe hn, she fins h one ope eks cusing he o fll. Wh is he minimum possile mss? Tpee 3T m /g 4T m /3g 3 5T m /4g 4 T m /g 5 T m /g FOOWING GOUPS OF QUESTIONS WI BE SEECTED AS ONE GOUP FO EAC TYPE TYPE Q# S Q# S Q# S 3 TYPE Q# S 4 Q# S 5 Q# S 6 TYPE 3 Q# S 7 Q# S 8 Q# S 9 TYPE 4 Q# S Q# S Q# S TYPE 5 Q# S 3 Q# S 4 Q# S 5 TYPE 6 Q# S 6 Q# S 7 Q# S 8 TYPE 7 Q# S 9 Q# S Q# S TYPE 8 Q# S Q# S 3 Q# S 4 TYPE 9
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