Phic Mechnic Rule #1: DRAW A PICTURE (Picoil Repeenion, Moion Dim, ee-bod Dim) Dw picue o wh he queion i decibin. Ue moion dim nd ee-bod dim o i ou in eein wh i oin on in he queion. Moion Dim: + ee-bod Dim: > < N icion N 1 3 Bll ollin Conn peed 1 3 4 C peedin up 1 3 4 Bo lidin o op D Enine Rule #: LABEL/LIST YOUR KNOWN VALUES AND THOSE DESIRED (Include uni!!) Lbel o li ll lue h wee ien o ou in he poblem. Alo, include n lue h wee no eplicil ed, bu cn be ineed om he poblem (i occu in mo poblem, bu oe unid, o li 9.8m ). Ll, lbel hoe lue h ou e eein well. Moion in One Dimenion (Tnlionl Kinemic) Equion o one-dimenionl moion ollow, bu i i impon o noe h no ll moion i one-dimenionl. In ode o ill ue hee equion, moion h occu in muliple dimenion mu be boen p ino one-dimenionl componen. The one-dimenionl equion m hen be ued o ech componen epel. Equion o One-Dimenionl Moion ( h been ued o denoe he poiion in n enel diecion; lo commonl ued) e unde - ph e unde - ph lope o - ph lope o - ph d d Equion o Conn + Veloci (zeo cceleion) Equion o Conn Acceleion 1 ( ) + + + + denoe "chne in" Time Poiion in n enel diecion Iniil Poiion inl Poiion Veloci Aee Veloci Innneou Veloci Iniil Veloci inl Veloci Acceleion Aee Acceleion Innneou Acceleion
Pojecile Moion Pojecile moion cn be impliied ino wo epe one-dimenionl moion: one moion o he objec oin up & down nd epe moion o he objec oin le o ih. Thee moion cn be conideed independenl. Once he moion e eped we e ee o ue he equion o one-dimenionl moion on ech componen. Equion o Pojecile Moion co (inoin i eince) in Hoizonl Rne Equion (dince eled when n objec lunche nd lnd me heih) Thi equion cn be deied uin equion o one-dimenionl moion, equion o pojecile moion, nd he c h. ( ) in Veicl Rne Equion (mimum heih o objec) Thi equion cn be deied uin equion o one-dimenionl moion, equion o pojecile moion, nd he c h he mimum heih. iue 1 ( in ) Lunch Anle o + i Iniil Veloci Iniil Veloci in diecion Iniil Veloci in diecion iue Acceleion in diecion Acceleion in diecion Acceleion due o i NOTE! h mniude nd diecion ince i i he eco o i (diecion would be poiie o neie in). h onl he mniude ince i i he cl o i (menin i lw poiie). Moion down icionle Inclined Plne ± in N Anle o Incline Acceleion down plne Acceleion due o Gi Gi in he diecion Gi in he diecion
Cicul Moion (Roionl Kinemic) Cicul moion eem lie il compliced wo-dimenionl moion, bu when boen down i cn be een h mn o he equion nd w we ppoch cicul moion e nel idenicl o he one-dimenionl equion. When looin he equion below ou m noice h he eem o be one-dimenionl equion h ju he dieen ible, nd h i ecl wh he e. eplce o o ddiionl equion o ole he ddiionl piece h ei when moion oe om line o cicul., eplce, nd eplce. The dieence wih cicul moion i we he whee whee, 1 1 3 3 + ne ne Genel Equion o Cicul Moion π T + ne e unde - ph e unde - ph lope o - ph lope o - ph d d Equion o Conn Anul Veloci/ Uniom Cicul Moion (zeo nul cceleion) + Equion o Conn Anul Acceleion/ Non-Uniom Cicul Moion (conn nul cceleion) 1 ( ) + + + + Rdiu T Peiod Tnenil Veloci Tnenil Acceleion ( in peed) Rdil Acceleion ( in diecion) Anul Poiion Iniil Anul Poiion inl Anul Poiion Anul Veloci Aee Anul Veloci Innneou Anul Veloci Iniil Anul Veloci inl Anul Veloci Anul Acceleion Aee Anul Acceleion Innneou Anul Acceleion Iniil Anul Acceleion inl Anul Acceleion
oce The bic ide behind oce i h oce i puh o pull eeed on n objec. We he ued equion o how n objec moion, nd now we ue oce o how wh n objec m be chnin i moion. When looin oce cin on n objec we will end o epe oce ino one-dimenionl componen ju we did wih moion bu we cn lo um ll he oce in hoe dimenion o ee wh we cll he euln oce o ne oce. The ide i h when numeou oce c on n objec ou cn dd hem ll oehe o ee wh he ne oce i, nd hi ne oce deemine wh ind o chne in moion he objec epeience. We ue he cceleion om hi ne oce o lin oce o ou moion equion. Genel oce Equion m ne m + + + + m 1 3... n Speciic oce Equion icion: n p n m n Gm m D C A D Noe on icionl oce When picin which icionl oce o ue i i impon o noe when ech one hould be ued. Sic icion,, hould be ued when he objec we e looin i no in moion o i bein poweed in i oll o bin. Kineic icion, uce. Rollin icion,, hould be ued when n objec i moin/lidin co, hould be ued when n unpoweed objec i ollin co uce. icionl oce lw poin in he diecion oppoie o he moion, o in he ce o ic icion, in he diecion o peen moion. Momenum & Impule Momenum cn be houh o quni h epeen how diicul i i o op n objec in moion o chne n objec diecion o moion. Ou min ue o momenum come om he c h in cloed em he ol momenum i conn (Coneion o Momenum). Thi c llow u o he bee undendin o he inecion o objec, picull in colliion nd eploion. Wh eem lie choic inecion in colliion nd eploion cn be boen ino p, nd o lon ou em i cloed, he um o he momen beoe he een i equl o he um o he momen e he een. I he em i no cloed, hen we he o e ino conideion n ouide oce in o iin momenum o ou em. Impule i he chne in momenum o n objec nd i equl o he poduc o oce nd he duion o ime h i i pplied. Momenum & Impule Equion p m J p J ( ) e unde - ph Coneion p o Momenum p p + p + p +... + p p + p + p +... + p 1 1 3 n 1 3 n oce m M Acceleion ne Ne oce oce in -diecion p Spin oce Spin Conn Dince Seched/Compeed n Noml oce Sic icion Coeicien o Sic icion Kineic icion Coeicien o Kineic icion Rollin icion Coeicien o Rollin icion D D oce (oppoie o moion) A Co-Secionl Ae ( o moion) C D Coeicien o D p Momenum J Impule Aee oce in -diecion Chne in Time Remembe: You cn onl ue he coneion o momenum i he em i ioled o cloed. Thi men h ou cn onl ue he coneion o momenum i hee e no ouide oce h e ddin o in momenum om he em.
Ene, Wo & Powe We cn hin o em hin ene, nd i hee e no ouide oce on hee em, hen he ene i coneed much in he w momenum i coneed. Ju n ouide oce cn chne he momenum o he em, n ouide oce cn chne he ene o em houh wh we cll wo. Powe i he e which ene i need o nomed. Ene & Wo Equion 1 K m U 1 ( ) p U m h o m " " U m Eh W d Ae unde - cue W, i i conn nd ih-line moion W co Coneion o Ene K + U + W K + U + E e h K Kineic Ene U p Elic Poenil Ene (Spin) Spin Conn Chne in poiion in n enel diecion U Giionl Poenil Ene h Heih Chne in Veicl Poiion E h Chne in Theml Ene W Wo Dince Teled in Sme Diecion oce W Wo Eenl e The coneion o ene i ueul in mn iuion becue, unlie he coneion o momenum, we cn ill ue he coneion o ene i hee e ouide oce. Ouide oce e en ino ccoun b wo done on he em. Powe E de P P co Roion o Riid Bod P Powe E Ene o he Sem The ollowin oionl moion equion cn be ued when ou he iid bod h i bein eoled ound ied poin. Time oce Veloci Roionl Moion Equion M m m + m + m + i i 1 3... 1 m 1 1+ m + m 3 3+... X ( mi i ) M i m1+ m + m3 +... 1 X dm M 1 I I dm m ii (o poin me) Ko I I + M d M Tol M X Cene o M in n enel diecion K o Roionl Kineic Ene Anul Veloci Rdiu I Inei Cene o M d Dince beween Ai o Roion nd Cene o M I Inei dince d om Cene o M bou pllel i Becue he inel o ind he inei bou cene o m cn be e diicul o ole, mo cle do no equie he clculion. Genel equion o he inei o dieen objec will be poided o ou o cn be ound in ou e.
Toque Toque cn be houh o he oionl equilen o oce. So o n emple when ou puh doo open ou e pplin oce o he doo, hi oce ee oque ound he pio poin (in hi ce i he hine) which will cue he doo o open. Poiie oque poide couneclocwie oion. Neie oque poide clocwie oion. Toque Equion τ τ ne τ I τ inϕ Pio Poin Ueul Tionomeic Equion opp in hp opp n dj Conn dj co hp c + b 4 M e M o Eh 5.98 1 6 Re Rdiu o Eh 6.3 1 m M moon M o Moon.36 1 6 Rmoon Rdiu o Moon 1.4 1 m 11 REO Rdiu o Eh Obi 1.5 1 m 9.81m 3 11 G 6.6 1 Nm ound Speed o ound in i 343m M o poon o neuon 1.6 1 mp me M o n elecon 9.11 1 31 1 ε Pemiii conn 8.85 1 C Nm 6 K Coulomb' lw conn 1 8.99 1 4πε Pemebili conn 1.6 1 Tm A 19 e undmenl uni o che 1.6 1 C 8 c Speed o lih in cuum 3. 1 m ϕ Cue No Roion 9 Nm C c hpoenue ( hp) Coeicien Sic Kineic Rollin Meil Rubbe on concee 1..8. Seel on eel (d).8.6. Seel on eel (lubiced).1.5 Wood on wood.5. Wood on now.1.6 Ice on ice.1.3 Mel Reiii(Ωm) Conducii(1/Ωm) luminum.8 1 8 3.5 1 coppe 1. 1 8 6. 1 old.4 1 8 4.1 1 ion 9. 1 8 1. 1 ile 1.6 1 8 6. 1 unen 5.6 1 8 1.8 1 Coneion τ Toque Dince om Pio Poin oce pependicul o ϕ Anle beween eco nd (Eended o mee one nohe) I Momen o Inei Anul Acceleion djcen ( dj) b oppoie ide ( opp) 1 mile 58 ee 169 mee 1.69 ilomee 1 inch.54 cenimee 1 hou 6 minue 36 econd 1 eoluion 36 π din 1 m.4 mi 3.8 h 19 1 ev 1.6 1 J 1 u 1.66 1 1. lb on Eh