HY Foula Sheet One Denson t t Equatons o oton l Δ t Δ d d d d a d + at t + at a + t + ½at² + a( - ) ojectle oton y cos θ sn θ gt ( cos θ) t y ( sn θ) t ½ gt y a a sn θ g sn θ g otatonal a a a + a t Ccula Fo Newton's nd Law Σ F c Vaables ntal poston ntal elocty ntal poston ntal elocty nal poston nal elocty dsplaceent n the -decton elocty y dsplaceent n the y-decton elocty n the -decton t ntal te y elocty n the y-decton t nal te a acceleaton t te a otatonal acceleaton θ angle between the poste -as & elocty ecto a t tangental acceleaton g gaty (9.8 /s² o 3 t/s²) adus ass F c centpetal oce Laws o oton Newton's Laws An object n oton tends to stay n oton a Δ Fo eey acton thee s an equal and opposte eacton Foce equals ass tes acceleaton ( ) Fcton oce coecent o cton tes ass tes the noal oce Knetc Fcton: F μ FN Statc Fcton: F μ F s N epnt wth pesson only: Chandle - Glbet County College Leanng Cente
HY Foula Sheet μ s N o o and Enegy Equatons y z F s Fscosθ Fd + Fydy + Fzdz y z sp Fsp d ( ) d ½ ½ Enegy Knetc K ½² otental U gh otal Enegy K + U owe l Δ t d F ds F Collsons dp oentu p F Fo an solated syste, Δp Ipulse I t F t Δp Elastc (bounce) Inelastc (stc) + + + ( + ) Vaables wo sp wo done by spng F oce F sp oce o spng F oce n -decton spng constant s dstance dstance spng stetched/copessed θ angle dstance spng stetched/copessed, y, z ntal poston n the, y, o z decton K netc enegy, y, z nal poston n the, y, o z decton ass powe change n te p oentu Δp change n oentu ass o st object ass o second object ntal elocty o st object nal elocty o st object ntal elocty o second object nal elocty o second object elocty U potental enegy h heght I pulse t ntal te t nal te epnt wth pesson only: Chandle - Glbet County College Leanng Cente
HY Foula Sheet Geneal Equatons s θ otatonal oton ω ϖ α t t θ θ ω t t Δω α l Δ t Δθ ϖ l Δ t dϖ dθ Equatons o oton ω ω + αt θ θ + ω t + ½αt ω ω + α (θ θ ) Conetng otatonal to Lnea ω a t α a ω Inetal oent I I l Δ Δ Fo ods: d Fo Cylndes: L d ρ d dv da L ( πd ) L) d dv aallel As heoe I I C + D² oque τ F sn φ F D τ (α) α τ Iα o: d F ds ( F sn φ ) dθ C ω a C α Othe dp dl τ F K ½I C ω +½ C otatonal+tanslatonal l p sn φ Iω Vaables s ac length ω angula speed α angula acceleaton adus ω ntal angula spee d α aeage angula acceleaton θ angle ω ntal angula speed I Ineta θ ntal angle ω nal angula speed ass o th patcle θ nal angle ω aeage angula speed ass o an object t ntal te dstance o th patcle to as o otaton t nal te a adal acceleaton D dstance o as lnea elocty a t tangental acceleaton K netc enegy ρ densty o an object L length o od / cylnde φ angle I c Ineta about an as though the cente o ass o an object τ toque l nstantaneous angula oentu F oce nstantaneous poston ecto a C acceleaton at cente o ass p nstantaneous lnea oentu V C elocty at cente o ass epnt wth pesson only: Chandle - Glbet County College Leanng Cente
HY Foula Sheet Cente o ass X C scellaneous Foulas C d ocety ( + Δ) ( + Δ) + Δ( e ) Δ Δ e d - e d d e d e ln Gaty Law o Gataton Keple's Laws Enegy F g G F G g da L constant ΔU G G E Δ d 4π G 3 G 3 G Fluds essue p F A Buoyant oce weght o dsplaced lqud Benoull's Equaton p + ½ρ + ρgy c Vaables X C cente o ass n -decton elocty ass o th patcle ass o ocet and uel poston o th patcle Δ ass o uel loss C adal cente o ass e ehaust speed ass Δ change n elocty o ocet ass ntal ass o ocet and uel ass o st object nal ass o ocet and eanng uel ass o nd object ntal elocty F g oce o gaty nal elocty G unesal gatatonal constant(6.673 - N ²/g² ) dstance sepeatng & L angula oentu o planet (constant) unt ecto peod o eoluton adus constant (.97-9 s²/³) Δ change n adus ΔU change n gatatonal potental enegy p pessue E total enegy F oce eeted on the pston ρ densty (ass / olue) A suace aea o pston g gaty constant (9.8 /s² o 3 t/s²) y heght c constant epnt wth pesson only: Chandle - Glbet County College Leanng Cente
HY Foula Sheet Oscllatons Sple Haonc oton A cos (ωt + φ) π π ω A + ω Enegy K ½ ½ ω A sn (ωt + φ) U ½ ½ A cos (ωt + φ) E K + U ½ A ae oton d ω Asn( ωt + φ ) d ω A cos( ωt + φ ) aes on a stng F F sn θ Fθ μδs μθ Fθ μθ F, F tenson, μ μ g y A sn π λ t angula wae nube π λ ω angula equency π dy ωa cos( ωt) a d ω A sn( ωt) Enegy ΔE ½Δω A de μω A Vaables poston K netc enegy ω angula equency ntal poston U potental enegy t te A apltude E total enegy φ phase constant o phase angle peod adus elocty ass θ angle ntal elocty spng constant λ waelength F total adal oce equency t te F oce o tenson ΔE change n total enegy a acceleaton μ ass pe unt length Δs length o sall segent o stng powe Δ change n ass epnt wth pesson only: Chandle - Glbet County College Leanng Cente