Data Scientific Method
3.
Uncertainty
1.
* units (metrics) Observation 2. Defi Define ne the the Prob Proble lem m * meas measur urin ing g 3. Test/ est/E E!e !eri rime ment nt * sig. sig. figs. figs. ". #$!ot he hes is is * Da ta ta %. &olle &ollect ct Data/ Data/'a 'ani ni!u !ula late te 'ani 'ani!u !ula lati tion on . &onclusion Accuracy vs. Precision ccurac$ closeness of results to a stan+ar+ Precision closeness of results to each other *use same !iece of e,ui!ment to collect +ata* Qualitative vs. Quantitative -ualitative more on !recision than accurac$ -uantitative numbers count an+ are im!ortant Sig. Figs. ++ition an+ ubtraction *least 0 !laces after +ecimal 'ulti!lication *!laces after +ecimal +ecimal count count as sig. figs. 2 . % cm 1 in Vectors ectors (velocit$) has OT# magnitude an+ direction calars (s!ee+) has magnitude O456 *time7 mass7 volume Metric System Abbr. Abbr. 'm 8 9m 8 hm 8 +9m 8 m +m 8 cm 8 mm 8 Mm(E8) 8 nm(E8:) 8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888
Mult. om!onent Vecctors Vecctors 1. 1;m +ue 2. 22m7 "<+e g. g. of of = 3. 1> m7 <; <;+e g. g. 4 of = ". 3> m +ue E *(=?E) um of the @ (>)A (822 cos"<)A(81> cos<;)A(3>) 12. :m *(4?) um of the @ (81;)A (822 sin"<)A(1> sin<;)A(>) 82". 3m *Besultant C ((12. :)2 A (2". 3)2)1/2 2<. %m * tan81(2". 3) (12.:) 2.>+eg R= 28m, 62deg 62deg S of E 8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888
"inematics Dis!lacement f A itFs =6 f itFs TO=BD Velocity #m$s% Gse O456 Hhen SPEED is CONSTANT 1. +oes +oes not not inc inclu lu+e +e acce accele lera rati tion on 2. +oes +oes not not incl inclu+ u+ee start startin ing g an+ an+ sto! sto!!i !ing ng in the same !lace v&
' t
Acceleration #m$s$s% *s!ee+ing u! or sloHing +oHn a& v t "inematic Formulas X Direction Y Direction (&(o)at gt ' & ' o o ) Vo t ) + a t , +gt, ' & ' o o ) + #( ) ( o% t ( , & ( o , ) , a # ' ' o o% ,g# &hange ' (o) (o) to 6(o) Pro-ectial Motion #alf * 6 +etermines time in air *com!liment angles of "%+eg have same range I . . 6 . ' & V @ t &+gt, T ' @ Jull * "%+eg has ma. range te!s
1.
( o cos o / ( o sin
%.
static Kstart ing JfL not moving (rolling) greater force than 9inetic 9inetic moving (rolling7 sli+ing7 flui+)
9:uilibrium Translational the sum of forces e,ual Qero Botational the sum of tor,ues e,uals Qero &om!lete must have OT# enter of ;ravity center of +istribution of mass
Jin+ Jin+ the the T'E T'E (che (chec9 c9 6) Ji n+ n+ th the he he ig ight / ra ra ng nge I . 6 . '&V' t t& ,(o . g ( ( o cos o) ( o ( o sin o) , y ma/ & ( o ,g 88888888888888888888888888888888888888888888 8888888888888888888888888888888888888888888888888888888888888888888 8888888888888888888888888 88 Force #0% 8 &auses a change in motion (causes acceleration) 8 s a E&TOB ,uantit$ E,uilibrium no acceleration 7 forces cancel cancel 7 Kat restL 0e1ton2s 3a1s of Motion 1. n obMec obMectt at rest rest Hill Hill remai remain n at rest rest until until acte acte+ + u!on b$ an outsi+e force 4EBT +irectl$ relate+ to mass
cceleration is directl relate+ directl relate+ to !orce to !orce indirectl relate+ indirectl relate+ to mass F&ma #4 5g m $ s, & 4 0e1ton%
?m!ulse change in momentum (hoH $ou feel ! change) Jorce J m a J m Δ v Δ t Time * hi++en variable* F Δ t & m Δ ( & Δ ! onservation of Momentum n the absence of an eternal force7 the total momentum of a s$stem is constant m4 ( 4 ) m, ( , & m4 ( 4 ) m, ( , or5 # B % &Fd * 4ee+ to a!!l$ force * im!lies motion Po1er # 1att 1 % P = . (J +) t t S 1 H 4 m 1 9g m, , s s s 1 horse !oHer <" H 9nergy bilit$ to +o Hor9 'echanical energ$ of motion or !osition Ninetic (N) motion N m ( , (S) Potential (G) !osition G m g h (S) (= J +) =hen not given +istance(or force) = m ( , m ( o, (= ΔK) (N final) (N initial) initial) onservation of 9nergy Energ$ change from one one to the other H/o an$ net loss 2 GTOP N OT OT (mgh 1/2mv ) ave Motion Sim!le Carmonic Motion re!eating motion in Hhich the acceleration is +irectl$ relate+ to the +is!lacement (+istance aHa$ from the e,uilibrium) an+ alHa$s +irecte+ toHar+s e,uilibrium.
8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 8
ircular Motion 'oving at a constant s!ee+ Hhile accelerating v s!ee+ constant +n constantl$ changing entri!etal Acceleration nHar+ see9ing c ( , . r entri!etal Force &auses centri!etal acceleration Jc m c (J m a) Fc & m ( , . #0% r 6ou 'GT have cent. J to 9ee! somethi ng moving in a circle &entrifugal bo+$Fs bo+$Fs inter!retation inter!retation of cent. cent. J DOE 4OT EIT feels inertia Botation s!inning on ais Hithin obMect Bevolution s!inning on ais outsi+e of obMect 3inear $ Angular 5inear s!eed & distance $ time ra+ius matters %<. 3+eg 1 BD4 1 rotation 2 R Ba+ians Ba+ians 3> +egrees ngular s!eed & = rotations or revolutions $ time ra+ius +oes 4OT matter * b$ +oubling the angular s!ee+ $ou +ouble the 0 of rotations 5inear ngular @ (m) @r (BD) C (m/s) C r # # (BD / s) a (m/s/s) a r $ $ $ (BD / s / s) J (4) Jt " " (4m) 'ass (m) (mr) Jma " $ Jor linear # & # o ) $ t ee other corner & o ) # o t ) + $ t , & o ) + ## ) # o% t # , & # o , ) , $ # o% >otational ?nertia Besistance to begin or sto! rotation •
o
2. 3.
2.
ctio ction n e,u e,ual al an+ an+ o!!o o!!osit sitee reac reactio tion n 8canFt have onl$ one force F a6 b & F b6 a 4ormal Jorce 8 able to change until brea9ing !oint of Hhatever itFs hol+ing 8 acts !er!en+icularl$ !er!en+icularl$ to Khol+ingL obMect 8 comes from groun+ (ece!t Hater) 0e1tons 4 0 & 7. ,,8 lbs. 'ass is constant J ma 888888 JH mg 4 9g (/ :. ;) Ng 4 ( :. ;) Friction #Ff% 1. tHo tHo or or mor moree thing thingss mus mustt be be touc touchi hing ng 2. energ$ energ$ is transf transferr erre+ e+ (heat7 (heat7 soun+7 soun+7 etc) etc) 3. tet tetur uree matt matter ers s 4OT 4OT GBJ GBJ&E &E BE BE & coefficent of friction friction (Batio of !arallel force to !er!. !er!. Jorce) Jf (3 +ecimal !laces) J 4 Jf m g Jf JH (on flat surface) tan (Hhen ( is constant) Pressure P Jorc e/area ". o!!ose o!!osess moti motion on Hhich Hhich causes causes +ecell +ecellera eratio tion n
De!en+s on amount of mass 4D Hhere
it is !lace+ oli+ !here ,$8 mr, oli+ Dis9 + mr, #olloH !here ,$@ mr , #olloH Dis9 4 mr, elocit$ is in+irectl$ relate+ to nertia • ha!e of obMect s!inning ma9es the • +ifference Hhile s!inning 3 Jorces Jorces acting u!on an obMect obMect in circular motion motion
1. 2. 3.
&entri!etal cceleration (c) ngular cceleration ($) 5ine 5inear ar cce ccele lera rati tion on ( a )
8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 8
onservation 3a1s Momentum # 0 s % 'oving inertia (4eHt onFs 2n+ laH) %omentum &S inertia'&nertia is NOT NOT momentum momentum 'omentum is DBE&T56 relate+ to mass an+ s!ee+ ! m ( (4 s) causes bo+$ to Hant to fl$ off tangent •
f = 1/T = 1/T osine urves & A cos #/ E % ) D am!litu+e ( >) hoH much energ$ it has &os !erio+ ( 2 PE / t) time7 1 oscillation & horQ. hift human error D vert. hift +istance7 to 8ais aves * Ura!he+ #'7 transfer of of energ$ ibration ibration =OBN to get energ$ energ$ Pro!agates Hhat Hhat energ$ moves through through 'echanical (light) Electromagnetic (soun+) 4ee+s a me+ium +oes 4OT nee+ a me+ium 'ore +ense better less +ense better Mechanical aves Transverse me+ium vibrates !er!. to energ$ 'ost common e. Uuitar string7 slin9$ 5ongitu+inal 5ongitu+inal me+ium vibrates !ara. to energ$ #as com!ressions e soun+ urface both !ara. !ara. an+ !er!. to energ$ K!h$sics bobL e earth,ua9es7 Haves Princi!le of Su!er!osition &onstructive nterference a++e+ Deconstructive subtracting (a++ing negatives) VW V f T Standing ave continuous Have train of e,ual am!litu+e (BD)7 Havelength (m)7 an+ fre,u. (#Q) (/sec) in the same me+ium creating no+es an+ antino+es. oun+ar$ change in me+ium (!art of energ$ gets reflecte+7 !art gets absorbe+) rigi+it $ hoH much energ$ gets OBED close rigi+it$ more absorbe+ +ifferent rigi+it$ more reflecte+ ?nterference in Diffraction &rest A crest antino+e &rest A tro!h no+e no+e 8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888 8
Sound range of longitu+inal Have fre,u. to Hhich the human ear is sensitive nfra sonic sonic s!ectrum ultra sonic (beloH 2> #Q. ) (2> #Q 2>7>>> #Q) (2>7>>> #Q A)
1. 2. 3.
!ro+uction nee+s vibration transit ion nee+s a me+ium
air
rece!tion must be hear+ V sound = @7 m$s V sound & @@4 ) . G #< #
Volume ( )) )) subMective #decibels% Belative ntensit$ 5evel lou+ness level
olume is DBE&T 56 relate+ to &ntensit to &ntensit olume is DBE&T 56 relate+ to !re*uen to !re*uenc c f stan+ar+ 17>>> #Q. ntensit$ Bange Threshol+ of hearing (o) 1 1> 812 H / m 2 Threshol+ of soun+ soun+ 1 H / m 2 β & & 47 log # # ? % 4 / 47 4, 1 $ m , L#oH man$ !oHers of 1> are in that numberXL Decibel 1 $ m , . 1 $ m , Pitch and
1. 2. 3. ".
f is 4DBE&T56 relate+ to lengt+ f is D?>9<3 relate+ to tension (Jt) tension (Jt) f is is 4DBE&T56 relate+ to diameter (+) (+)
f is is 4DBE&T56 relate+ to densit (D) densit (D) eats the resultant interference !attern of 2 notes close in fre,uenc$ but not eact &reat no+es (shar!s an+ flats) Do!!ler Effect the the a!!arent a!!arent change in fre,uenc$ of a soun+ +ue to the relative motion of either the observer or the source of both Besonate Hhen Hhen $ou cause something to vibrate at its natural fre,uenc$ 'usic re!eating Have !attern 4oise no re!eating Have !attern &onsonance soun+s UOOD Dissonance soun+s D Decibel . 1 1> 12 > +b 11 1 1> 1> +b 1 1> 1> 2> +b 888 888 1 1> 2 1>> +b 1 1> 1 11> +b 1 12> +b 0atural Fre:uencies l 1<> / #Q rass/tring n name s$nm Havl (V) l f f fun+. 1st har. 2l V v/2l v/2 l st n+ 2 1 ov. 2 har. V v / l f 2 l f 3 3 2n+ ov. 3r+ har. 2/3l 2/3l 3/2 V 3v/2l 3v/2l f " " 3r+ ov. "th har. 1/2l 1/2l 2 V 2v/ l f n& n ( hn & , l f n & 0 f 1 , l n =oo+Hin+ n name s$nm Havl (V) l f f fun+. 1st har. "l 1/" V v/"l v/"l f 2 f 2 888888 8888888 88888 88888 8888 8888 f 3 3 1st ov. 2r+ har. "/3l "/3l 3/" V 3v/"l 3v/"l f " f " 888888 8888888 88888 88888 8888 8888 f % % 2n+ ov. 3r+ har. "/%l "/%l %/" V %v/"l %v/"l f n f n&n( hn & l l n ?nstruments tring Pro+uce+ b$ !luc9ing string7 boHing boHing &hange !itch length7 +iameter7 tension7 +ensit$ rass Pro+uce b$ buQQing mouth !iece &hange !itch length of !i!e (valves)7 buQQing =oo+Hin+ Pro+uce+ b$ ree+ vibrati ng &hange !itch !a+s7 holes E+ge tones narroH streams of air s!lit b$ e+ge #elmholtQ Besonance e+ge tone Hith bottle (o!en hole) 888888888888888888888888888888888888888888888 88888888888888888888888888888888888888888888888888888888888888888888 8888888888888888888888888 3ight Particle =ave A 4eHton sai+ so A Thomas 6oung 2 slit e A eams / =aves A reflection7 refraction7 A travel in straight lines +iffraction7 interference A#ertQ light is energ$ A Einstein Have !article !article +ualit$ PolariQe+ 5ight 5ight oriente+ to one !lane (calc.) 5i,ui+ Jilter Dis!la$ lets onl$ onl$ one one +egree of light light in isible !ectrum Ba+io * 'icro * nfrare+ * Gltraviolet * Ira$s* Uamma ig Havelength mall Havelength B e+ Orange 6elloH Ureen lue n+igo iolet e+ Trans!arent Trans!arent see through it an+ light !asses (=in+oHs7 (=in+oHs7 glass) Translucent can 4OT see through it7 light !asses (froste+ glass) O!a,ue can 4OT see through it7 4O light !asses ource ma9es an+ emits light 5uminous sun 5uminate moon 5ight 6ear ta9es ;. 3 min. to get light from sun Dis!ersion brea9ing u! light into colors (!rism) olors &ones in e$e !ic9 u! 3 !rimar$ colors of light Additie Primar$ econ+ar$ 5GE 6E55O= BED &64 UBEE4 'UE4T * 'ore than one light source
* righter colors
Su-tractie Primar$ econ+ar$ 6E55O= 5GE &64 BED 'UE4T UBEE4 * onl$ one light source * +ar9er colors Shades of olors #ue !ro!ortion of color aturation amount of Hhite mie+ Hith color rightness amount of blac9 mie+ Hith color >eflection mooth i r Diffuse Kscatters lightL obe$s laHs still >efraction n & @ / 47 H n+e of Befraction v (s!ee+ in Hhatever me+ium) ir 1. >> =ater 1. 33 Ulass 1. %2 Snell2s 3a1 * n is 4DBE&T56 relate+ to * n is 4DBE&T 56 relate+ to s!ee+ * ( is DBE&T56 relate+ to n4 sin 4 & n, sin , 3asers &ritical angle ( c) the that !ro+uces the angle that is larger than c . Total nternal Beflection no refraction I!tics Beflection mirrors Befraction lenses Mirrors &oncave converging an+ u!si+e +oHn after foc. !t &onve +iverging7 u!right an+ smaller M & hi . 'agnification 'Y1 big ho 'Z1 small hi & ho di f & do di do & di f di & do f do do ) di di f do f
3enses &oncave corrects nearsig+tedness +iverging &onve corrects farsig+tedness converging
&f ou +ae t+is
Do t+is
To get t+is
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