Oe of he commo descipios of cuilie moio uses ph ibles, which e mesuemes mde log he ge d oml o he ph of he picles. d e wo ohogol xes cosideed sepely fo eey is of moio.
These coodies poide ul descipio fo cuilie moio d e fequely he mos diec d coeie coodies o use; hey moe log he ph wih he picle. The posiie diecio fo y posiio is lwys ke owd he cee of cuue of he ph. Theefoe o posiio eco is equied.
We ow use he coodies d o descibe he elociy d cceleio. Fo his pupose, we ioduce ui ecos e i he -diecio d e i he -diecio. Duig diffeeil iceme of ime d, he picle moes diffeeil disce ds log he cue fom A o A: ds= db whee b is i dis.
I is uecessy o coside he diffeeil chge i bewee A d A fo diffeeil ime peiod. ds d db d b b e
The mgiude of elociy: ds d b db d db b d Theefoe, he elociy i eco fom is e b e
d The cceleio of he picle is defied s, d d we obsee h he cceleio is eco which eflecs boh he chge i mgiude d he chge i diecio of elociy. We ow diffeeie he elociy pplyig he odiy ule fo he diffeeiio of he poduc of scl d eco d ge d d d e d e e
e The ui eco ow hs ozeo deiie becuse lhough is mgiude sys he sme, is diecio chges. As he picle moes fom poi A o A, he ui eco e becomes. e de e The ecoil diffeece is: e e de e
e To fid we lyze he chge i duig diffeeil iceme of moio s he picle moes fom A o A. e I he limi, he mgiude of will be de e db db. Fo diffeeil ime iel, he diecio of be cosideed pepedicul o. Theefoe, he diecio of d de e d e e c c be cosideed he sme s h of. de e e db e e
The deiie of de db e e will be obied s, o de e db By diidig o d de d db e d e be b e e b e, b
e e e e e e e e e e e e e e b b b e e e e
Hee, s b b b b b b b (Chge i diecio of he elociy) (Chge i mgiude of he elociy)
Rdius of Cuue (Eğilik Yıçpı): If jecoy is gie s y=f(x), he dius of cuue c be deemied wih he followig fomul: 1 dy dx d y dx 3/ The bsolue lue sig is used o guee h will lwys be posiie +.
The elociy ecos A d A' e dw o s sme poi i ode o expli he chge i he mgiude d diecio of he eloicy eco d how hese chges geee he oml d geil compoes of he cceleio eco. The chge i elociy eco is d d i idices he diecio of he cceleio eco. Whe d is diided io wo compoes oe oml d he ohe ge o he elociy, he oml compoe is defied s d d i he limi i will be equl o he c legh obied by oig he elociy eco wih mgiude fo gle of db. d db The oml compoe of cceleio will be equl o he ime deiie of d. d d b
The geil compoe of is d. Is mgiude is equl o d o he chge i he legh of he elociy eco. d The geil compoe of cceleio will be equl o he ime deiie of d d d d d s
The oml compoe of cceleio is lwys dieced owd he cee of cuue. The geil compoe of cceleio, o he ohe hd, will be i he posiie -diecio of moio if speed is icesig d i he egie - diecio if he speed is decesig. Figue shows he schemic epeseios of he iio i he cceleio eco fo picle moig fom A o B wih () icesig speed d (b) decesig speed. A iflecio poi o he cue, he oml cceleio goes o zeo sice becomes ifiie. 0
Cicul moio is impo specil cse of ple cuilie moio whee he dius of cuue becomes he cos dius of he cicle d he gle b is eplced by he gle mesued fom y coeie dil efeece o OP. d d (Agul elociy) = = cos d d (Agul cceleio)
1. Six cceleio ecos e show fo he c whose elociy eco is dieced fowd. Fo ech cceleio eco descibe i wods he iseous moio of he c.
. A flywheel oes wih ible elociy. A cei ime, he geil cceleio of poi A o he flywheel is 1 m/s, while he oml cceleio of poi B o he flywheel is 0.6 m/s. Deemie he elociy of poi A d he ol cceleio of poi B. A 00 mm B 150 mm
3. A bsebll plye eleses bll wih he iiil codiios show i he figue. Deemie he dius of cuue of he jecoy () jus fe elese d (b) he pex. Fo ech cse, compue he ime e of chge of he speed.
4. A mble olls dow chue which is be i he shpe of pbol. Is equio is gie s y (m) y=x 6x + 9 [m] The mble psses poi A wih speed of 3 m/s, which is icesig he e of 5 m/s. Deemie he oml d geil compoes d, of he cceleio of he mble s i psses poi A. Also deemie he gle bewee he elociy eco d he cceleio eco poi A. y=f(x) A x=5 m x (m)
5. The pi P is cosied o moe i he sloed guides which moe igh gles o oe ohe. A he is epeseed, A hs elociy o he igh of 0. m/s which is decesig he e of 0.75 m/s ech secod. A he sme ime, B is moig dow wih elociy of 0.15 m/s which is decesig he e of 0.5 m/s ech secod. Fo his is, deemie he dius of cuue of he ph followed by P.
6. A bll is how hoizolly fom he op of 50 m cliff A wih speed of 15 m/s d lds poi C. Becuse of sog hoizol wid he bll hs cos cceleio i he egie x-diecio. Deemie he dius of cuue of he ph of he bll B whee is jecoy mkes gle of 45 o wih he hoizol. Neglec y effec of i esisce i he eicl diecio.
7. I he desig of cool mechism, he eicl sloed guide is moig wih cos elociy x = 150 mm/s duig he iel of is moio fom x = -80 mm o x = +80 mm. Fo he is whe x = 60 mm, clcule he - d -compoes of cceleio of he pi P, which is cofied o moe i he pbolic gooe. Fom hese esuls, deemie he dius of cuue of he ph his posiio.