Kev txav yog ib qho tseem ceeb ntawm cov teeb meem hauv peb lub Ntiaj Teb. Tseeb tiag, txawm tias nyob rau ntawm qhov kub tsis txias, qhov kev txav ntawm cov teeb meem tsis nres kiag li. Hauv physics, kev txav yog piav qhia los ntawm ntau qhov tsis muaj, qhov tseem ceeb ntawm qhov yog acceleration. Hauv tsab xov xwm no, peb yuav nthuav qhia ntau ntxiv txog cov lus nug ntawm dab tsi ua tangential acceleration thiab yuav suav li cas.
Acceleration hauv physics
Nyob rau hauv acceleration to taub qhov ceev uas qhov ceev ntawm lub cev hloov thaum nws txav. Ua lej, lo lus txhais no yog sau raws li nram no:
a¯=d v¯/ d t
Qhov no yog kinematic txhais ntawm acceleration. Cov mis qhia tau hais tias nws yog xam nyob rau hauv meters ib square thib ob (m/s 2). Acceleration yog vector yam ntxwv. Nws cov kev taw qhia tsis muaj dab tsi ua nrog kev coj ntawm kev ceev. Qhia acceleration nyob rau hauv cov kev taw qhia ntawm kev hloov ceev. Obviously, nyob rau hauv cov ntaub ntawv ntawm uniform zog nyob rau hauv ib tug ncaj kab, tsis muajtsis muaj kev hloov hauv kev ceev, yog li acceleration yog xoom.
Yog hais tias peb tham txog acceleration raws li ib tug ntau ntawm dynamics, ces peb yuav tsum nco ntsoov Newton txoj cai:
F¯=m × a¯=>
a¯=F¯ / m
Qhov ua rau kom muaj nuj nqis a¯ yog lub zog F¯ ua rau lub cev. Txij li qhov loj m yog tus nqi scalar, lub acceleration yog qhia nyob rau hauv cov kev taw qhia ntawm lub zog.
Txoj kev thiab nrawm nrawm
Hais txog acceleration, speed and the distance traveled, ib tug yuav tsum tsis txhob hnov qab txog lwm yam tseem ceeb yam ntxwv ntawm txhua yam kev txav - lub trajectory. Nws yog to taub raws li ib tug xav txog tej kab uas kawm lub cev txav. Feem ntau, nws tuaj yeem ua tau nkhaus lossis ncaj. Txoj kev nkhaus tshaj plaws yog lub voj voog.
Xav tias lub cev txav mus raws txoj kev nkhaus. Nyob rau tib lub sijhawm, nws ceev hloov raws li ib txoj cai lij choj v=v (t). Nyob rau hauv txhua rooj plaub, lub trajectory yog qhia tangentially rau nws. Qhov ceev yuav qhia tau raws li cov khoom ntawm nws cov modulus v thiab theem pib vector u¯. Ces rau acceleration peb tau:
v¯=v × u¯;
a¯=d v¯/ d t=d (v × u¯) / d t
Kev siv txoj cai rau kev suav cov khoom ntawm cov khoom ntawm kev ua haujlwm, peb tau txais:
a¯=d (v × u¯) / d t=d v / d t × u¯ + v × d u¯ / d t
Yog li, tag nrho a¯ thaum tsiv raws txoj kev nkhausyog decomposed rau hauv ob yam. Hauv tsab xov xwm no, peb yuav xav txog qhov nthuav dav tsuas yog thawj lub sijhawm, uas yog hu ua tangential acceleration ntawm lub ntsiab lus. Raws li lub sij hawm thib ob, cia li hais tias nws yog hu ua ib txwm acceleration thiab yog coj mus rau qhov chaw ntawm curvature.
Tangential acceleration
Cia peb xaiv cov khoom no ntawm tag nrho acceleration as at¯. Cia peb sau cov qauv rau tangential acceleration dua:
at¯=d v / d t × u¯
Qhov kev sib npaug no hais li cas? Ua ntej, cov tshuaj tivthaiv at¯ characterizes qhov kev hloov ntawm tus nqi kiag li ntawm qhov ceev, yam tsis xav txog nws cov kev taw qhia. Yog li, nyob rau hauv tus txheej txheem ntawm kev txav mus los, lub nrawm vector tuaj yeem ua qhov tsis tu ncua (rectilinear) lossis hloov pauv tas li (curvilinear), tab sis yog tias qhov nrawm modulus tseem tsis hloov, ces at ¯ yuav sib npaug rau xoom..
Thib ob, qhov tangential acceleration yog qhia raws nraim tib yam li lub nrawm vector. Qhov tseeb no tau lees paub los ntawm lub xub ntiag nyob rau hauv cov mis sau saum toj no ntawm ib qho tseem ceeb nyob rau hauv daim ntawv ntawm ib tug elementary vector u¯. Txij li thaum u¯ yog tangential rau txoj kev, cov khoom siv at¯ feem ntau hu ua tangential acceleration.
Raws li lub ntsiab lus ntawm tangential acceleration, peb tuaj yeem xaus: qhov muaj nuj nqis a¯ thiab at¯ ib txwm coincide nyob rau hauv rooj plaub ntawm rectilinear txav ntawm lub cev.
Tangential thiab angular acceleration thaum tsiv hauv lub voj voog
Saum toj no peb pomtias qhov kev txav mus los ntawm ib qho curvilinear trajectory ua rau cov tsos ntawm ob feem ntawm acceleration. Ib hom kev txav ntawm txoj kab nkhaus yog kev sib hloov ntawm lub cev thiab cov ntsiab lus ntawm cov khoom raws lub voj voog. Hom kev txav no tau yooj yim piav qhia los ntawm cov yam ntxwv ntawm lub kaum sab xis, xws li angular acceleration, angular tshaj tawm thiab lub kaum sab xis ntawm kev sib hloov.
Nyob rau hauv lub angular acceleration α nkag siab qhov loj ntawm qhov kev hloov ntawm qhov ceev ntawm lub kaum sab xis ω:
α=d ω / d t
Angular acceleration ua rau kom muaj kev sib hloov ceev. Obviously, qhov no ua rau kom cov linear tshaj tawm ntawm txhua qhov chaw uas koom nrog kev sib hloov. Yog li ntawd, yuav tsum muaj ib qho kev qhia hais txog lub angular thiab tangential acceleration. Peb yuav tsis mus rau hauv cov ntsiab lus ntawm qhov derivation ntawm cov lus no, tab sis peb yuav muab tam sim ntawd:
at=α × r
Tus nqi at thiab α yog ncaj qha proportional rau ib leeg. Tsis tas li ntawd, at nce nrog nce nyob deb r los ntawm kev sib hloov axis mus rau qhov xav tau. Tias yog vim li cas nws thiaj yooj yim rau siv α thaum lub sij hawm tig, thiab tsis yog t (α tsis nyob ntawm lub voj voog sib hloov r).
Example problem
Nws paub tias cov khoom taw tes tig ib ncig ntawm lub axis nrog lub vojvoog ntawm 0.5 meters. Nws qhov nrawm nrawm hauv qhov xwm txheej no hloov raws li txoj cai hauv qab no:
ω=4 × t + t2+ 3
Nws yog ib qho tsim nyog los txiav txim siab nrog qhov kev sib tw tangential acceleration qhov taw tes yuav tig lub sijhawm 3.5 vib nas this.
Yuav daws qhov teeb meem no, koj yuav tsum xub siv cov mis rau lub angular acceleration. Peb muaj:
α=d ω/d t=2 × t + 4
Tam sim no koj yuav tsum siv qhov sib npaug uas hais txog qhov ntau at thiab α, peb tau txais:
at=α × r=t + 2
Thaum sau cov lus kawg, peb hloov tus nqi r=0.5 m ntawm qhov xwm txheej. Yog li ntawd, peb tau txais cov qauv raws li qhov tangential acceleration nyob ntawm lub sijhawm. Xws li lub voj voog tsis sib npaug nrawm. Txhawm rau kom tau txais cov lus teb rau qhov teeb meem, nws tseem yuav hloov lub ntsiab lus paub hauv lub sijhawm. Peb tau cov lus teb: at=5.5 m/s2.
