Tangential thiab ib txwm acceleration. Tangent thiab normal acceleration

2024 Tus sau: Angel Austin | [email protected]. Kawg hloov kho: 2023-12-17 05:28

Txoj kev kawm ntawm physics pib nrog kev txiav txim siab ntawm kev siv tshuab. Hauv qhov xwm txheej dav dav, lub cev txav mus raws cov kab nkhaus uas muaj qhov sib txawv. Los piav txog lawv, lub tswvyim ntawm acceleration yog siv. Hauv kab lus no, peb yuav xav txog dab tsi tangential thiab ib txwm acceleration yog.

Kinematic ntau. Kev nrawm thiab nrawm hauv physics

Kinematics ntawm txhua yam kev txav yog ib ceg ntawm physics uas kawm thiab piav qhia txog kev txav ntawm lub cev hauv qhov chaw. Kinematics ua haujlwm nrog peb qhov tseem ceeb:

• traversed path;
• nrawm;
• kev nrawm.

Nyob rau hauv cov ntaub ntawv ntawm kev txav raws lub voj voog, cov yam ntxwv zoo sib xws yog siv, uas txo qis rau lub hauv paus ntawm lub voj voog.

Txhua tus paub txog lub tswv yim ntawm kev ceev. Nws qhia tau hais tias tus nqi ntawm kev hloov nyob rau hauv lub coordinates ntawm lub cev nyob rau hauv motion. Qhov ceev yog ib txwm qhia tangentially rau txoj kab uas lub cev txav mus (trajectories). Tsis tas li ntawd, qhov linear tshaj tawm yuav raug qhia los ntawm v¯, thiab qhov nrawm nrawm los ntawm ω¯.

Acceleration yog tus nqi hloov ntawm v¯ thiab ω¯. Acceleration kuj yog vector kom muaj nuj nqis, tab sis nws cov kev taw qhia yog kiag li ywj siab ntawm lub velocity vector. Acceleration yeej ib txwm qhia nyob rau hauv cov kev taw qhia ntawm lub zog ua rau lub cev, uas ua rau ib tug hloov nyob rau hauv lub ceev vector. Kev nrawm rau txhua hom kev txav tuaj yeem suav nrog cov qauv:

a¯=dv¯ / dt

Qhov ntau qhov kev hloov pauv ntawm lub sijhawm ncua sijhawm dt, qhov ntau dua yuav yog qhov nrawm dua.

Yuav kom nkag siab cov ntaub ntawv qhia hauv qab no, nws yuav tsum nco ntsoov tias kev nrawm tau tshwm sim los ntawm kev hloov pauv ntawm qhov nrawm, suav nrog kev hloov pauv ntawm nws qhov loj thiab nws cov kev taw qhia.

Tangential and normal acceleration

Xav tias ib qho khoom taw tes txav raws qee txoj kab nkhaus. Nws yog paub tias nyob rau qee lub sij hawm t nws ceev yog sib npaug rau v¯. Txij li qhov ceev yog vector tangent rau txoj kev, nws tuaj yeem sawv cev raws li hauv qab no:

v¯=v × u_t¯

Ntawm v yog qhov ntev ntawm vector v¯ thiab u_t¯ is the unit velocity vector.

txhawm rau xam tag nrho acceleration vector ntawm lub sij hawm t, koj yuav tsum nrhiav lub sij hawm derivative ntawm qhov ceev. Peb muaj:

a¯=dv¯ / dt=d (v ×u_t¯) / dt

Vim qhov kev hloov pauv ntawm qhov nrawm thiab chav vector hloov pauv lub sijhawm, tom qab ntawd, siv txoj cai los nrhiav cov khoom siv ntawm cov khoom siv, peb tau txais:

a¯=dv / dt ×u_t¯ + d (u_t¯) / dt × v

thawj lub sij hawm nyob rau hauv lub mis yog hu ua tangential los yog tangential acceleration tivthaiv, lub sij hawm thib ob yog qhov ib txwm acceleration.

Tangential acceleration

Cia sau cov qauv rau kev suav cov tangential acceleration dua:

a_t¯=dv / dt × u_t¯

Qhov kev sib npaug no txhais tau hais tias qhov tangential (tangential) acceleration yog coj mus rau tib txoj kev raws li qhov nrawm vector ntawm txhua qhov chaw ntawm txoj kev. Nws tus lej txiav txim siab qhov hloov pauv hauv qhov nrawm modulus. Piv txwv li, nyob rau hauv cov ntaub ntawv ntawm rectilinear motion, tag nrho acceleration tsuas muaj ib tug tangential tivthaiv. Qhov ib txwm acceleration rau hom kev txav no yog xoom.

Yog vim li cas rau qhov pom ntawm qhov ntau a_t¯ yog qhov cuam tshuam ntawm lub zog sab nraud ntawm lub cev txav.

Nyob rau hauv cov ntaub ntawv ntawm kev sib hloov nrog tas li angular acceleration α, lub tangential acceleration tivthaiv tuaj yeem suav nrog cov qauv hauv qab no:

a_t=α × r

Ntawm no r yog lub vojvoog ntawm kev sib hloov ntawm cov khoom siv taw qhia, uas tus nqi a_t.

yog suav

Ib txwm lossis centripetal acceleration

Tam sim no cia peb sau qhov thib ob ntawm tag nrho kev nrawm dua:

a_c¯=d (u_t¯) / dt × v

Los ntawm kev txiav txim siab geometric nws tuaj yeem pom tau tias lub sijhawm derivative ntawm chav tsev tangent mus rau trajectory vector yog sib npaug rau qhov piv ntawm qhov nrawm modulus v rau lub vojvoog r hauvpoint hauv lub sijhawm t. Ces cov lus saum toj no yuav sau li no:

a_c=v² / r

Cov mis no rau kev nrawm nrawm qhia tau tias, tsis zoo li qhov sib xyaw tangential, nws tsis yog nyob ntawm qhov kev hloov pauv ntawm qhov nrawm, tab sis txiav txim siab los ntawm square ntawm lub modulus ntawm qhov ceev nws tus kheej. Tsis tas li, a_c nce nrog txo qis ntawm kev sib hloov ntawm qhov tsis tu ncua v.

Kev nrawm nrawm yog hu ua centripetal vim nws tau coj los ntawm qhov nruab nrab ntawm qhov loj ntawm lub cev tig mus rau axis ntawm kev sib hloov.

Qhov ua rau ntawm qhov nrawm no yog qhov tseem ceeb ntawm lub zog ua haujlwm ntawm lub cev. Piv txwv li, nyob rau hauv cov ntaub ntawv ntawm kev sib hloov ntawm cov ntiaj chaw nyob ib ncig ntawm peb lub hnub, lub centripetal quab yuam yog gravitational attraction.

Ib txwm acceleration ntawm lub cev tsuas yog hloov cov kev taw qhia ntawm kev ceev. Nws hloov tsis tau nws module. Qhov tseeb no yog nws qhov tseem ceeb sib txawv los ntawm tangential tivthaiv ntawm tag nrho acceleration.

Txij thaum centripetal acceleration ib txwm tshwm sim thaum lub nrawm vector tig, nws kuj tshwm sim nyob rau hauv cov ntaub ntawv ntawm kev sib hloov puag ncig, nyob rau hauv uas lub tangential acceleration yog xoom.

Hauv kev xyaum, koj tuaj yeem hnov qhov cuam tshuam ntawm kev nrawm nrawm yog tias koj nyob hauv lub tsheb thaum nws tig mus ntev. Nyob rau hauv rooj plaub no, cov neeg caij tsheb raug nias tawm tsam kev sib hloov ntawm lub qhov rooj ntawm lub tsheb. Qhov tshwm sim no yog tshwm sim los ntawm kev ua ntawm ob lub zog: centrifugal (tshem tawm ntawm cov neeg caij tsheb los ntawm lawv lub rooj zaum) thiab centripetal (siab rau cov neeg caij tsheb los ntawm sab ntawm lub qhov rooj tsheb).

Module thiab kev taw qhia ntawm kev nrawm nrawm

Yog li, peb pom tias qhov tangential feem ntawm qhov xav tias lub cev muaj nuj nqis yog coj mus rau tangentially rau txoj kev txav mus los. Nyob rau hauv lem, qhov ib txwm tivthaiv yog perpendicular mus rau lub trajectory ntawm lub muab point. Qhov no txhais tau hais tias ob qho kev sib xyaw ua kom nrawm yog perpendicular rau ib leeg. Lawv vector ntxiv muab tag nrho acceleration vector. Koj tuaj yeem suav nws cov qauv siv cov qauv hauv qab no:

a=√(a_t² + a_c²⁾

Txoj kev taw qhia ntawm vector a¯ tuaj yeem txiav txim siab ob qho tib si txheeb ze rau vector a_t¯ thiab txheeb ze rau a_c¯. Ua li no, siv qhov tsim nyog trigonometric muaj nuj nqi. Piv txwv li, lub kaum sab xis ntawm tag nrho thiab ib txwm acceleration yog:

φ=arccos(a_c / a)

Kev daws teeb meem ntawm centripetal acceleration

Ib lub log uas muaj lub vojvoog ntawm 20 cm tig nrog lub kaum ntse ntse ntawm 5 rad / s ² rau 10 vib nas this. Nws yog ib qho tsim nyog los txiav txim siab qhov kev nrawm ntawm cov ntsiab lus nyob rau ntawm qhov chaw ntawm lub log tom qab lub sijhawm teev tseg.

Yuav daws qhov teeb meem, peb siv cov qauv rau kev sib raug zoo ntawm tangential thiab angular acceleration. Peb tau txais:

a_t=α × r

Vim tias qhov sib npaug nrawm nrawm rau lub sijhawm t=10 vib nas this, cov kab nrawm tau txais lub sijhawm no yog sib npaug rau:

v=a_t × t=α × r × t

Peb hloov cov qauv uas tshwm sim rau hauv cov lus qhia sib xws rau kev nrawm nrawm:

a_c=v² / r=α² × t ² × r

Nws tseem yuav hloov cov txiaj ntsig uas paub rau hauv kab zauv no thiab sau cov lus teb: a_c=500 m/s².