Cov Vectors hauv Physics: Cov Ntsiab Lus thiab Cov Kev Siv
Cov vectors yog ib lub tswv yim lej tseem ceeb hauv physics. Tsis zoo li scalars, uas tsuas muaj qhov loj (lossis tus nqi), cov vectors muaj ob qho tib si qhov loj thiab kev coj. Kev nkag siab zoo txog cov vectors thiab lawv cov ntawv thov hauv physics tuaj yeem pab peb piav qhia txog tej xwm txheej ntuj tsim kom raug thiab nkag siab zoo dua.
Kev Nkag Siab Txog Cov Vectors
Hais yooj yim xwb, ib lub vector yog ib qho lej uas sawv cev los ntawm ib tug xub qhia txog kev taw qhia thiab muaj qhov ntev tshwj xeeb uas sawv cev rau nws qhov loj. Qhov ntev no feem ntau hu ua "qhov loj" lossis vector quantity.
Yuav kom nkag siab zoo dua txog lub tswv yim no, xav txog kev taug kev ntawm qhov chaw A mus rau qhov chaw B. Qhov deb ntawm ob lub ntsiab lus no yog qhov ntau scalar, tab sis qhov kev taw qhia ntawm kev mus los ntawm A mus rau B qhia txog lub tswv yim ntawm vector. Koj qhov chaw kawg piv rau koj qhov chaw pib tsis yog nyob ntawm seb koj taug kev deb npaum li cas xwb tab sis kuj nyob ntawm qhov kev taw qhia uas koj taug kev.
Kev Sawv Cev Vector
Hauv kev sau lej, cov vectors feem ntau yog sau ua cov ntawv tuab xws li v, lossis ua cov ntawv nrog tus xub saum toj ntawm lawv xws li \( \vec{v} \). Cov vectors ob-seem tuaj yeem sawv cev ua cov khub txiav txim \( (v_x, v_y) \), qhov twg \( v_x \) thiab \( v_y \) yog cov khoom ntawm vector hauv x- thiab y-kev taw qhia.
Rau ib lub vector peb-seem, qhov sawv cev dhau los ua \((v_x, v_y, v_z) \). Cov khoom no feem ntau pom los ntawm kev tso tawm ntawm lub vector pib rau ntawm x, y, thiab z axes, thiab tuaj yeem piav qhia hauv Cartesian coordinate system.
Kev Ua Haujlwm ntawm Vectors
Kev Ntxiv thiab Rho Vector
Kev ntxiv vector yog ua los ntawm kev ntxiv lawv cov khoom. Piv txwv li, yog tias \(\vec{u} = (u_x, u_y, u_z)\) thiab \(\vec{v} = (v_x, v_y, v_z)\), ces tus lej vector \(\vec{w} = \vec{u} + \vec{v}\) yog:
\[
\vec{w} = (u_x + v_x, u_y + v_y, u_z + v_z)
\]
Kev rho tawm vector yog ua tiav tib yam, uas yog los ntawm kev rho tawm nws cov khoom. Yog li, \(\vec{w} = \vec{u} – \vec{v}\) yog:
\[
\vec{w} = (u_x – v_x, u_y – v_y, u_z – v_z)
\]
Kev Sib Npaug ntawm Vectors los ntawm Scalars
Kev sib npaug ntawm ib lub vector los ntawm scalar \(k\) yog ua los ntawm kev sib npaug txhua feem ntawm lub vector los ntawm scalar ntawd. Piv txwv li, yog tias \(k\) yog ib lub scalar thiab \(\vec{v} = (v_x, v_y, v_z)\), ces qhov tshwm sim ntawm kev sib npaug ntawm ib lub vector los ntawm scalar yog:
\[
k \cdot \vec{v} = (k v_x, k v_y, k v_z)
\]
Kev Sib Npaug Vector (Dot Product thiab Cross Product)
Muaj ob hom vector multiplication tseem ceeb, uas yog dot product thiab cross product.
Cov dot product yog ib qho kev ua haujlwm uas tsim cov scalar product. Piv txwv li, rau cov vectors \(\vec{u}\) thiab \(\vec{v}\):
\[
\vec{u} \cdot \vec{v} = u_x v_x + u_y v_y + u_z v_z
\]
Txoj haujlwm no siv rau ntau yam kev siv, suav nrog kev txiav txim siab qhov projection ntawm ib qho vector mus rau lwm qhov.
Ib qho kev sib tshuam yog ib qho kev ua haujlwm uas tsim ib lub vector tshiab uas yog perpendicular rau ob lub vectors qub. Piv txwv li, rau vectors \(\vec{u}\) thiab \(\vec{v}\):
\[
\vec{u} \times \vec{v} = (u_y v_z – u_z v_y, u_z v_x – u_x v_z, u_x v_y – u_y v_x)
\]
Cov khoom sib tshuam yog siv dav hauv physics, tshwj xeeb tshaj yog nyob rau hauv cov xwm txheej uas muaj kev sib hloov thiab lub zog.
Cov Kev Siv ntawm Vectors hauv Physics
Kauj ruam tom ntej yog saib seb cov ntsiab lus no siv li cas hauv physics.
Kev Tshawb Fawb Txog Kinematics
Hauv kinematics, qhov chaw, qhov ceev, thiab qhov kev nrawm tuaj yeem sawv cev ua vectors. Qhov chaw ntawm ib yam khoom ntawm ib qho taw tes \(t \) tuaj yeem qhia ua qhov chaw vector \(\vec{r}(t)\). Qhov ceev, uas yog qhov nrawm ntawm kev hloov pauv ntawm qhov chaw piv rau lub sijhawm, yog thawj qhov derivative ntawm qhov chaw piv rau lub sijhawm:
\[
\vec{v}(t) = \frac{d\vec{r}(t)}{dt}
\]
Kev nrawm, uas yog tus nqi ntawm kev hloov pauv ntawm qhov ceev piv rau lub sijhawm, yog thawj qhov derivative ntawm qhov ceev lossis qhov thib ob derivative ntawm txoj haujlwm:
\[
\vec{a}(t) = \frac{d\vec{v}(t)}{dt} = \frac{d^2\vec{r}(t)}{dt^2}
\]
Kev hloov pauv
Hauv dynamics, kev siv cov vectors yog qhov tseem ceeb. Newton txoj cai thib ob, piv txwv li, hais tias lub zog ua rau ib yam khoom yog cov khoom ntawm nws qhov hnyav \(m\) thiab nws qhov kev nrawm \( \vec{a} \):
\[
\vec{F} = m \vec{a}
\]
Hauv qhov no, ob qho tib si lub zog \(\vec{F}\) thiab qhov kev ua kom nrawm \(\vec{a}\) yog vectors. Qhov no txhais tau tias kev tshuaj xyuas cov zog ntawm ib yam khoom yuav tsum xav txog qhov xwm txheej vector ntawm cov zog no.
Cov Hluav Taws Xob thiab Cov Nroj Tsuag Sib Nqus
Hauv thaj chaw ntawm electromagnetism, lub teb hluav taws xob \(\vec{E}\) thiab lub teb sib nqus \(\vec{B}\) kuj yog vectors. Lub zog thiab kev coj ntawm lub teb hluav taws xob ntawm txhua qhov chaw hauv qhov chaw yog txiav txim siab los ntawm lub teb hluav taws xob vector \(\vec{E}\), thaum lub teb sib nqus \(\vec{B}\) piav qhia txog lub teb sib nqus cuam tshuam li cas rau qhov chaw ib puag ncig. Lawv cuam tshuam rau cov khoom me me uas raug them hauv txoj kev uas tuaj yeem kwv yees los ntawm cov kev cai ntawm physics uas siv vectors.
Kev Siv Tshuab Ua Kua
Hauv kev kho tshuab kua, cov vectors siv los piav qhia txog qhov ceev thiab qhov vorticity ntawm cov kua. Qhov ceev ntawm cov kua \(\vec{v}(\vec{r}, t)\) ntawm qhov chaw \(\vec{r}\) thiab lub sijhawm \(t\) yog ib qho vector. Kev kho tshuab kua yog qhov nyuaj heev thiab feem ntau vam khom Navier-Stokes equations, uas yog vector partial differential equations.
Optics thiab Waves
Hauv kev kawm txog nthwv dej, tshwj xeeb tshaj yog hauv cov hluav taws xob electromagnetic, cov teb hluav taws xob thiab cov teb sib nqus uas tswj kev nthuav dav nthwv dej tuaj yeem sawv cev ua cov vectors. Cov xwm txheej xws li polarization ntawm lub teeb cuam tshuam nrog kev tshuaj xyuas vector ntawm lub teb hluav taws xob vim tias qhov kev taw qhia ntawm lub teb hluav taws xob txiav txim siab qhov polarization.
Kev sib piv
Hauv txoj kev xav ntawm kev sib piv, lub tswv yim ntawm vectors tau nthuav dav kom suav nrog lub tswv yim ntawm "plaub-vectors," uas suav nrog ob qho tib si lub sijhawm thiab peb qhov chaw. Ib qho piv txwv ntawm plaub-vector yog "plaub-momentum," uas muab lub zog thiab momentum ua ke rau hauv ib qho vector.
Xaus
Cov vectors yog ib qho ntawm cov tswv yim lej tseem ceeb tshaj plaws hauv physics. Lawv muab txoj hauv kev yooj yim dua thiab raug los ua qauv rau cov xwm txheej ntuj, tshwj xeeb tshaj yog thaum kev taw qhia yog qhov tseem ceeb. Txij li kinematics mus rau txoj kev xav ntawm kev sib piv, kev siv cov vectors ua rau nws yooj yim dua los nkag siab, txheeb xyuas, thiab kwv yees ntau yam xwm txheej ntawm lub cev. Yog li ntawd, kev paub txog lub tswv yim ntawm vectors yog ib kauj ruam tseem ceeb rau txhua tus neeg uas xav kawm physics.
