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01.03.2013 Views

araTanabari (cvladi) moZraobis damaxasiaTebeli mniSvnelovani veqtoruli sididea. davuSvaT, (1) wertilSi t drois momentSi wertilis siCqarea v 1 , xolo t + Δt momentSi (2) wertilSi v v + Δv saSualo aCqareba Δ t droSi 2 = 1 (nax.4), v = v2 − v1 15 nax. 4 a Δ , Δv = , xolo myisi aCqareba Δt a = lim a Δt→0 Δv dv = lim = . Δt→0 Δt dt mrudwiruli moZraobis dros aCqareba icvleba rogorc sididiT, aseve mimarTulebiT. imisaTvis, rom davaxasiaToT TiToeulis cvlileba cal-calke, gamovTvaloT Δv da warmovadginoT is ori mdgenelis saxiT. nax. 4-dan Cans, rom n v v v Δ + Δ = amitom sruli aCqareba a iqneba: Δv Δvτ Δvn a = lim = lim + lim , Δt→0 Δt Δt→0 Δt Δt→0 Δt dv dvτ dvn a = = + , dt dt dt Δ τ da v = v2 − v1 Δ , dvτ sadac = a τ tangencialuri (mxebi) aCqarebaa da axasiaTebs siCqaris dt dv n sididis cvlilebas, xolo = an _ normaluri aCqarebaa da axasiaTebs dt siCqaris mimarTulebis cvlilebas.

2 dv v1 a τ = τ , an = n dt R τ da n erTeulovani veqtorebia, a τ mimarTulia siCqaris gaswvriv traeqtoriis mxebad, xolo an _ radiusis gaswvriv centrisken. R_simrudis radiusia (nax. 5). amgvarad, mrudwiruli moZraobisas sruli aCqareba: a a + misi moduli a = τ n , an a = τ + n, 2 2 a = aτ + an nax. 5. 16 dv dt = ⎛ ⎜ ⎝ dv dt dv dt 2 ⎞ ⎟ ⎠ 2 ⎛ v ⎞ + ⎜ ⎟ ⎝ R ⎠ aCqarebis tangencialuri da normaluri mdgenelebis gamoyenebiT SeiZleba movaxdinoT moZraobis klasificireba: 1) a = 0, a = 0 _ wrfivi Tanabari moZraobaa, τ n 2) a τ = a = const, a n = 0 _ wrfivi Tanabarcvladi moZraoba da Δv v2 − v1 aτ = a = = , Tu aTvla iwyeba 1 0 Δt t − t = t momentidan, maSin t = t 2 1 2 2 da v 2 = v, xolo v 1 = v0 - sawyisi siCqarea, gveqneba v − v0 a = , t saidanac v = v0 + at, gavlili gza S = t t 2 at ( , 2 ∫vdt = ∫ v0 + at) dt = v0t + 0 0

araTanabari (cvladi) moZraobis damaxasiaTebeli mniSvnelovani<br />

veqtoruli sididea.<br />

davuSvaT, (1) wertilSi t drois momentSi wertilis siCqarea v 1 ,<br />

xolo t + Δt<br />

momentSi (2) wertilSi v v + Δv<br />

saSualo aCqareba Δ t droSi<br />

2 = 1 (nax.4), v = v2<br />

− v1<br />

15<br />

nax. 4<br />

a<br />

Δ ,<br />

Δv<br />

= , xolo myisi aCqareba<br />

Δt<br />

a = lim a<br />

Δt→0 Δv<br />

dv<br />

= lim = .<br />

Δt→0<br />

Δt<br />

dt<br />

mrudwiruli moZraobis dros aCqareba icvleba<br />

rogorc sididiT, aseve mimarTulebiT. imisaTvis, rom davaxasiaToT<br />

TiToeulis cvlileba cal-calke, gamovTvaloT Δv da warmovadginoT is<br />

ori mdgenelis saxiT. nax. 4-dan Cans, rom n v v v Δ + Δ =<br />

amitom sruli aCqareba a iqneba:<br />

Δv<br />

Δvτ<br />

Δvn<br />

a = lim = lim + lim ,<br />

Δt→0 Δt<br />

Δt→0<br />

Δt<br />

Δt→0<br />

Δt<br />

dv dvτ<br />

dvn<br />

a = = + ,<br />

dt dt dt<br />

Δ τ da v = v2<br />

− v1<br />

Δ ,<br />

dvτ sadac = a τ tangencialuri (mxebi) aCqarebaa da axasiaTebs siCqaris<br />

dt<br />

dv n sididis cvlilebas, xolo = an<br />

_ normaluri aCqarebaa da axasiaTebs<br />

dt<br />

siCqaris mimarTulebis cvlilebas.

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