.
: x(t), y(t), z(t) || : r (t)=x(t)* i +y(t)* j + z(t)* k
: - , .. . : (, ), , , S(t). , .
V =∆ r /∆t; : V =lim∆ r /∆t=d r /dt tà0
: r (t)=x(t)* i +y(t)* j + z(t)* k || V (t)=dx/dt* i +dy/dt* j +dz/dt* k
V =V* τ; τ -
: ∆ V = V (t+∆t)- V (t); a =∆ V /∆t; a =d V /dt; a =d V /dt=d V x/dt* i +d V y/dt* j +d V z/dt* k; a =ax* i +ay* j +az* k; V =v* τ, :
a =d V /dt=d V /dt*τ+ V *d τ /dt
\ aτ / \ an /
.
. . .
d τ /dt=d τ /dS*dS/dt=V*d τ /ds; , an =V2/R* n. a=sqrt(aτ 2+ an 2); . .
1) r = r '+ r 0 r '=inv ∆t=inv. ∆t=∆t';, .2) V = V' + V 0 3) a = a' + a0 a0 =0 è a = a'
.
. .
.
ω- : ω =d φ /dt ω=2π/T V=ωR; . β : β =d ω /dt an = ω 2R aτ = β R
, .
r↔V↔a φ↔ω↔β || d r =d φ x r;=> V =d r /dt=(d φ /dt)x r = ωxr;=>a = βxr + ωx (ωxr);
. .
1) , , . . , . - .
2.1) F: d p /dt= F
2.2) .
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3) , .
. .
. .
. (f) (F). : d p i/dt= f i+ F i; d Li /dt= M + M ;
m=∑mi, p =∑ p i, L =∑ L i . , , ∑(p i)=const
.
, -
R =∑(mi r i)/m
.
.
, .. , , , .
( - ), .. ( )
- . - .
. .
. β = M / I. M dt=d L =d(Iω)
M , I . .
M = F *S, S - , .
: I=∑(m i R i 2); ρ=lim(Δm/ΔV), ΔV→0, ρ. dm=ρdV=>dI=r2ρdV=>I=V∫r2ρdV. - . .
: I I C , , m a : I=I +ma2
I: : mr2/2;: mr2 ;: 5/2 mr2;: 1/12 ml2
7. . :
p= m v ..; L = r x p
L=rp= m rv= m rω R=> L= ∑(Li)=ω*∑(m i R i 2); L=Iω= m vr= m vR
: M dt=Id ω
:
: p = ∑pi=∑mivi; d p /dt=∑ F i=0( F i≡0∑ F i=0); d p /dt=0=> p =const=> ∑pi =const; ∑ F i=0; .. .
L=∑Li= ∑ Iiωi; d L /dt = ∑ M - .
∑ M =0=>d L /dt=0=> L =const=>∑ L i=const . .. .
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