Лебединская. Динамика материальной точки
.pdf' 1.11
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M = I ε , |
(11.1) |
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'. 11.1 |
' – 4-4 , -4 |
, I – ( , ε – .(11.1) ,
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I1ε1 = I2ε2 , |
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ε2 / ε1 = I1 / I2 . |
(11.2) |
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(11.4) |
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( 4 . , (11.4) (11.3), :
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I = I0 + 4I0 + 4m0l |
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(11.5) |
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(11.5) ** -
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I1 = I0 + 4I0 + 4m0l |
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(11.6) |
* l 2 , ( |
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I2 = I0 + 4I0 + 4m0l |
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(11.7) |
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I1/I2, , (11.2).
(11.1). . :
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+ ( *,
(11.6) (11.7)
I1 − I2 = 4m0 (l 12 − l 22 ) . (11.8)
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(11.1)
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= M1 − M 2 . |
(11.9) |
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F . 1- *,
m. II -
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mg + F |
= ma , |
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mg − F = ma . |
(11.10) |
(11.10), - 4-4
M = m(g − a)R . |
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(11.11) |
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h = at 2 , a = |
2h . |
(11.12) |
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ε = a / R . |
(11.13) |
, (11.11), (11.13) (11.12), (11.9) ( 2
(11.11) - a ,
64
g), - 2
( **
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1 |
− I |
2 |
= mR2g (t2 |
− t2 ) . |
(11.14) |
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/, (11.1)
(11.8) (11.14),
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(l 2 |
− l 2 ) = mR 2g |
(t 2 |
− t2 ) , |
(11.15) |
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2., m
t h.
3., m0 l 2 3 .
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5. , (11.15).
! #!&) ,! #! ,
1.% ( , .
2.% . 1 ?
3.% , . ,
2 * . 1 * ?
* ( * - ?
4.! 3 . 8 .
5.4 .
6.1 - M ε ? (11.15).
m0 = 200 83 ( ).
# (#
1.! . . 1 . +. 1. – .: , 1989. – !. 94–116.
2.+ +. . 1 . – .: . ., 2001. – !. 34–46.
65
' 1.12
+ + ++ 7 ; :
9 &)# ! ,: .
+# !#, # & . !: , -
, .
( ! * !'* # %
& ( . 12.1)
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(12.2). / 2, ( * - 4
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. , - 4 3. &
1, , - 4
&&. , 4-4 3
( .
'. 12.2
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2 « » fmax , *. , (
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( * . ,
T , 4-
t , n
T = nt .
! ² – ² , -
, * . +
- (
), * ² – ²
mυl = (I +ml 2 )ω0 , |
(12.1) |
m – , υ – , l |
– - |
4 &&, ω0 –
, I – ( 4. , ( ml 2 -
( , (12.1) -
,
υ = |
I ω0 |
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(12.2) |
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ml |
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(12.2) : υ ,
, ω0 , (
I . + , *4 .
* * 2. 0 *,
2
(2 :
I ω02 |
= |
Dφmax2 |
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(12.3) |
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D – 2 ( , φmax – -
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- * ( . 1.3):
T = 2π |
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(12.4) |
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D |
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(12.4) - 2 ( D,
- (12.3) -
ω0 . , ω0 (12.2) - -
υ = 4π2I φmax . |
(12.5) |
ml T 2 |
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(12.5) - ,
( I. , 3
( . 8 (
, ( * * R1 R2 4:
I |
= I |
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+ 2MR2 |
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I2 = I0 + 2MR22 , |
(12.6) |
I0 – ( * -
( * , M – .
(12.6), * ,
I1, I2, *
I = I1 − I2 ,
I = 2M (R2 |
−R2 ) . |
(12.7) |
1 |
2 |
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% * * ( - (12.4). 8- (12.4) * 3
T1 = 2πDI1 ,
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T2 = 2p |
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I2 |
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(12.8) |
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8, (12.8) ( ,
I2 = I1 + |
I , - |
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T 2 |
DI . |
(12.9) |
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I1 = T 2 -T 2 |
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, (12.9) (12.7) (12.5), - |
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υ = |
4πφmaxT1 |
M (R2 |
-R2 ) , |
(12.10) |
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(T 2 |
-T 2 )ml |
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+!# ! , !& # ! ,
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R1
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2.8 . % *
* -, 2
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3.&, * ,
² ², * . , *
φmax .
4. / *1. % 2
t1 , 10–15 * .
5./ l ′
.
6.% R1 2, 3, 4, 5 * .
7., 4 R2 .
8.% R2 * 2, 4 5
* .
9./ 4
l : l = L − l ′ , L – 4
. % L
. 10.' (
69
n R1 t1 T1 <T1> R2 t2 T2 <T2> l ′ <l ′ > φmax <φmax>
1
2
3
11./ , . &,
= 168 .
12., * 4- (12.9)
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13./(
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2.9
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4.1 * * 2
?
5.* (
1.3).
6.1
(12.9)?
7.8 * ² –
².
8.8 *2 ² – ².
9.(12.9) .
# (#
1.! . . 1 . +. 1. – .: , 1989. – !. 94–116.
2.+ +. . 1 . – .: . ., 2001. – !. 34–46.
3.8 . .., + /. . 1 . +.1. – .: , 1972. – !. 59–70.
70
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: : + 7 ; :
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1 2 ( μ - F |
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( N ( , III - , |
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F , -4 ) |
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m = |
F |
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(13.1) |
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N |
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% 2 (
( . 13.1). 3 ,
&, - - ,
b . 0
71
α0, *-4 .
n αn . 8 * *
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'. 13.1
( . 13.1 ) ( -
F , -4 mg ,
N = mgcosβ, |
(13.2) |
m – , g – .
! 4- *2.
, *2, ,
n , - (2
F S = mg h , |
(13.3) |
F S = A – , S – , |
n |
, mg h = E – ( 2
, h – * . ! (13.2) (13.3) (13.1) :
μ |
= |
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h |
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(13.4) |
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S cosβ |
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%, . 13.1 , |
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h = |
l sinβ, |
(13.5) |
l – ,
.
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