D2_metodichka_obschie_teoremi_dinamiki

J

= J

+ m (2a)2

=

1

m a2

+ 4m a2

=

49

m a2 .

1x

1xC

1

12

1

1

12

1

J

= J

+ m (2a)2

=

1

m a2

+ 4m a2

=

73

m a2 .

2 x

2 xC

2

18

2

2

18

2

V = ω

d

.

4

2

( , Lx (2.14)

L

= (J

+ J

+ J

+ J

)ω =

1

Aω,

(2.15)

x

1x

2 x

3x

4 x

2

A =

293

m a 2

+

1

(m

+ 2m

)d 2 .

3

4

18

1

4

ω

dω

=

1 t

∫

∫dt ,

gm d − 4ω

A

0

4

0

1

ln(gm d − 4ω) −

1

ln(gm d ) =

1

t ,

4

4

4

4

A

1

4t

ω =

gm d (1 − e

A

).

4

4

t = t = 0,1 c

ω = 6,02 c−1 .

1

(

,:

m2

=

1

m1 , S = ON

= πt ( ) , a = 4 ,

4

R = 3 , ω =1 c−1 , t = 4 c.

0

1

dLz

v

= ∑M z (Fke ) ,

(2.16)

dt

# z

(2.10)

L = L0 = const .

(2.17)

z

z

) L0

z

$ (2.6):

L0

= L0 + L0

,

(2.18)

z

1z

2 z

L0

L0

– $

1z

2 z

.

t = 0, S = 0 , #-

, 0 , ,

L0

= 0 . $

2 z

#

z -

"

,

$ (2.7), –

L0 = J

ω ,

J

1z

– ! $ . ,

1z

1z 0

z1 , # ! C1

$ -

. ! J

=

5

m a2 ,

1zC1

3

1

J 0

=

5

m a2 + m a2

=

8

m a2 .

1z

3

1

1

3

1

L0

L0

$ (2.18),

1z

2 z

L0

=

8

m a2ω .

z

3 1

0

(

Lz

–

t :

Lz

= L1z + L2 z .

(2.19)

( ONC = CON = π − ϕ ONE = ϕ ,

2

2

2

ϕ

ϕ

=

2R sin

2 ϕ

,

ON = 2R sin ,

OE = ON sin

2

2

2

V =

dS

= π / ,

V = ω ON = 2ω R sin ϕ ,

ϕ =

S

=

π

t c−1 .

r

dt

e

2

R R

- L

= 2m R(2Rω + π) sin2 ϕ.

2 z

2

2

$ (2.19)

L =

8

m a2ω + 2m R(2ωR + π)sin2 ϕ.

z

3

1

2

2

0 (2.17)

ω $

8m a2ω − 6πRm sin2 ϕ

ω =

1

0

2

2

.

(2.20)

8m a2

+12R2 m sin2 ϕ

1

2

2

T '=

mV

2

,

2

m – , V – .

% " –

-

"

T = ∑

mkVk

2

.

(3.1)

2

2

T = ∑

mkVCk

,

(3.2)

2

T =

1

MV 2

=

1

MV 2 .

(3.3)

2

2

C

T =

1

J zω2 ,

(3.4)

2

J z – z ,

ω –

.

3. -

" "

T =

1

MV 2

+

1

J

ω2 ,

(3.5)

2

C

2

C

VC – , JC –

-

T − T0 = ∑ Ake + ∑ Aki .

(3.6)

% T0

– -

, T –

( ) , ∑ Ake

– -

T − T0 = ∑ Ake .

(3.7)

,

, T0 = 0

(3.7) $

T = ∑ Ake .

(3.8)

.

2. ($

A(P) = ±mgh .

(3.9)

(3.9) h – . -

, A >0, –

A <0.

'

A(P) = ±mghC ,

(3.10)

A(M z ) = M zϕ .

(3.11)

) (3.11) , M z – -

z

-

A(F ) = −F S = − fNS ,

(3.12)

f – , N

– -

T = T1 + T2 + T3 + T4 ,

(3.13)

(3.3)

m V 2

T = 6m V 2 .

T =

1 1

1

2

1

4

1

ω =

VA

; V

A

= V ; ω =

V1

.

2

R2

1

2

R2

, ,

T =

1

m V 2 .

2

4

4

1

# 3 (3.5)

T =

1

m V 2

+

1

J

ω2 .

2

2

3

3

C

C

3

* ω3

V1 . # P -

3, ω =

VD

;

3

DP

V = V ; V

B

= ω r ;

V =

V1

; DP = 3r ; ω =

V1

.

D

B

2 2

B

2

3

3

6r3

% V

= V =

V1

T =

1

m V 2 .

4

C

6

4

72

4 1

T =

457

m V 2

T = 63,47V 2

'.

72

4

1

1