, , () , - :
. (1.3.43)
.
:
.
:
. (1.3.44)
.
* .
, .
ê ê= rFsina, (1.3.45)
l = rsina,
l .
() , z, :
Lz = Iw, (1.3.46)
I ,
I = mR 2. (1.3.47)
:
, (1.3.48)
Mz z.
Oz, :
.
I = const,
, (1.3.49)
,
* .
(1.3.49) .
I ( ).
,
* , , S Mz = 0, ( ) : Lz = Iw = const. .
:
I = S miR 2 i.
, . dV dm = rdV.
,
I = ò R 2 dm = ò R 2 rdV, (1.3.50)
R dV .
17. m l , , .
l /2
dm
x
O C dx
. , , ( ), . dm dx. , , (1.3.50), , dV = dx, , ( ) r = m / l:
|
|
.
18. (. 17) , ( ).
. (1.3.50),
.
, :
: IC = mR 2; (1.3.51)
(): IC = (1/2) mR 2; (1.3.52)
: IC = (2/5) mR 2. (1.3.53)
IC , , , , d :
* , , :
I 0 = IC + md 2. (1.3.54)
19. m l , ( ), .
. , 17, IC = ml 2/12. d d =l /2. (1.3.54) :
I 0 = IC + m (l /2)2 = ml 2/12 + ml 2/4 = ml 2/3.
20. 1 1 , . 30 . . 10 /2.
: m = 1 ;
l = 1 ;
a = 30;
g = 10 /2.
: e.
.
a
r C
: = l, = = l /2, ( , , ) r = (l /2) cosa. , (1.3.49), :
M = Ie,
e = M / I. (1.3.55)
(8.3):
= mg = (mglcosa)/2. (1.3.56)
, , 18: , , (1.3.56) (1.3.55), :
e = M / I = (3 mglcosa)/(2 ml 2) = (3gcosa)/(2 l) = 13 (/2).
: 13 /2.
21. . L (t) = At 2 + Bt + C. 0,5 2 /2. 0,5 . = 1 ×2/3, = 2 ×2/2, = 1 ×2/.
: L (t) = At 2 + Bt + C;
t = 0,5 ;
e = 2 /2;
= 1 ×2/3, = 2 ×2/2, = 1 ×2/.
: I (t), I.
. (1.3.49), :
.
0,5 , :
I = (1/2)×(2×1×0,5 + 2) = 1,5 (×2).
: I (t) = ; I = 1,5 ×2.