a) i××=m[ 0+2 - rutgers physics &...
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10€ a) I××=m[ 0+2 .la?ia4t3Ca4a2D=lOma2z I×y= - m [0+0+0]=0^
2m
a-... -• In = - m [0+0+0]=0
:
, Iyy=m[ ah + 2. a2 + 3. a
'
]=6ma2← 8 Iyz=-m[0+2 .a2 . 3a2]= ma'
M• 1
2 a ,
×'
Izz=m[a2+2a2+3a2]=6ma2.
a-. - -.
3mm@ (9,0/0)
Rm @ ( 0,9 ,a )
3m @ ( 99 ,
- a) ¥=ma2|l§!§ )
Toto0 e=4b
§total) ( E) =3 (§) Da*o→x=• a.⇐ %
→ 96=0I I1-- -1
£= ( 1,90 ),
ti=iO
block diagonalloa = × a
ii ) a=o {4- 6) b-
e=0←det=omatrix : 6b+c= X b - b + ( x . 6) e=0
det=dets°det2|bt6c=×C( 7-65-1=0,
,¥s
fit: t - 6=±L
3×3=7d. = ( 1,0 ,o ) → toward m
,) ,=1Oma2
£2 :(
HE,
- ⇒ → toward 3m,
> z=suaz { 6btC=5b ⇒ b= . c
6bte=7b ⇒ b=e
£3 .=(o,'E
,⇒ → toward 2m,X3i7ma2 fyz=5,£z= ( 0
,'Fz
;±rz )
Xs - 7,
£3 ' ( 9h,
'Fz )
10.39
0k¥IEEE .III.'÷i, 1¥20 = 188 radls
( derived in lecture
/¥if'
⇐ teams{*caffeine" "
= rms.IN.
§edz=.nl?g.tah4=atarpkti==Im.mYT=tz.nrat=.3Tw.oZF=3awr==Mg8m3YI=EEteoaE.PPjj?#.ra2&rad/s
1@ y.io,. ( x ,
- XD wzw3=T1
Xzioz - ( Xs - 7.) wsw , =Tz
it ,#Yes's 'nma=r .
I !¥!s
> iwiio ,tlizwiw .
+ Xiswsis = w ,wzw3[ X ,
YrYDtHXXDt+ X}(Y ,-Yz ]
feet xiwitxiwitxiwi )=oF- L = ( 1W , ,
tzwz,
Xsws )
if dftl '=o ⇒ test
10.4¥Inertia tensor at the book
# a= 3cm ( see 10,25,
previous mw )
##=]c= 30cm
a an Iaetzmlboj"
aloe'aka . )X. = tsmcliteyXz=tzM ( ate
' ) Xi > tz > 73 spin around £,
W,
= Wacanst D wz,
Wz
ys=zM( btta '
) yjwz = ( Xs - XDW was
in =
ate '
{His = ( X ,
- 7.) wwz
{a.=a¥÷I:3 .
in " ÷÷ www.twitter.nuR= www..GE#atagtg=o.g7w=l74rpm
if spinning around £3, r= wf.MY#gIe?g=ao.6l.w= 110 rpm
o.gg#EnyIEIItIIs:iieo,÷= .
Wz = W }o + 1%3 - t
in,
=L W
} wz y= witiwz
|iz=-Lwzw,g. = i. + ii.
y• = L w} ( wz - iw
, ) = - idw } ( iwz + w, ) .
. - idw}y
g. = - it ( wsot ¥,
t ) .
y yH=o)= wio
dyg. = - it ( wsot Fat ) .
y =µ.
.
a ( btcttiy
ln1= a ( btetl . t
y= A . €
at + btz7°
ye = A eat + be
.( a +
z←yyg
.
,
ealbtett't
atZbt
= -idwso - it ryyt
a = - idwso,
b = - it Ex,
y= A. did ↳ + Est )t= A ( as Ldlwsoeraatttftisinl ] )w
,= Wio . cos [ ¥3 ( w
3.+ East
)t]y5 component in xy plane
has fixed magnitude ,
and rotates with freyeeuywz= Wio . sin [ ¥3 ( w }ot Fat)t] increasing with time|
- - W } uniformly increasesWz = Wzot ¥3 l
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