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