Rotation Dynamics Solution

- --- A I­ !6' I I I y. J / ! 6)~ ?f c:.. l # ) )f~6) r ) ! I .z: ~) Tog ~!J ----~ £ :1/z- ::::...

1 downloads 45 Views 3MB Size
-

---

A



!6'

I

I I

y. J

/

!

6)~

?f

c:..

l

#

) )f~6)

r

)

!

I .z: ~)

Tog

~!J

----~

£

:1/z- :::::::-

($

A

L'IA

t/~~)

!

'2.­

= n.~.11,----.

~

:::.

Yv1

JJ.J L

----}V(J~~

~ ~ f11 1t ~ ~

zz:

YV1Jd

f 'Y( I

-

-

----I ____ I _

/r'/)/// - - )

--/ i.~ /

I

.' .

!

I'

-.

-)<

: i

l

, I_---l.---~

/

,~------------ ~

;vrCD

-+ G) Le­

----.J

C



.65

L..

III J

-i-

fa IC

~.

-

-:l(i) -==

-:LeI -r

-r-@ -:::--

'1.-(" -t

JV1

CPC0~

f{) ~ rc. ::/) fVI (f



-r@;> 1m

(1­

t-1

"

--(

L

. L .- ;vl G

.1-, _

~_

) Z­

:r.

--r

"'~~ .sz: M.r L

I

/2--

-2.-­

=

((

7f

-z;

I

I 2-.

, I"

A

12.

X



~.~

1~

'\ LP ~

-7

/ y(

CJ / ;;~ X

/

\

'1



~)11. ~~

I

:::

d-.j

d~ ~.~~() ~

L

~L

.(j '

0L./ --2-­

/"

"1M If -=:-

rv1J 2­ -= ~ -r- fV1 {-~I -;" rt: ) 2-­

'L

')f

1

1

1 1 1 1 1 1 1 1 1

--

1 1

~~.

\'-/2.-

/#----

~

o

"'\

1

L-ocuS::;;.

c' f-cLE

1

~\

1

/

1

\ 1 1 1 1 1

~----------; :::::--lc -r--

1

(/

1 1

fVlt;I 2.­

'If;/? ~~ ~ cI-:::- 0

1 1 1

1

I

t

o

3). ~ ~ -r

----

1r

;Z T;

~~~Lr:;) ::::: cf/l4t L ( z,

-

::::-

-

f niL )



~-----3

, .I

-

-

M

------------------

--­ &. vi

l'l-Vl

N,=-

~ ?r

--4­

1"'\

I.

/

/'

0

14

____..

___

__

~

~

­





c:

A

I>

...--- ----

-I!V'"

--'}'

L

b

-::::

-c-:

..

C!:J



L.

.. ~·O(Y) ~

f~·~t) -r(3r'jC{)

. ~#=- @~~. ~

Lv

-==- ~

0~~ e;~ej)~

j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j

­-

ffz­

"~~r

~ -,---"'"

r 1: ,I

____ . , :. "," .~. ':·~'i.:~'::·

Wl1-v . 1.--' _

"."

~

... .

".

-.

-

..--

-

.' , l

-

~

-.

"-.

fl~~

fr~)(~v)r~) -=- 9 .

?-v?~

::::;;:-Iw

: : : Gn i)w

---

~-

---......

f

I (~~w'- ~ fA)' -.z:

)h -tz

fIJ~((~~o)

4;j. (r ~ c>-; 0)

---3:::.~

cf4

~,4~ f/VI' U=

a». _

~,N=-O. :::;>

(I't.p &-::> C9

-if

7VJ--6n &::::- 3-Cnc9

=

---'\{:= ~o

fVL

;VI r.v'-:

r:

(4-'J (i ~~ 67) 5.lK

J, '( - «c; 1:"'2. /;

~e~

.~

6)uFrT'o uS

~OPONDER Q.l

--? Q.2

Shouldthere be any matterat thecenter of gravityof an object? The torque exerted by a force about some axis dependson the choice of axis. Howcan the condition,

I

ti,ext

= 0, be satisfiedfor anychoice of axis?

Q.3What is the path ofa 'particle in a rigid object rotating about a fixed axis? "

::"

Qi1!l> "Wangi,d objectnasoillytnli1$l~tib~ mottQu(for example, the-body of a cartraveling in a ~ght lin~ on a:f1~troad), ~etb:ere~Y'pointswithin,theobJectthat alwayshave the

same velocity.:as thecenter 0 f

mass'? Ifso, whichones?

Q:.5 : 'rfa:iigidobj~tb:as onlyrotationalmotion abouta fixed.axis are thereany points witbjptb.~objectthat ~~~'llilve:tlie @:TIe velocitYastheQ~q:ter'0fm~~11f $0 :whicho9~§.?:," - . . . - Q.6 . .' It';f\:lJigidopj!.1ctmQveS with. both traR~ili9.Q ~drQtaJio.Q. about an: axis with a fixed9QeI1ta,liop{((or ..;,>:". §'j~JQUjpgWh~l),are ther~ any P9Ints within the objectthatalways havethe :Yelci.HYii'$-:-fue 'oftn~s?It so, which.ones? .

s.ame

~~-th~-'olre?tion ofthe angular' velocityofa rigi4objectrql~tingabo1,Jt~fixe4~i~?Wh!iU$Jhe velocityof a particle-in a rigidobjectrotatingaboutci f1Xed.~P '~: ", '.' .. .

:~a;9f~etmear

'~?~~t~'''~' t¥-i7s'qb~j¢ctro~g about afixedaxishas-nonzercangulaevelocityand angularaeeleration. R~q!~A ~t:;~' ;.~!~':as Illifrom theaXiwe,61ationaspt>lticlJ>B.W'W1/iS the ratio oftho Jollo.w!ng

.

,i . Qi9:"; H(:)theangUlarvelocitiesofthehandsofa·wallclockporntiotothewall0foutofthewaU?At,~-jw;wt . -tH&'elock is unplugged, do theangular.accelerationsofthe handspoint intothewallor outefthe wan? .0,10 A,.®:r is movingforwardandslowingdOWIl. Isthe direction ofteangular velocity of thewheelstoward :_nO.. ;-tii~iinvee~leftot: rlght?What is the direction of the angularacceleration of the wheels?, . .-:: . . -:

-:

- .. _--.,. "

o

7 -::

PJ

----._­

:i (1-0'\ - : : ­

Jr

)

rj Ai ~

c-

0< ~_ -

J{­

rr~ (~~)

I

'-(J

J'YtXAA-t( --0

~~

~~~ -

~~.

r;;vl/Cur

I

o&~

~ ~ ~~

-

1J- e(ACD)

.

£x~ ~ oY'~~ ~ z-~

~~.

~

~

--s-

It? t=- r

-:::::

I>

ez-

~/

LL

__

I'

O(J

-

fAJ~~,

~ c1e~

If·r ~

i-n~

j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j J

j j j j j j

f

j j j

c

j j j j j j j

G-Gy~ f-

j j j

7Cp~~

j j

(A)

/lr;) ~ /'.

c:

?'(~: O~

j j

YT

{51- {- cr I \

L

v:T

w=

V

.L..

-VL

~

w.

3~

S(Vf-v~)

2-

-r

-r

Cf-.IZ.

Vl­

"5 Vf --+- \12.­

4:"

~

V~ -r-­ ~t> cu,Jl,e

V,o

2...

-.

v

C

r

L-

V"-

i-

r

cu~ f'

-+-

r::/~VL

)

't'

l'

V

L

JO~Js ~. /O-?f/ Y1--:::~

tv:::: i\1,

:i)

Y, -:;.

X

O. I :< 4-

-0::0

~ y~ -z:

Q

rJil­

VvI

. >_0.2..

S - .x:: O?

/

~

-_

. c f

~_~-f .-vl{(,V1,'t, :::

QO)~{))1-(O·'l-4-)

::: 1J.4N P: _

-r -

_-r

o:l.-y

'Yf,1 I

)

-:::: fi ct---~--i-f"-- .

~ 3GN

f

~ ~M,J--

/

-r~

.. If::> 0/-7/

.

Yz/7

-fJ==?

Ml.