1 . To throwa curveball,a pitchergivesthe ballan initialangularspeedof 36 radls.
Whenthe catcherglovesthe
ball0.595s later,itsangular
(dueto
speedhasdecreased
air resistance)
to 34.2radls.
a. Whatis the ball'sangular
it
acceleration,
assuming
to be constant?
^ ,-?
i
-: t , r -rc{ T"
w\
iw +. \.
o(
*
\
L
"
v,*
*/
|#l
. ', \ ',
.,..--:--*-"-.**i-"
rcetfA
3C.Arc'of5 - 3t
+
- 3,O3 radf5l
r-A
\J. D*1)-
S
b. Howmanyrevolutions
doesthe ballmakebeforebeingcaught?
tO.qFad 1r .,r
AO = ili+'***t"t
Ae -- 3G.i41a:!35s)*
(O . E qS )a
rcic5,i6\
b l-:.63
3.33r*v
2. Ona ceftaingameshow,contestants
spina wheelwhenit is theirturn. One
givesthewheelan initialangular
speedor 3.4rad/s.It thenrotates
contestant
throughone-and-one-quafter
revolutions
andcomesto reston the BANKRUPT
lr?I1.,.4fl$od
I n'rt
space.
rm
a. Findtheangular
acceleration
of thewheel,l.8Scoo
assuming
it to beconstant.
(.r-)g E=1-r-1;a-+ Q*i A€
o 4 = --C" rl3 6
ro " o t f = a
b. Howlongdoesit takefor the wheelto
cometo rest?
\
t-,J+ -- ui" 'r ct( \
L , J r--L ! i
- +
s(
n'tqt'l j - - av,, qrod/'
t)
w
tt
- c.tl3
6 roorfla
q. G s =
-t
In a microhematocrit
centrifuge,
smallsamples
of bloodareplaced
in heparinized
,
capillary
tubes(heparin
isan anticoagulant),
Thetubesarerotated
at 11,500
rpm,
withthe bottomof thetubes9.07cmfromtheaxisof rotation.
a. Findthe linearspeedof the bottomof the
11.,500
rpm
tubes.
,F
u= l L W =
\,lyyg ir o fl*
\
\r"os
t.\.t
>A
f t^.1= O, OaOI.n ( \,?xr63.onls)
\;
"
;
i
\*= loq 'ys
b.Whatis the centripetal
acceleration
at the
bottomof the tubes?
\, l
LA c -- vT
F
=(oq *ls\' = \ 3t,0OO'-/*"'-e,oqo.J,-,-.,
whatangledoesit turnin 2 ms?
4. Anelectric
drillrotatesat 1800rev/min.Through
angular
acceleration?
thisspeedfromrestin 0.64s, whatis itsaverage
If it reaches
O = c':t
Q =amf +
$ :an (H) to,cc 3i)
Q* c.3 '] rncl
S x;a o
o{ = t'r - IDS:l^
*
ir
rr
f,ff (H\(tc--)
q,d = tq5 rod,fua
5. A lightchopperconsistsof a diskspinningat 40 rev/sin whichis cut a holeof
of 5.4 cm fromthe axis. A verythin laserbeamis
diameter1.0mm,a distance
directedthroughthe holeparallelto the axisof the disk. The lighttravelsat 3 x 108
by the chopper?
m/s. Whatlengthof lightbeamis produced
(qcre''rl*
u =Jff+ =a'ii
,J,t - vt = rc.:t
\ * vr
-t
\
t.Lr)
A
t
uJ-- eE\
-
A/ai
\- J' \- r \^J|n\
T -
:***---Q,oS"t'*(t:i1
t" F
?,38X r6-s 5
Len6th: sp*t:gol llo,h*x*
[ * = Snigr * , lS{ ' ; . 1X' x , r 0s: '}
"L
? x{ t}1,"p
A wheelhavinga uniformangular
acceleration
staftsfromrestandrotates
through
-:.
=?.5
150radin 2.5s. Find
=
i
i
f
$ t5O.cd
S U),:O4S
a. theangular
acceleration^ a
,,Y,,,,,,,:,.
:
"
AO=,iy{t"s<\*
)+=O==<=
&Jrsonc.a)
_
\o /s*
= \X-adfr
t-
f]e.T.r--
b .th e angul arv e| o€i ty atthe e n d o f t h e 2 . 5 s in t e r v a |
UJ- t^:i +o<t
Lor= O*{s *
,}X""d/s,(O.S=)
GJ+= la Oro\o / S
c. thenumber
of revolutions
turnedthrough
in 2.5s
\f,Orc.d \ lre,/
.-ff1ffi:
lqrcvi5(3,Se\: lY.lreV
7. A diskof radius40 cm is spinningat a constantangularvelocityof ro= 30 rad/s.
a. Findthe velocityof a pointon the rim of the disk.
\=t-ot^=
l1)co,c\/- tC-+O*) = lE-/5
b. Findthe acceleration
of a pointon the rimof thedisk,
Or=OTsa
.\
C.- = (-^-)'I^
ce'=Q"*lY(o.q.,\
C.=
jb0
*/:a
parts(a) and(b)for a pointone-third
of the radiusoutfromthecenter
Repeat
of thedisk.
(ry)-\ = c^-rr:- 36(ccys
H^1/S
r *fScn"%)"(g#) = f Eonlsa
*q= r.*Je
The spin-drier
of a washingmachinerevolvingat 900 rpm slowsdownuniformlyto - 300rpmwhilemaking50 revolutions.
Find 16orpn 3ryiT
: : ,: 1.,
-d/s
a. the angularacceleration
3oorP*- -) tor-r."d15
'J
e,l{? -r1-1;,a + Q*fu
o<- :
r^ri=-t-:,b_
JG-=
(ut"y/.)t-
(:o,ir
ro16)3
b. thetimerequired
to turnthroughthese50 revolutions
e:
\)
t=#."u=t$*ui3!
5 (t^1,,*6)
-\
=\{)
\
9. Thebobof a pendulum
90 cm longswingsthrougha 15 cm arc,as shown.Findthe
angle0, in radiansandin degrees,
throughwhichit swings.
O= x _ g , t t n ,
v
'
o.Qo,-
C.iL'1.oo{
10.Awheelrotateswith a constant
angularacceleration
of 3.5 radls2.If the angular
speedof the wheelis 2.0 rad/sat t = 0,
a. Throughwhatangledoesthe wheelrotatebetweent = 0 andt = 2.0 s? Give
youranswers
in radians
andin revolutions.
= u: it * 5o\ a
AO =u:it
^. lc - ac l/ / r
f,f,
/\ A =
\,
! f(],,greerfs\1f
t
5f
- Jn"d/s(a:\**
Ae
- *)l
-rnrqt
lffi
b. Whatis the angularspeedof the wheeldt t = 2.0s?
(.Jp=1r;'
+ o.t
L:f = ]rod/5 + 3.5caotf=a
(f)
t^Ja= Q. C .od/S
\r.qmeLL\rev
- l.JS re
1. A nair p l a n e p r o p e l | e r s | owsfr o m a n in jtja | a n g u la r sp e e d o f1 2 .5rev/stoa.fi n
angular
speedof 5'00rev/s' Duringthisproie;;,til. propeller
rotaiesthrough21.0
revo|utions.Findtheangu|aracce|5ratioil;il;;;opel|erinradianspersecond
r''v,-v"v' rrrrqurorr)p
squared,assumingitrsconstant.
? \ r e v ( a f\L a c\=
\? f\,
\ \"u
G)l = \?. S€
l
(.^.t*=
s"o €
G ) s2 =(!i r
L!+
o',ir o.o\
t %d)
(ry1
= ?sfi racr/5
= lCn-radf3
+ )"tAe
"- u J;a =o{
t^e
-
(on)"- (ast)a
I fffiTT
G. oS fi -'dls a I
1_I
12'Atireplacedon a balancing
machine
in a service
stationstartsfromrestandturns
through4'7 revolutions
in t.z s befot.r...hingr:t!'rin.tangular
speed.calculate
its
angular
acceleration.
O __l.TTf rc^o\ t = l, ?s
or = "'
L)i = O-dls
3td = Qtr YiT-ad
rrtl
T;V
A O= ,r"#"***<.tQ
J}e =*
+a
a( 9 . q f i * a )
=
l , l s)l
\\t*{s=o (