Rotational Motion
eT. ms fy com ty =
aR ae 2
Ves 0 mn emt
7am ol paatete ta cont — | Condinaler 9) Coe
woth ankle axe stoltonay
Mea? Mime dmame
m tm:
Sum = mah Amys
Tar
a alin
Fons tant + qua then
ro
Corre §) enon WO nase
CM 6, 40 panktdle _syetan fn shficae
ido a
Lada
Ye ae
Sei sdf ty m0 amar + me, Anis symouh
a mm.
Hom ond Gs tae + mg = mt p-
mm tm rm, om
com ti Tom O + t= mney + mys ma
H com i oe tan 0 ta + ns
mem,
wm
coneCoke 8, mate some stl ‘ody
Oki
Vs
de
3) Vathom sod:
&
A) Wty oe cha
7a
@) Rectangulac stack
6) Spa Cond flo
1) Grd (sled $ an)
Got hese
8) cou Caltd § Yalan)
ttt. Nelle
Any
N=}
4) bunt tad rng
aay
1) St Galen, die:
u) Std Vemesphue
13) Haina tndephee
2
Questtory
8) Ow mm
a Pace
pe al
20m
+ ae sep = Ake : oem
10
Aum
Hem = MA 4 Ma % 43,43
Mm rm, Ms -
\ xb + 5x0
10
= thMem = 1x04 anrehe|
tae ™ (440)
Yom > (x04 2x0 rx SB 1m, (0, f)
1
yem = 48 aitf)
me
=
N
wd Gon =m =m)
ral m, (£8)
x
m, (s,£)
i Ay ~ t a2
(0,0) (440) ie olf 2 ms (436)
» GT
(46)
m, (te, &)
Ist)
o «
”
id. sphue
= ™M
114 Yom = ML 4 (lO)
rm xhaml = Abide LL or
mam, ap
Yeon ay Veloci Com
Fi
qt Tom + Mate seh
et ($4) Gu =n) ‘
ft mf) vom * din
em = mV. 4mNe
mm,9) Ake ey g) tivo bodfeg
nfs tos wo Ys
“| me Aen: Mage, 9
zi merme
Wan > Mxa= be ~O-2 o/s - Cot tate: X) « om
, 4 Had
9) Y= 4 ak !
y= -4 + yak Gem = Mx9 + Msx9 “Lt
5 myam,
Ms 24g mrhke ee)
Cos gu)
Ay bk Bem: Myx -Mxa
errr hai
Halt)
aM a= mx9 -™g
reve
a: @m)g
the = mame
Mb mt. mgd my 2A hnlanal force on Wee _systemn
Met we aR vse 2h yen at em =_muas_4 evar
m tm;,.
Vem = meva aii Vad Mae Vy um.) Aim = Myavam,Ay
m tm, tms +m:
i+ Aj 4g -
to
Kineos momentum 8p system
Vem > mv emu
Cr
Mam)vem = mT AmieConservation. & Com.
p= mn) Vem
Fent: dp
dt
Fent -O j de <0
dt
P< constant
j (on smi) Vem « cout
Fs an = Usk
te dn Ihe absence gb eat fue Ven
Sumain constant
Enomptes
)) Anploin body ak Acct
u:0
we am
ny, NE,
(a0 ent force)
mG: Me
2) Exploston. £} « body in matron
M2Ve
ch
&
Vem
me,
3) enplocten 4 fuel falling ‘body.
my
my mM,
4) Anplotin in posabolic pall
cu Mh
yy = Te
m
5) ‘Tsalley oman, system,
emtebth
Taking trollry {man a3 a sys be
Fext & zoo: Heme CM doesnt shift
Hence bor the CM we Aurela const
The haley will chiff back ag the
man move ferwacd-
ate
—————
eecla
L disploument 6 wal alee flay
disp. hellay wet gound
Pr- dip Ro mn wet qousd:
w(t-n) = Mn
> mb
mM
COM 8) residual _ bodies
om,
nem a
ff Me el xf
m-firext af
Metfa » He hoo pple aw movieg
- de
% aco aae be
a ge ee = Fowerdr cach ole by pulling
vt a shelled shing Hey Mod a
COM ™
om
Gwe: Wem Zi ath
cm
™
& Ther aed mot be any muss
st Bh
Sf same ™ @ com
onthy mene x lv a uniform —qeauitalinal field
COM clndde wil
> rink _about_Com eC a body with veuy laige hk is
plaud verlically abv the ff
+4 the botal Feat & acting on -Com| Qenth te Chr w 4 Gil below CM:
een Ctowa halkine
han vody wadlugo pure hanslalery wt koodudat) %,
molten etoem
+60-M & tadependint 4 dein Ny
)) aloia
+ fake cvedes Of CM depends ov ALIN
chon etgin.
Om depend on sit, shape % | SP a bedy plowed hertronkly
Maw dishthuttor- m te wae csth then CO
* CM can be faside » oubside of on windde with Cm
tw sutue B @ Indy
TF hoo porticles ae moving x gyse with depth
ech hee with mutual ath bcos Co i eet Chg halting
they will meet at their conke 9 cua fe
tom
CT i pf
@) x, @ %Moment drut. Cletatot avila)
dis 4 quantthy dent fo mass fo now
molten that depend on mass 6 rotating ody
5 ik disktbutim
ee cpu
“gm(n9)*
by Lov) wt
fy-14w? I-»m*
ce & monent J
«gt ts sealex is
Monat 3} Taula Q a pathicle-
Ht She peoducd 9 max
G padi 4 oy Ae“
Jo distance from Hu avis
Yate
Le m0 my (re)™
Ht In A patticle sys TF poutele be om
some fine as CM then
Yemht 4G: my
mim, mim
Te mrt. mn
o
Te mytumyr,! emg.
Te ma0s Mal? emt?
44
T's My L* 4 malt +msr0
4
*
1". myxha Mm, x0 amd
Te mx 0 1m*01r mv
smu
™
it" = Cotyammpemas om)
1" @um)a ju ast
> Moment _t} Joan rigid body
y
Mata
qT: Zm*
T Mor
4 & an Tmaginary dist hom
ans fo
fo get OT by Ink gration rubbed
4% Ring .
‘Tomy Riemes bes OL)
L4enssm made *
K= \MRE
4
KRAMestum d) pasalle! ants DA all pastcler ax at same sep
seeplale tall sigid te r ion ants then thal sop* gties_k
Teds fecpie te fom! 8) Hall parttely au te crak with aris
3
We Kk @ Hul body u xero as T-0-
T= Tem Mat D Mamal 9, Jnutta }, calaia stil ‘bodte
Pheaum_f lac ants A) Ciaau tng cae
© cant Be appt fr all tyid CES, wt
bodtu 4 con be applted fra fs on osc
plane Lomina.(M Wody. rei regigt 4 tag
Hifcknen)- i
4 Tem 12,
(Te: tne ty « Ten ye Dee
Ie eae ie @
AE
“ody fie ow
1-Y plane
4) ME dagend on mute boty
DMT depend om dlstrtbutton mux Q
aly G1:
) ME duped on arte % toe 4 body PO
0) Mpls 9 /
9) Rod qyation aot He dist biv
kT MRE MR”
cM & anis a adn gid Nt
Q) K & th tm: dislane A, ofl pastel
hom ath Aolalion. —
masa 6 Q|
@
2 3.
DOr MAE emt ¢ Met
P a
ee Tem > 2iy
2 ce at
ne OF Mite ME
4 age
Tomer ae
(oe Madependaat 9 cog)
z
9 Tr
Ten: 21!
Gs MLE ey hentai
qh mut 4 & La (e-4o')4 fame stand
0? 4 [292 4 mat)
“(2
(br)
”
Ts don tm
13m
.
3
Gaica]
Soe TVA
she +4
> Tem 22h) 2Ts
TosBas thet )H r
4) Hotlny cylinder
) Sded spe : ons ed Cowon” 5) ag)
Tom = 2 MR cme {_*
Bs ame™ eee
Thome?
ale ameter 4 2 met
Te ameec a gineHigh Body Cad
41) Any lu diglaament (6)
oo Wu ange subkaded by pestlin vector
ad att, ta gun tinue taker
S
a) vga vdledly(«)
de
dt
ay: 28.
oR any
DRL Whi Line {engl veloiy
aia ts
ayn
4) Magudne auc
ted Hf 0 - ceut
at «=O
« : dee
lt
9) Re tf linea ¢ angular ace
Os rk
Fons Maton Gath angle ax)
WO -torstl
ws G4 240
Oo wet + Lett
2
Tou Coromat 9 feu)
£Aecpe 6 «by
FCT which depend
onlE| dina, Fg
fetnt 8 apace A face
¢
Tague abt @ _petat
egus uty andy a a prod
¥ 4 Fem {4 dit bem wipe
be tt hot QF
* Lauing mw body ah 0 =O
foes @ bw 6 ¢ wler'= 0
Un VOM £20 a woe Com
eet
le (0) owefat
T= Fano Ck)
Fg. Me, TE
NES tee PRE
7
et,
a Je EAE Gree aktg mata) tt
Loto.
nee ae < 4 momen § snuth_ady-
fh acs certe faut
qh Oh nal
+ Tealaiad gb Feet 0
2 Reatnal gh © Lact =0
Sedna GY foot $200) 0
> dramplar 3 eghn
cemip te Nia oinccte
os
:
t
&
ge RE: fat RAE =O
ow =O
ag + Tete oy Fatt-0
2 Angular wtemuntum I, a movin bedy abt «
at a cg to pad | PG Cem dit hom 0 be
Wine Cincox eevee)
Wg = Ter bo rma| Gonwation ie
cana 2 Zeb = AT
i Ab
Led =O
dt -0
dt
A = conulant-
Jn the abserce ext cM ngulen revmnha
sytem samate. cont
bu btw
‘Tw -coustant
* fore ngs meenlan abt 8 >0 (0-0)
So te ab eal Cup To change 0 cay
Rate ai
i wo
c a
a 1
digs
ah abt 400 te
J mu
.
4
ts :
whan A480
4 aq
‘tome
| Sa eta
ad 4.5,
Oa
Otome
a dite ||
, tee
ew cats 78
eo ate)
a 2 ae change angul =
eae seostaoy EV MEE ee
ent Z acktyy on tk1 SN tt enpand (Ae) T the wo ve oe
Gap
then TF think The wre
when sod shtka the agit Laut
ound =f 2
Werk _dew bby Tag.
© Compastion lu Cae § Aelabiotad milion
Franslational — molten Rotational motion
m T
$s 6
v wdd
lt
Ped - Ede
mae a aw
(Pew) ae
f <
Angulaw Smprdie e L
t e=! _ er
Loar Ee dmwt sada” aid
aa ber dtu Perr
2 2hPose selling clony vzete. alae.
ACD
Yo Tle
Couln fer proe selng is *
~ walely pA cont to ground
A tue
man
pest pe
Kt ing tro
Ge bl ae
Es ddete Lye
2 a
dh pute sally wa by te +0
Sime thar no 906
#411 a? in
“ie aap
Ecdravt tLmk iy? Wore)
28 Teo]
fo v
easel vy 100
ily alia tally att
Seraned.Slping 6 fa aig
in eckinud dean £ KE i ait
comsenud (v tag) § body undego
arse lla Cading il py
ME not cercered
Ww YU
Adling ith batkwaed tering
Fan ta forced dine tony vf
Hsing Ww
ME not concerned -
Cn saling f an he brads
batkwad — dependin on denn 8)
Hippie)
Peay tn on cn _taclingd lang
>
‘ se mgein® he vel Gv
cue 0
Wd ic smth Yay 41 puod z 4 tad
‘unduge pe ading made A) two
es Tangential fous -0
cong #40 ure dow
0 jaa) thar bey
0 will not velake ndogg pre silly
vs wo
aeAyan fm Zi frRe ae
gem ng. «mae fee)
grab steak’ Ease
4
getty
au" selling hu A fowgh
—
Vdouly at lowe petal
Ash Ll ok Z|
ee
tow Haken ho _rtauh ee tout
ye urat
ket | 2ae ‘age = Ot IsinG E
tel vip cies
EM TR ise
Mintewn condition bv biter fe
WN four inadlcient
tae nage apn aing
> marine -f ma
gan -f = mgrind
ee
f- mg sin® [i 2]
Sey 1 depend ov B
sreomenhum.
holMor
qT,
«Luh 1 -
ir T
ae et 1
()
nite dc
Tem = 4a )R2
ee
2 Mlk)? 4 Mn?
2eA a |e a @e-4 att
bun 0 @) © &) © O© y a
mt
n nit) 9~ (ay
n+l
aya(( n=}
nt \
@-)'4
Cay WePonce in vel Q besthuy uv} (0 ms
ol iy alr
sea Gm Ba
5) Ty"
Yun = Me yy #Me ye
merry.
dsm > me dy, tWtrdye
mtmr-
I= toxt 4 30 «dye
40 -
Oma OMsml erat
30 4
-lum