Unformatted text preview: volvoment of inertia iore
ou candlE f t €d exacdya partide
an I a
man oF,
that yw sums ivide a complicadnd biecli
r
dt
r
ω I a.trn uch mor€it follows tcanitevaluateitut omheseex.mpks omort[il
partides i
ate
understandingof dre omcnts f i nertia1t1, I por nd otunmingt otalm if yy
calculatinS2, oint i he c than lle mrom
picresw ith v arious process equal thicknesr . ,atnnsbiectourse,aut iom
m
1.
o quired at his f . a hc o bicct's tIpicresw
b nn
cylinder
ihin
of in€rt
memorizint he r + 12 . (asat p mblemCmomentof inertia is evalua
feten
of
rtia
long a wC found.
problem ach96.1.
+
or dist in€ is I t= tpaiticular resultsthatsec 9A.l). For easyfuture r€
sph€ri(al
MR1
arious the mbiccb i o inertia o
havelisted mornentsoI inertiaaor vSinceasimplc oomentn ftableC9.ltat
f xis),b€causeobicrt's momentofor bf. e
iMR.
a
iMi' same
iML,
f inenia
iML, shel for btation6reround the ith the methodsofny
If y simply a portion
pi€'e is ou a familiar w of tlle sufi oI nr,riatnteFal oibiect.For ou cane€
or that t follows epi€f i v
xample
partides in i n oF, calculus,ythat i'ews
ate he sums lE m €d exacdyapicres aith v arious nEgrals. Tnto iieno
nd more spher€ y
his va
b
cantevaluateitnvolvoment of inertia oIweasilyusintdiividing itoifcandists
i nertia ExerciseC 9X.6 m omcnts prc<6s,(l
you I = i 12
quired at this point i the course, nnromc{rtso nteEstedin . he long a t e
b
cylinder
(as disks
solidequal thicknesr andnsunming of iut irtia is areif trnertia of tth6cequal sh
ihin tlle €f
ihin
++
at p mblemC 96.1.
problem 9A.l).
or d€ri(al
ist
C
Consideran around the sameaproblec
for
xis),b€
sph
sph€ri(albtation6obiectconsistin8ot two Frin
iMR.
iML,
sum
rt,' over al
Sinceany obicrt's momentof€'e is simply a ofortion offLnand mass
iMR. shelnected byis srod p alenttho tlle sufi oI n
iMi'
shel
pi inenia a imply iMi'
partides in an oF, it follows amund an axisivide atcomplicad cobiec
that if w€cand going hrough the enter
can evaluatetlE moment of inertia oI a
picresw ith v arious omcnts f i nertia1 1, 2,. . , t hc o bicct'sotalmrom
m 1.
oequal thicknesr and sunmingt tl...
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 Spring '08
 cramer
 Magnetism, Trigraph, dt, IMR, vide dle disk

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