11/29/17

Lecture# 32

.

rigidbody

* .?YIIFI¥IIt÷€ ,gangumtmrepm

HE = MI .net -

tI=±#inertia matrix

Moment of inertia : wrt point Q and an axis a

a

,;¥÷IO÷E¥¥.Iaaf

.Pam{ I ,a= a #a) }For us

E=I,and Q will frequently be the

Center of mats . Iaszz = Ia ,fQ = Center of mass Izz

Composite bodies .

÷Fan = IF;+Iqz @ B=Q+Bz

exempts moment of inertia of a solid cylinder

t¥E¥÷etftp.Iqgti#iiaIEsaia:zYP=tfp-zh-DIgI=m=R2r=aMy

-

Fexample thin rod =¥j>Ftd : Iszn #one IMF - Kam -

f.es?sdx=sEx3kI=,mzL2example:_the sphere

n4et⇐t#E¥#I * '

sina.AE#*I*IEn.EE*.t0IFE

out

www.YIIF.yyamsta.no#ag.example_moment of inertia of a flat lollipop .

*

If.EE#rmaisa=9g.

K .Fini

,

I.io#mrod=1g=solution: Fdo "i= ( to )3e + (F) 7e=(¥)=

HgIii=I;f+±d¥fOIdd,yn={ invoke parallel axis }= mdik (xcdisilycdise ) + Idgisp'

= 9

(72+0)-9=11.10

;¥ = mmd ( xiod?

+ yard'

) +Igel= I ( 32+02 ) x ( l

0⇒ 1.62=12

Motion in the plane

¥FE¥¥÷¥I¥e¥iaI÷¥Cannot o translate I direction

° a and y axis

Coordinates Xc

]Centerof mass coords

: I axis orientation.

eueisertigmIII.EE#eIIf