Lecturelt.ROationdDynamicstIFreeRot
ation
Consider an object spinning off in emptyspace
W
a guess foraxis of rotation
centripetal force IF dm w Fon dm
no externalo F fDE w J dmforce
fdm F o implies that fo i
bottom line objects in emptyspace rotate about
there center of mass
Physicalpendulum
pivot
gravityacts todecrease G
Z Ims r sine
9c
we will see laterfor small G LL l this defines oscillatory
motion w the period
MFI G7 tuff
Compare a simple versus stick pendulum
Is mi and r L
I
m Tsimp2T
z2T
density
r
Isaac fake IdeEte
Mz f m L
Tstick 21T f 2T
Tsimp Isaac
Rollingwithovtslipping
Energy Conservationffind Lgib
Mgh t mu t t I w
initial state onlytfind state only
has potential energy has kineticenergy
numericaldefine I k m R constant
mgh Emr't tkmR p
2gh v l I t k
Iv F
type 1 YESH
point 0 I
ring 1 Fa n 0.71
disc Fg 0.82
shell tf o 77
ball Is fsf 0.85