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