Phy53 lecture		dr. brown		5 october 2010

rotation

	can independently treat translational and rotational parts of the motion

	having done translational 'tis time to focus on rotational

key point -- rotation about pivot point -- all bits of mass rotate through same angle [rigid body]

torque  \tau = r F_t --> sums -- external [internal cancel] -- Moment of inertia and 

Newton's second law for rotation    \tau = I \alpha

Calculating I for various symmetric objects  I=\int{r dm}

	Rod of mass, M and length, L :  I = 1/12 M L^2  
		[about axis  perpendicular to rod and through center of mass]
 
	Disk of mass, M and radius, R : I = 1/2 M R^2 [about axis perpendicular to 

parallel axis thm !

Total torque due to gravity 

example: hoop w/pivot on edge of hoop

kinetic energy of rotation

K_{tot} = K of CoM  + K about CoM

example: rolling disk down incline