Re: ROTATION

["Richard J. McNamara" <richmcn@EARTHLINK.NET>]

"Spagna Jr., George" wrote:

> David Abineri asks:
>
> > -----Original Message-----
> > From: David Abineri [mailto:dabineri@CHOICE.NET]
> > Sent: Thursday, September 07, 2000 7:09 AM
>
> > If a long thin rod is rotating about one end is it also rotating about
> > its center?
>
> Yes!
>
> > If so, what is the relationship between its angular
> > velocity about its end and its rotational velocity about its center?
>
> The angular velocity is the same for both reference frames.  Think of a
> wheel which rolls without slipping as the superposition of two motions: the
> center of the wheel is in translational motion at constant velocity. The
> rest of the wheel is in rotation about the center.  In the case of your rod
> example, the center of the wheel is in uniform circular motion.  The rod
> itself is in "pure" rotation at the same angular frequency.

The issue you need to address then for dynamics, momentum or energy problems is
what is the appropriated moment of inertia. If you choose to focus on the
center of mass of the rod, then you'll need to address the C of M's linear
motion, momentum and energy of  that center point and  use the moment of
inertia about the center of the rod for rotational quantities. If you choose to
focus on the axis of rotation (the end of the rod), then you have pure rotation
and don't have to address linear quantities, but you must then use the moment
of inertia for a long thin rod rotating around it's end.

Either way you'll end up with the same results because of the differences in
the moments of inertia. I not sure I could explain why it works, but it has
every time I've tried it.

Cheers,

Rich