Re: [Phys-l] Coriolis effect puzzlement

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

I'm going to assume a bowl-shaped ice skating rink so that as viewed
from an inertial reference frame a component of the normal force is that
which is providing her centripital acceleration and as viewed from a
co-rotating reference frame that same component of the normal force is
balancing the centrifugal force so that she can indeed, from either
viewpoint, be at rest on the frictionless surface on which she is
standing.  I'm also going to assume that one of the weights is closer to
axis of rotation than her center of mass is and the other is farther.
Now she brings them both in so that each is closer to her center of mass
than it was.  When she first does this the inner weight is now on a
bigger circle about the rinks rotation axis but its tangential velocity
is too slow to keep up with a point on the ice at that same distance
from the rink's rotation axis so it falls behind.  The outer weight is
going too fast for its new circle so it gets ahead of a point on the
ring at the same distance from the rink's rotation axis.  Thus she is
spinning relative to the ice.

Another way of looking at it, neglecting the separation of the weights
in the after picture and approximating the weights as point masses for
purposes of calculating their contribution to the moment of inertia with
respect to the rink's axis of rotation:  Let the "weights" each have
mass m and be at distances r1 and r2 from the rink's axis of rotation
respectively with r2 > r1.  After she pulls them in let them both be
(r1+r2)/2 away from the axis.  Before, her moment of inertia with
respect to the axis is approximately m*r1^2 + m*r2^2 = m(r1^2 + r2^2),
and after it is approximately 2m[(r1+r2)/2]^2 = m[r1^2 + r2^2
-.5*(r1-r2)^2 ].  The latter moment of inertia with respect to the rinks
axis of rotation is smaller so the pair of weights must have some spin
angular moment for the total angular momentum to be the same in both
cases.

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of Bob Sciamanda
> Sent: Friday, December 02, 2011 1:09 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] Coriolis effect puzzlement
>
> To further bring home the phenomenon at issue here, consider:
>
> A skater stands way off center on a rotating ice rink, partaking only
> of the
> platform motion, and holding weights in her outstretched hands.
> If she brings in her arms, will she begin to spin about her platform
> position?
>
>
> From: Bob Sciamanda
> Sent: Friday, December 02, 2011 9:26 AM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] Coriolis effect puzzlement