Re: What is the origin of the precession of a mounted rotating wheel ?

On Jul 12, 4:38 am, Gordon <gordo...@xxxxxxxxxxxxxxxx> wrote:
On Wed, 11 Jul 2007 09:33:39 -0000, tareq....@xxxxxxxxx wrote:
A simple experiment that most of us have seen or gone through is that
when you tilt the axis of a rotating wheel that rotates in a vertical
plane in a vertical direction while standing on a freely rotating
plate, the wheel will exert a torque upon you to rotate you in a
horizontal direction to keep angular momentum fixed. What is the
origin of this torque? I don't wait for a descriptive answer like:
the conservation of angular momentum, but a more deep answer that
explains exactly how this torque was generated from the deepest level
(or the most microscopic level).

This problem is exactly the same as the precession of a rotating wheel
mounted from a rope from one end of its axle. Gravitational force on
the other end produces a torque similar to the one you produced by
your hands in the first case, and the wheel acquires a horizontal
precession around the robe.

PS. Professor Lewin in his video lecture on MIT OCW mentioned that
this phenomenon is amazing and very non-intuitive.
Thanks

The simplest way to get this conceptualized is to think of an
incremental bit of the wheel's mass that is at the top of the
wheel and moving away from you. Now, if you attempt to rotate the
axis by dropping your right hand and raising your left hand, you
impart an impulse to that same bit of mass, resulting in a
velocity component toward your right. Add this new velocity
component to the original velocity component away from you and
the result is somewhere off to the right of straight ahead.

Now, this incremental mass can't move away from the rest of the
wheel, so it, and all the other incremental mass entities drag
the front edge (that edge that is farthest from you) to the
right.

The same thing is going on at the lower tangent of the wheel,
except these incremental mass entities will be induced to move to
your left. the two (bottom and top of the wheel) effects sum up
to precess the wheel in a clockwise direction, as viewed from
above.

Gordon, a piece of the upper half of the front edge of the wheel will
have a net velocity off to the right of straight ahead as you said.
However, a a piece of the lower half of the front edge, will have a
net velocity off to the left of the straight backward direction. How
will these two effects add to drag the front edge to the right ?? They
work in opposite directions, and nothing can favor dragging the front
edge to the right or to the left.
This is the system I described in my prev. post:
http://www.youtube.com/watch?v=IEwAry0GARw

Thanks

.

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