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

On Jul 15, 12:20 am, Gordon <gordo...@xxxxxxxxxxxxxxxx> wrote:
On Sat, 14 Jul 2007 11:50:25 -0700, tareq....@xxxxxxxxx wrote:
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

You have it almost right but you need to divide the gyro wheel
into four quarters, then analyze each quarter. Place a vertical
plane through the gyro wheel such that it includes the axle. This
plane separates the front half of the gyro wheel from the back
half.

Place a horizontal plane through the gyro wheel such that it also
includes the axle. This plane separates the top half from the
lower half.

Looking at these four quarters of the gyro wheel we see that;

Every particle above the horizontal plane will tend to move to
the right when you lower the right end and raise the left end of
the axle.

Every particle below the horizontal plane will tend to move to
the left when you do this.

Now, break the gyro wheel on down into quarters.

Look at the particles above the horizontal plane and in front of
the vertical plane (top, front quarter). These particles will
tend to drag the front of the gyro wheel to the right when you
lower the right end and raise the left end of the axle.

Next, look at the particles below the horizontal plane and in
front of the vertical plane (bottom front quarter). These
particles, also, will tend to drag the front of the gyro wheel
to the right. That is, the impulse that induced a velocity to the
right in the top front quarter must now be reversed and that
velocity component brought back to zero as these particles of
mass approach the lower edge of the gyro wheel.

Next, look at the particles below the horizontal plane and behind
the vertical plane (bottom rear quarter). These particles will
tend to drag the rear half of the wheel to the left.

Next, look at the particles above the horizontal plane and behind
the vertical plane (top rear quarter). These particles will tend
to drag the rear of the gyro wheel to the left. As in the lower
front quarter described above, the impulse that induced a
velocity to the left in the lower rear quarter of the gyro wheel
must now be reversed and that velocity component brought back to
zero as these particles of mass approach the lower edge of the
gyro wheel.

Combine all these effects and the rear half of the gyro wheel
will be dragged to the left, while the front half will be dragged
to the right. This will cause the gyro wheel to precess in a
clockwise manner, as viewed from above.

Gordon

Let's number the four quarters in this way:
top front: 1
bottom front: 2
bottom rear: 3
top rear: 4

any piece on the wheel is moving through 1-2-3-4-1... etc.
only the net velocity on parts of quarters 2, 4 tend to rotate the
wheel in the proper direction. the other two quarters tend to rotate
it in the opposite direction.
For me and using this analysis I see that nothing favors one
direction form another since the problem is symmetric in the sense
that whatever you can say about a direction , you can say it about the
other direction and the direction of wheel rotation 12341 or 14321 is
irrelevant in favoring one direction over the other one using this
argument.
Tareq

.

Relevant Pages

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