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Spinning Bycle wheel on string (precession)

Trying to analyze all the dynamics of gyroscopic type motion.

Assume the Z axis is vertical (which the wheel precesses about)Have a spinning bicyle wheel, that is held up via string on one end, the biycle wheel begins to precess about the vertical axes via torque induced from gravity.

I'm trying to get an idea of the correct behavior of the system specifically when we analyze the angular momentum contribution in the z direction due to precession.

For a faster spinning disk, the precession speed is smaller. One can see this through derivation or by noting that the gravity induces the same torque in the same time, and a faster spinning disk signifies a longer angular momentum component perpendicular to the disk... which means that the change in angular momentum (from torque) would correspond to a smaller angular displacement.

quot;You can think of lifting/pivoting the ends of a meterstick and ruler through 1cm, the ruler since it is smaller in length will displace a larger angular distance.quot;Ok thats not my question yet...

If you attempt to make an increase to the Lz angular momentum manually by moving the spinning disk along with the precession, its angle of tilt increases, and it also quot;seemsquot; that in doing so the speed of the disk decreases.

The angle of tilt increasing I can perceive through the torque introduced by myself, consquently the precession speed does increases too, however the change in the disks speed Is what puzzles me.How do I know the disks speed changes? I tried/  performed the experiment with a bicyle wheel as described above, a piece of paper tickers past the spokes crudely informing me of the angular speed of the wheel. I notice that trying to torque the wheel so that its precession increases quot;seemsquot; to reduce the wheels speed and tilt it more upright.

Thanks for you comments.

AZ  

                                  Originally Posted by azaharak                   Trying to analyze all the dynamics of gyroscopic type motion.                  
On :
See this post from last november about gyroscope motion.More detailed discussion is in the gyroscope physics article on my website.

                                  Originally Posted by azaharak                   If you attempt to make an increase to the Lz angular momentum manually by moving the spinning disk along with the precession, its angle of tilt increases, and it also quot;seemsquot; that in doing so the speed of the disk decreases.
[...]
How do I know the disks speed changes? I tried/performed the experiment with a bicyle wheel as described above, a piece of paper tickers past the spokes crudely informing me of the angular speed of the wheel.

AZ                  
To obtain a comparison I take the following setup:
A wheel is spinning, the axis is horizontal. Then the center of mass of the wheel is accelerated, in horizontal direction, perpendicular to the spin axis.

I expect that in the case of a spinning wheel the acceleration will be somewhat less than in the case of a non-spinning wheel. I expect that some of the work done will be in decreasing the spin rate of the wheel, rather than accelerating the center of mass. But even this case is tricky.

The case of a precessing wheel, with a torque applied that increases the rotation rate around the z-axis, is more complicated because of freedom to climb or slump down. Gravity is doing work. Right now I don't have an answer.

That's a really interesting problem you've raised. I'll be thinking about it a lot.
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