The angular speed of precession for a gyroscope is given by

[Opus_723]

The angular speed of precession for a gyroscope is given by ω_{p} = T/ω_{g}.

So that the rate of precession increases as the gyroscope, top, or wheel slows down. This agrees with observations of a top, which wobbles around very quickly as it slows down.

If I hold a bicycle wheel in my hand, spin it very fast, and then apply torque to it, I will see a precession effect. But if it is spinning slowly, I see little or no precession, and the bicycle wheel behaves like a normal, non-spinning object. Why does the above equation not seem to hold in this case?

 

[Opus_723]

Any help would be appreciated. I've been wrestling with this for awhile, and my prof didn't know the answer offhand.

 

[Opus_723]

I guess I'll bump this one more time, then I give up.

 

[pumila]

The precession rate slows down as spin rate goes up and the forces become immense. Conversely At very low spin rates the precession rate is very high and the forces become very weak, so that they cannot overcome losses or even the force of your hand holding the wheel. As the spin rate tends to zero The precession forces fade to nothing as the precession frequency tends to infinity.

 

[Ryoko]

I think you need to define how you are holding the wheel in your hand as it slows down. I'm guessing that your are supporting the weight of the wheel with your hand which is canceling the torque due to gravity.

 

[BobG]

But if it is spinning slowly, I see little or no precession, and the bicycle wheel behaves like a normal, non-spinning object.

How is this possible? If one axle is supported by a string, rope, whatever and gravity is causing the opposite axle to fall towards the ground, isn't the bicycle wheel still spinning? Just on a different axis?

And once the wheel clears the string/rope/etc, doesn't it continue spinning on that new axis even after there's no longer any gravitational torque?

Under the conditions, a non-spinning object would not be normal.

 

[pumila]

For a given torque (the gravitational downward force) the precession rate is inversely proportional to the spin. This precession in turn generates the reverse torque that balances the downward gravitational force. As the spin rate drops the precession rate needs to rise to create the same balancing force. At some point the precession rate reaches some practical limit where that precession rate is damped by friction or even air damped. When this point is reached the precession cannot run fast enough to generate the necessary balancing force in full, and the gyro ceases to operate perfectly.