The angular speed of precession for a gyroscope is given by

In summary, the angular speed of precession for a gyroscope is affected by the spin rate of the gyroscope. As the spin rate decreases, the precession rate increases, which is consistent with observations of a top. In the case of a slowly spinning bicycle wheel, the precession effect may not be as noticeable because the forces are weaker and may be overcome by external factors such as friction or gravitational torque.
  • #1
Opus_723
178
3
The angular speed of precession for a gyroscope is given by ω[itex]_{p}[/itex] = T/ω[itex]_{g}[/itex].

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?
 
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  • #2


Any help would be appreciated. I've been wrestling with this for awhile, and my prof didn't know the answer offhand.
 
  • #3


I guess I'll bump this one more time, then I give up.
 
  • #4
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.
 
  • #5
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.
 
  • #6
Opus_723 said:
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.
 
  • #7
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.
 

1. What is the angular speed of precession for a gyroscope?

The angular speed of precession for a gyroscope is a measure of how fast the gyroscope rotates around its axis due to an external torque.

2. How is the angular speed of precession calculated?

The angular speed of precession is calculated by dividing the external torque applied to the gyroscope by the product of its moment of inertia and its angular velocity.

3. What factors affect the angular speed of precession for a gyroscope?

The angular speed of precession is affected by the external torque applied to the gyroscope, its moment of inertia, and its angular velocity.

4. What units are used to measure the angular speed of precession?

The angular speed of precession is typically measured in radians per second (rad/s) or revolutions per minute (RPM).

5. Why is the angular speed of precession important?

The angular speed of precession is an important property of gyroscopes as it determines their stability and ability to maintain a constant orientation in space. This is crucial in various applications such as navigation, robotics, and aerospace engineering.

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