Cause of upward motion of a nutating top

In summary, the rotational axis of a symmetrical rotating top with a fixed base can exhibit nutation, which is an oscillation caused by initial perturbation from the neutral angle where the gyroscopic torque balances the force of gravity. This can occur when the precession rate is higher than the rate required to balance gravity, resulting in an upward turn of the top axis and subsequent oscillation.
  • #1
Kashmir
468
74
IMG_20211212_114148.JPG


The locus of the rotational axis of a symmetrical rotating top with a fixed base is shown. This shows a nutation bounded by two circles.

What is the intuitive explanation as to why the top axis turns upwards at the lower circle and moves up? ( I understand the circular precession caused by gravity and would be grateful for an explanation only for the nutation).

Thank you :)
 
Physics news on Phys.org
  • #2
It depends on initial conditions. For any given angle wrt vertical, there is a matching precession rate that will involve no nutation, because the gyroscopic torque balances the gravity exactly. If the initial condition is of this sort, there will be no nutation.

On the other hand, if the precession rate is, say, higher than required to match the gravity, then the top will nutate upwards for a moment until the balance is achieved. However, it will overshoot the balance point due to inertia, and so an oscillation will be set up. So nutation is an oscillation around the angle at which gyro torque balances torque due to gravity -- an oscillation due to initial perturbation from the "neutral" angle.
 
  • Informative
  • Like
Likes berkeman and vanhees71

Related to Cause of upward motion of a nutating top

1. What is a nutating top?

A nutating top is a type of spinning top that has a slightly tilted axis, causing it to wobble or "nutate" as it spins.

2. What causes the upward motion of a nutating top?

The upward motion of a nutating top is caused by the combination of its spinning motion and the force of gravity. As the top spins, its tilted axis causes it to wobble, which creates a lifting force that propels it upwards.

3. How does the shape of the top affect its upward motion?

The shape of the top can affect its upward motion by changing the distribution of weight and the angle of the tilted axis. A top with a more spherical shape will have a more stable and consistent upward motion compared to a top with an irregular shape.

4. Can the surface on which the top is spinning affect its upward motion?

Yes, the surface on which the top is spinning can affect its upward motion. A smooth and level surface will allow the top to spin more smoothly and maintain a consistent upward motion. A rough or uneven surface may cause the top to lose balance and disrupt its upward motion.

5. Are there any real-world applications of nutating tops?

Yes, nutating tops have been used in gyroscopes and other navigation devices to measure and maintain orientation. They have also been studied in physics and engineering to better understand the principles of rotational motion and stability.

Similar threads

Replies
7
Views
1K
Replies
0
Views
578
  • Mechanics
Replies
6
Views
874
Replies
13
Views
4K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Replies
8
Views
1K
Replies
6
Views
4K
  • Mechanics
Replies
6
Views
2K
Replies
2
Views
1K
Back
Top