A Cause of upward motion of a nutating top

  • A
  • Thread starter Thread starter Kashmir
  • Start date Start date
  • Tags Tags
    Cause Motion
AI Thread Summary
The upward motion of a nutating top is explained by the balance of gyroscopic torque and gravitational torque. When the precession rate exceeds the necessary rate to maintain balance, the top experiences upward nutation until equilibrium is restored. This overshoot occurs due to inertia, leading to oscillations around the angle where the torques balance. The initial conditions significantly influence whether nutation occurs, as specific angles can lead to a stable state without nutation. Thus, nutation is fundamentally an oscillation resulting from deviations from this equilibrium angle.
Kashmir
Messages
466
Reaction score
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
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
The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
Thread 'Beam on an inclined plane'
Hello! I have a question regarding a beam on an inclined plane. I was considering a beam resting on two supports attached to an inclined plane. I was almost sure that the lower support must be more loaded. My imagination about this problem is shown in the picture below. Here is how I wrote the condition of equilibrium forces: $$ \begin{cases} F_{g\parallel}=F_{t1}+F_{t2}, \\ F_{g\perp}=F_{r1}+F_{r2} \end{cases}. $$ On the other hand...
Back
Top