Why does a sleeping top resist torques and return to its original position?

[fisico30]

Hello Forum,

a sleeping top, rotating fast on its vertical axis, will resist small perturbation, small torque that try to move the rotation axis away from the vertical: if the top is moved a small angle away from the vertical, it will act so that the axis quickly returns to the vertical position?
Why?

The small perturbation, small torque does not cause precession. Why? Is it because the perturbative torque only acts for a very short time and then disappears?

Still, why does the top manage to return to the vertical position?

A football tracking the parabolic trajectory responds the same way: the slight disturbance is such that the spinning ball, starting with zero initial torque, wants to maintain the zero initial torque condition and so moves its axis to align it to the trajectory.

What is the main principle that explains why there is this action by the football or spinning top?

thanks
fisico30

 

[Andrew Mason]

Hello Forum,

a sleeping top, rotating fast on its vertical axis, will resist small perturbation, small torque that try to move the rotation axis away from the vertical: if the top is moved a small angle away from the vertical, it will act so that the axis quickly returns to the vertical position?
Why?

The small perturbation, small torque does not cause precession. Why? Is it because the perturbative torque only acts for a very short time and then disappears?

Still, why does the top manage to return to the vertical position?

A football tracking the parabolic trajectory responds the same way: the slight disturbance is such that the spinning ball, starting with zero initial torque, wants to maintain the zero initial torque condition and so moves its axis to align it to the trajectory.

What is the main principle that explains why there is this action by the football or spinning top?

Can you draw the angular momentum vector for the spinning top before perturbation and after perturbation? Can you draw the torque vector for the perturbing torque and the angular momentum that it imparts to the spinning top? How does it compare in magnitude to the total momentum?

In order to conserve the angular momentum prior to perturbation, what must the top do in response to the perturbing torque?

AM

 

[fisico30]

Well,
initially both angular velocity and angular momentum point in the same direction (vertically upward).
After perturbation, the angular velocity still points upward while the angular momentum points sideways: they don't point in the same direction...

Now the angular momentum is changing direction as the top rotates after perturbation, i.e. there is a torque (time change of angular momentum)...

Still, I am not sure why the top will tend to return to its original position, the one before perturbation..

thanks
fisico30