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

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In summary, the conversation discusses the behavior of a sleeping top and a football when they experience small perturbations or torques. Both objects exhibit a tendency to return to their original positions after being moved slightly, due to the principle of conserving angular momentum. This is because the perturbing torque only acts for a short time and then disappears, causing the objects to align their axes with their trajectories. The conversation also explores the concept of angular momentum and torque and their relationship to the motion of these objects.
  • #1
fisico30
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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
 
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  • #2
fisico30 said:
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
 
  • #3
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
 

1. What is a "sleeping top"?

A sleeping top is a type of toy or object that spins when placed on a flat surface. It is usually made of metal or plastic and has a pointed tip at the bottom.

2. How does a sleeping top resist torques?

A sleeping top resists torques, or rotational forces, through its angular momentum. When the top is spinning, it has a certain amount of rotational inertia that makes it resistant to external torques, causing it to continue spinning in a stable manner.

3. What factors affect a sleeping top's resistance to torques?

The main factors that affect a sleeping top's resistance to torques are its mass, shape, and the surface it is spinning on. A heavier top with a pointed tip and a smooth surface will have a higher angular momentum and therefore be more resistant to torques.

4. Can the resistance to torques in a sleeping top be increased?

Yes, the resistance to torques in a sleeping top can be increased by increasing its angular momentum. This can be done by increasing the top's mass, making it spin at a higher speed, or using a smoother surface for it to spin on.

5. How is the concept of a sleeping top resisting torques applicable in real life?

The concept of a sleeping top resisting torques is applicable in many real-life scenarios, such as the stability of spinning objects like gyroscopes and tops, the stability of rotating bodies like planets and stars, and the balance and control of spinning movements in sports and acrobatics. Understanding this concept is also important in fields like physics, engineering, and robotics.

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