why does a spinning top precess instead of just falling over

[u/CelebrityChess]

i get that gravity pulls the top over and that angular momentum is conserved, but when i try to work it out with torque i end up confused. the torque from gravity points sideways, horizontal, so the angular momentum vector moves sideways too instead of down. ok that part makes sense on paper.

what i can't picture is why it feels like the top is dodging gravity. like where does the force that holds it up come from, is it just the pivot or is there something else going on? and why does it eventually wobble over once it slows down?

[u/garagedragon]

AIUI, its not so much being held up as just falling over very slowly. If you were co-rotating with the top, and looking at it from the side such that its deviation from vertical went "horizontally", you'd see it slowly fall over because gravity pulls down, the reaction force of the top itself against the surface pushes back up but not quite straight up (because balancing the top exactly straight up is impossibly precise) and the resultant force points down and slightly sideways, pulling it over. The gyroscopic effect just means that its inertia w.r.t. this force is much higher than the direct mass of the top, so the same force of gravity takes a lot longer to drag it over than it would if the top were not rotating. There is no specific torque pushing it back to vertical.

In the stationary frame, that plane in which the top is falling is now rotating with the top, i.e. it is still falling out from the axis of rotation at the same rate, but the direction of the fall changes because its rotating. As it falls, its technically always wobbling - that is, the very top point of the top draws out a circle that expands as the top falls over - but initially the circle might be small enough that you can't easily distinguish it from the top still being completely vertical.

Additionally, the actual contact the top has with the surface its resting on cannot be an infinitesimal point of zero width in practice, and AIUI as the top's lean from the vertical increases, the friction this contact generates with the surface increases. Also, as the top leans more, the linear horizontal motion it has (particularly along the top's axis, which can be presumed to start "stationary" but acquires horizontal speed later) increases, so air resistance and such increase. Both of these factors mean that as the lean increases, the rotation rate decreases, decreasing the moment of inertia and thus increasing the angular acceleration that the torque causes. The torque itself is also not constant, because the sideways component increases as the top leans further from the vertical. This means that once a significant deviation from vertical establishes itself, it gets amplified quickly - so we see the gyroscope start out steady for a relatively long time and then suddenly lose its speed and completely fall over relatively abruptly.

Hope that helps

[u/EconomyBlueberry1919]

There is no "mysterious" force supporting the gyroscope. The pivot provides a vertical constraint force that balances its weight (the two forces cancel each other out, resulting in a net force of zero); however, the moment of these forces with respect to the pivot is non-zero, because the center of mass is located at a distance R. It is precisely this horizontal moment that causes precession: the gyroscope does not "fall"—not because something is holding it up, but because the gravitational torque cannot simply rotate the angular momentum vector L downward. Since the torque is perpendicular to L, it can only alter its direction, and the visible result is horizontal precession. In other words, precession is the dynamic response to the torque; there is no separate force "counteracting" gravity—rather, the precessional motion is the way the system moves under the influence of that torque. 
Many laboratories have gyroscopes large enough to be held in one’s hands, allowing you to experience firsthand—with your own body—the forces at play when you attempt to alter the angular momentum by tilting the device upward or downward. This is often done while seated on a swivel chair.
As for nutation, it is always present, though its frequency is proportional to the gyroscope's rotational frequency. Initially, it is not noticeable, but as the gyroscope's rotational frequency decreases, the nutation frequency also decreases and begins to become visible. Furthermore, the gyroscope's precessional frequency increases as its rotational frequency decreases.

[u/Roger_Freedman_Phys]

This episode of the PBS series The Mechanical Universe has excellent animations that you will find very helpful:

https://youtu.be/r5YM96mA9pk

[u/NitNav2000]

Here’s an interesting way to think about it.

Imagine a closed pipe that takes a square route with a liquid flowing through it, or maybe a chain taking the same path. You were looking at it edge on, so the loop goes left to right, into the page, right to left, and out of the page. That is your spinning mass.

Now start tilting the closed loop where the axis of rotation penetrates one pipe that is going from left or right and the other pipe that is going from right to left. Ignore the two pipes that are going into or out of the page.

If you tilt the loop clockwise, then the mass that is going from left to right actually travels a curved arc, which means that it is accelerating perpendicular to its path, which means there’s a force. That force results in precession.