Undergrad Can every shape precess like a top (toy)?

[Tazerfish]

The main question is in the title.
1.I have wondered if a regular pencil would precess and rotate stable for multiple seconds if spun fast enough.

[Coins, plates, bowls and similarly shaped objects can rotate in a stable way for extended periods of time.
And a lot of other household objects can be put into some kind of stable rotation. That is what inspired this question.
Though technically the rotation described above is fundamentally different from a top, since the point of contact constantly changes.
(I wouldn't mind learning something about the kind of motion mentioned above, but the main question is the one from the title)]

Yet there are examples which are basically identical to tops, for instance a cube(dice).
2.Could rectangles which aren't cubes spin on their corners ?

If the answer to the main question is no, only specific objects can rotate in a stable fashion on a flat surface for long periods of time, then 3. I would like to know the criteria necessary for a suitable shape.

Does it have to be symetrical I am some sense?
Does it have to have a certain minimum ratio of moment of inertias between its "falling over axis" and "spinning axis" ?

4.I would also be interested how to calculate the minimum angular velocity necessary to produce stable precession (dependent on some parameters).(for example for a pencil)

Sorry that there are so many different questions.Feel free to just answer one of them.

 

[wrobel]

see the Lagrange top

 

[Tazerfish]

I might have to add that I am only an 11-grade student.
The math in solid body rotation can be a little heavy and I am having trouble interpreting what exactly some of the equations say.

A more specific and "easy" answer to one of the questions 1 to 4 may be more useful to me than a general very complex one.
PS: I didn't really get how "the Lagrange top" explains my question.
PPS:I am very new to analytical mechanics.

 

[wrobel]

perhaps those participants of the forum who have better pedagogical talents than me can give you a baby version of this theory. I will not try to do that since it does not make sense in my opinion. Your questions are completely reasonable but they essentially exceed the school level.

Though technically the rotation described above is fundamentally different from a top, since the point of contact constantly changes.

In this case you need to study theory of the top called "tip-top" or "chinese top" that is over the standard university's program in classical mechanics. But it simpler as first step to study the Lagrange top

 

[Tazerfish]

I can see the problems with this.
The topic is obviously far more complex than I initially assumed.
I guess I will just have to wait and learn it sometime later after learning the sufficient basics.

Nonetheless, there is one simple question which I would like to know the answer to, even though I probably won't be able to understand the reason behind the answer.
Can you spin a regular pen (fast enough) to make it act like a top ?

A yes or no answer will be unsatisfying, but still appreciated.
EDIT:It is like I must know it

 

[nasu]

It may be helpful to read about principal axes of rotation for a rigid body.
The basic idea is that there are three so called "principal axes" for the rotation of a rigid body.
In general the moment of inertia has different values for these three axes. The rotation around the two axes with the extreme values of the moment of inertia is stable. The rotation about the intermediate one is unstable.
For a rectangular block with uniform distribution of mass, the principal axes are along the sides (length, width, height).
So the diagonals are not principal axes and I believe the rotation won't be stable.

You can get some feeling for this if you throw up a box while spinning around various axes. You will see hot the spinning around the unstable axis changes into a more complicated motion whereas the spinning around the other two is stable.

Here is a lecture about these things, but it uses some math you may not be familar with yet.
http://www.physics.arizona.edu/~varnes/Teaching/321Fall2004/Notes/Lecture34.pdf