Cuboid stability when rotating along different axes

[jmora]

Homework Statement

If we have a cuboid like this one
*It won't let me upload the picture or include a link but if you Google cuboid its the first picture*

We know that the mas moment of inertia through the centroid is different for each face. So the yellow has the greatest mass moment of inertia the orange face has the second greatest moment of inertia, and the green face has the smallest moment of inertia. Now if i hold this cuboid along any two opposing faces on their center and throw it up in the air with the intent of the it spinning smoothly it will not work out so well for the orange face (the one with the second biggest mass moment of inertia). Why?

Homework Equations

Why does the box only spin nicely along two of the axes/faces but now along the other one?

The Attempt at a Solution

This is not really a homework question. Professor just brought it up in class and did not tell us the answer. It is weird because it is the face with the second biggest/smallest mass moment of inertia that does not spin nicely. By spinning nicely i mean that when thrown up in the air it has no stability and moves in and out of the plane very quickly. But when it is thrown along the other two it spins nicely and stays in the plane the entire time. The only thing i know is that somehow the moments are causing stability.

It is a hard question to explain. Sorry for any confusion and please ask if any clarification is needed. Thanks in advance to anyone who helps.

 

[anathema]

Hello, thank you for bringing up this interesting question. The reason why the cuboid only spins nicely along two of the axes/faces is due to the distribution of mass and the principle of inertia. The principle of inertia states that an object will remain in its state of motion unless acted upon by an external force. In this case, the cuboid is spinning along its axis when thrown in the air, but the moment of inertia of each face affects the stability of the spin.

The moment of inertia is a measure of an object's resistance to change in its rotational motion. It is dependent on the distribution of mass and the distance of the mass from the axis of rotation. In this case, the yellow face has the greatest moment of inertia because it has the most mass and is furthest from the axis of rotation when spinning along its face. This allows for a stable spin.

On the other hand, the orange face has the second greatest moment of inertia because it also has a significant amount of mass, but it is closer to the axis of rotation compared to the yellow face. This means that it requires more force to rotate the cuboid along this face, making it less stable when thrown in the air.

The green face has the smallest moment of inertia because it has the least amount of mass and is closest to the axis of rotation. This means that it requires the least amount of force to rotate the cuboid along this face, making it the most stable when thrown in the air.

In conclusion, the distribution of mass and the principle of inertia explain why the cuboid only spins nicely along two of the axes/faces. The yellow and green faces have the greatest and smallest moments of inertia, respectively, allowing for a stable spin, while the orange face has a significant moment of inertia that makes it less stable when thrown in the air. I hope this helps clarify the concept for you.