Rotations Per Minute Needed to Balance a Top

[skulliam4]

I have little to no experience with this area of physics, so don't assume I know certain things. A cone is spun (with the tip down) at a constant, not decreasing, RPM (Rotations per Minute). What is the minimum RPM for it to stay there without falling, and (if possible) the minimum RPM necessary to make it seem as thought it might be stationary? If dimensions are needed, I would not be able to give them, but I can give ratios, or I can put it in units that have no real world value.

 

[FrenticEfreet]

If we aren't considering other real-world factors, the cone could balance without rotating at all.

 

[skulliam4]

If we aren't considering other real-world factors, the cone could balance without rotating at all.

Realistically, it is quite hard to achieve that. But at what rpm could it stay balanced?

 

[FrenticEfreet]

Making the cone "seem as though it might be stationary" is just a matter of properly aligning the center of mass and the angle of rotation.

If we're ignoring friction, what forces are you imagining would make our cone fall over, at any RPM?

Unsure what "realistically" has to do with a scenario where we are ignoring friction.

 

[skulliam4]

If we're ignoring friction, what forces are you imagining would make our cone fall over, at any RPM?

I thought that gravity would pull it down on the side that is closest to the ground. If you set a top down on it's tip without spinning it, it will most likely topple.

 

[FrenticEfreet]

I thought that gravity would pull it down on the side that is closest to the ground. If you set a top down on it's tip without spinning it, it will most likely topple.

Sure, in the real world, this is correct. However, it is only correct because in the real world, we didn't put the cone down so that it was balanced with its center of mass over top of the point of contact with the surface it is sitting on. (Or we did balance it and movement of air knocked it over.) If we could balance the cone, and if we're ignoring movement of air/other forces, the top should balance while not spinning.

Further, in order to "appear stationary," by which I assume you mean no procession (wobble), the top would need to be spinning in this balanced position anyhow. If the top was spinning from any other position, there would also be some wobble/procession, although the amount of wobble is inversely proportional to the rate of rotation. (That is, the faster we spin the cone, the less noticeable the wobble will be, but it will still wobble if it wasn't balanced.)

 

[skulliam4]

Yes, I meant wobbling but the word didn't come to me. So can you do something like: this RPM gives this much wobble, and this higher RPM gives this much wobble…? And what is the lowest RPM where the top can wobble as much as it wants but will still stay balanced?