Why Does a Spinning Top Stabilize After Wobbling?

[Borborygmus]

So I get that conservation of angular momentum makes a spinning top stable. Same mechanism behind gyroscopes.

When you first spin a top, there's a lot of wobble (precession), but it quickly dissipates. Why does this happen? The lack of wobbling must be a lower energy state if it is reached spontaneously. But this seems very counter intuitive. If we assume conservation of angular momentum (aka, no loss through friction), the angular momentum of the wobble gets converted to spin.

However, at low speeds, spin gets converted back into wobble.

Another question - how does center of gravity of top affect it's spin characteristics? My guess is the lower the CG, the higher the frequency of the wobble, in order to achieve the same angular momentum.

 

[netgypsy]

The stability is related to the amount of mass rotating far from the center of gravity. For example a motorcycle wheel and a bicycle wheel can have the same radius and be rotating at the same number of rpm's and the motorcycle wheel will be much more stable. Now regarding the wobble, a force is created by the rotation ( you can look up the formula) that is a restoring force or a force that actually fights the wobble. The faster you spin a top, the stronger this force is. As the top slows gravity becomes stronger than this restoring force and the wobble begins to increase as the rpm's decrease and the restoring force also decreases.

So it's not so much how high or low the center of gravity is that has an affect, but how far the majority of the mass is from that center of gravity as it spins and just how much mass is far from the center and how many rpm's that mass is making that determines the stability. You can see that if there is a high center of gravity oh the top that when it slows and if it doesn't have a lot of mass far from the center, that gravity will produce a larger torque on it and tend to tip it over more easily

 

[Borborygmus]

Ahhhh, I didn't know there was a way to calculate the restoring force on a top. This is exactly what I'm looking for. What is the equation?

 

[netgypsy]

http://mb-soft.com/public/precess.html

Sorry it took so long to get back to you. Most of the sources on this topic are so mathematical it takes forever to find anything. See if this one gives you what you are looking for. Remember when the top is spinning it has angular momentum so think about what is happening to that angular momentum.

If you google forces on a top there are some really great illustrations you can watch after reading this site that should help also. Have fun.

 

[ahsanxr]

I think with a lot of the more complicated problems in classical mechanics it's difficult to attribute a single property of motion to certain laws, and this is where the Lagrangian approach comes in. All you can do is write down the Lagrangian and crank out the equations and see where they take you. At least that's how I think of it, someone with a better understanding may be able to tell you which property of motion is due to which law, but I just find it easier to crank out the equations and go from there. And the Lagrangian approach is how the motion of a spinning top is solved for. The wobbling you're talking about comes out quite nicely out of the equations.