Wow, thanks for the homework! I may need some help with the calculations. My Big Top, Dorothy Dot, measures 95cm tall x 72cm max diameter, 30kg. Hand carved (hollow) on a lathe, inside and out. Spin times starting with an impact gun indoors average 6 - 8 minutes.
What a beauty! Impressive spin time, too.
The first surface speed formula I gave still applies, but there are no easy formulas for the moments of inertia of a simple solid peg top, let alone a hollow one. And you need at least the axial moment for the energy estimate you're after.
However, there
are formulas for the moments of a roughly similar shape — the
solid spherical cone. And there are ways to subtract out the moments of the wood lost to hollowing if the finished top's walls are of roughly uniform thickness.
With the following info, I'd be happy to tackle that in a Google sheet you could play with online. (You know you're a hopeless nerd when you enjoy challenges like this.)
Q1. What kind of wood? Same throughout?
Q2. Any steel inside? If so, what size and shape, and where? Weights of the steel parts if you have them?
Q3. What's the dominant wall thickness? Any big departures? Where?
Q4. What's the distance from the contact to the max diameter, taken along the spin axis?
Q5. Long shot: Do you happen to know the distance from the contact to the top's CM, taken along the spin axis?
A rough cutaway sketch of the void and steel with some dimensions would be a big help.
No worries if all this is more work than you bargained for. You could also measure the top's moments with a heavy-duty custom-built trifilar pendulum, but there'd still be time-consuming measurements and calculations after the construction.
However, it would be nice to have human power take over. I imagine traction of the whip will be key so an average rope might not be ideal. If there is a rubberized material or similar traction type material that anyone can recommend, that would help. I can scale images of other whips from videos to get dimensions and play with what works/fails.
I fear for your top's beautiful paint job. The pole whips in the video jim linked above look promising to me. Strips of leather or vinyl or heavy-duty inner tube come to mind for the soft ends.
With your top's shape, the whippers will need to land their blows near the widest diameter to be effective. Judging from jim's video and the large muscle groups involved, could be a challenge (think golf). Cylindrical whipping tops present a much bigger target area.