Remember those fancy tippe tops that challenged your intuition when you were a kid? Let’s revisit those memories and figure out how those tops actually work. Well, to be honest, if you are a guy like me who just came to know what tippe tops are, here is a photograph of it.
It’s a spherical top, truncated a bit at the top with a cylindrical stem protruding out. When spun with the stem facing the top, the toy eventually flips and end up rotating on its stem.
I had no idea how it flipped after the first glance. The only thing that popped into my mind was the Dzhanibekove effect. But that was not causing it.
Taking a trip to my fortress of solitude and playing with some tippe tops, I found that the actual reason why a tippe top stands up or flips itself is because of its geometry — asymmetric mass distribution to be precise — and the friction induced by the surface on which the top spins.
As you can see in the picture, the tippe top is only half a sphere with a stem on top of it. This results in a centre of mass, a bit lower than the geometrical centre — the centre of curvature.
Now when you spin the top, it rotates around a rotational axis that passes through the two centres initially. But due to friction, when the top precesses around, the rotational axis passes only through the centre of mass. The point of contact will now align with the geometrical centre. Due to this, the surface friction at the point of contact creates a torque on the top as it spins. And gradually, the secondary spin induced by the torque causes the stem to touch the ground. The top finally stands up on its stem due to the extra friction it gets when the tip of the stem (usually grooved) further moves on the surface.
Is the energy conserved?
Duh! Yeah! It might appear that the centre of mass is raised ‘magically’ without any work. Or in other words, it would seem that the potential energy of the top is increased somehow. The fact is, due to the moment of inertia of the top, the kinetic energy is lowered as the potential energy increases, which helps to flip the top. So yeah! Energy is conserved!
To conclude, the surface friction and asymmetric mass distribution (moment of inertia) are the key factors in tippe tops that make the top flip or tip over on its stem. You can verify this by spinning it on a frictionless surface, where the tippe top would not flip. Similar to this, there are also a few other crazy toys like Rattleback top, phi top, and Euler’s disk out there that are intriguing.